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Multiplying by Multiples of 10 and 100: Interactive Questions

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Finding the Range

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Prime Numbers to 20

Prime Numbers to 20
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Composite Numbers

what are composite numbers?

  • Composite numbers can be broken down into two other smaller whole numbers.

  • We say that composite numbers are numbers that can be made by multiplying any two whole numbers that are both larger than 1.

  • In this example, 4 is broken down into 2 × 2.

  • Because 4 can be made by multiplying 2 by 2, we say it is a composite number.

  • Not all numbers can be made by multiplying two smaller whole numbers.

what are prime numbers

  • Prime numbers are numbers that cannot be broken down into two other smaller numbers.

  • Prime numbers can only be written as 1 × themselves.

  • The number 2 is the first prime number.

  • It can only be written as 1 × 2.

  • We say that a prime number has exactly 2 factors, which are just 1 and the number itself.

  • 2 is the only even prime number.

  • A number is not prime if it is in the times table of another number.

List of Prime Numbers to 20

List of prime numbers to 20

The list of prime numbers to 20 is: 2, 3, 5, 7, 11, 13, 17 and 19.

Prime numbers cannot be made by multiplying 2 other smaller whole numbers.

Composite numbers can.

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11 is a prime number

  • 11 is an example of a prime number.

  • 11 cannot be made by multiplying two smaller whole numbers together.

  • 11 can only be written as 1 × 11.

  • We cannot divide any other whole number into 11 exactly.

  • We can try dividing by 2, 3, 4, 5, 6, 7, 8, 9 or 10 and see that they do not go into 11 exactly.

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Prime Numbers to 20 Worksheets and Answers

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prime numbers to 20 worksheet answers pdf
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Prime and Composite Numbers to 20

What are Composite Numbers?

A composite number is a number that is made by multiplying two other whole numbers.

For example, 4 is a composite number because it can be made by multiplying two 2’s together.

4 is an example of a composite number

Composite numbers can be broken down into two smaller whole numbers. 4 is broken down into two 2’s. 2 is a different number to 4 and it is a smaller number than 4.

To test if a number is a composite number, try to divide smaller whole numbers into it. If a whole number can divide into it exactly, then it is a composite number.

The numbers that divide into a composite number exactly are called factors.

What are Prime Numbers?

A prime number has exactly 2 different factors, which are the number 1 and the number itself. This means that a prime number cannot be made by multiplying two other whole numbers.

Apart from the number 1 and the number itself, no other whole numbers will divide into a prime number exactly.

2 is the first prime number. It is also the only even prime number.

It can only be made by multiplying 1 × 2.

2 is the first prime number and the only even prime number

There are no other numbers that can divide into 2 exactly.

The only way to make 2 by multiplying is 1 × 2.

When we do this, we still end up with a 2 that is multiplied by 1. It is the same number that we started with and it did not get any smaller.

Because only the number 1 and the number 2 itself can divide into 2, we call it a prime number. We can see it only has two factors, the number 1 and the number 2.

A number is not prime if it is in another number’s times tables.

Prime numbers are hard to find because there is no pattern or rule to find them. We must try and divide all of the smaller whole numbers into a number to test if a number is prime.

Is 1 a Prime Number?

1 is not a prime number. 1 is also not a composite number. It is neither prime nor composite.

This is because the definition of a prime number is a number that has exactly two factors. These are the whole numbers that divide exactly into a number.

Basically, 1 cannot be broken down into smaller whole numbers.

The number 1 can only be written as 1 × 1.

The number 1 is not a prime number and it is not a composite number

Therefore it only has one factor, which is the number 1. It does not matter that there are two of them, it is still the same number. A number needs exactly 2 different factors to be a prime. 1 does not have enough factors.

To be a composite number, the number needs to be made by multiplying two other smaller whole numbers.

1 is only made by multiplying 1 by 1. This is the same number and it is not smaller. 1 is not a composite number either.

1 is neither prime nor composite.

It is worth pointing out that it is a common mistake to count 1 as a prime number. This is because people think of prime numbers as numbers that cannot be broken down, whereas the proper definition is to check if it has two factors, which the number 1 doesn’t.

Apart from the number 1, all whole numbers are either prime or composite. If they are not prime, then they are composite and if they are not composite, they are prime.

Finding Prime Numbers from 1 to 12

We will look at the list of numbers to 12 and identify the prime numbers.

1 is neither prime nor composite because it cannot be made by multiplying two smaller whole numbers.

The number 1 is not a prime number and it is not a composite number

All of the other numbers larger than 1 are either prime or composite.

2 is a prime number. It can only be made by multiplying the whole numbers 1 × 2.

2 is a prime number

2 is special because it is the first prime number. It is also the only even prime number.

This is because any other even number can be divided by 2 as well. A prime number cannot be divided by any number apart from 1 and the number itself.

It is a common mistake to think that 2 is not prime because it is even and it is worth highlighting this number when teaching prime numbers.

The number 3 is also prime.

It can only be written as 1 × 3. So it has 2 factors, 1 and 3.

3 is a prime number

The only other smaller number than 3 is 2. We can try dividing 2 into 3 to check, but 2 does not go exactly into 3 because 3 is an odd number.

4 is a composite number made from 2 × 2.

Even though it can still be written as 1 × 4, we have this extra option of 2 × 2.

4 can be broken down into smaller whole numbers.

4 is a composite number

4 is even and all even numbers, apart from the number 2, are prime.

Because 4 is composite it is not prime.

5 is a prime number. It only has 2 factors, 1 and itself. This means that it can only be written as 1 × 5.

5 is a prime number

To check if 5 is prime, we can try dividing other smaller numbers into it.

2 does not go into 5 because 5 is odd.

5 is not in the 3 times table or the 4 times table either.

6 is a composite number.

It is even and so it is in the 2 times table.

6 is a composite number not prime

6 can be made from 2 × 3 and so it is not a prime number.

7 is a prime number.

It can only be made from 1 × 7. It has no other factors.

7 is a prime number

8 is a composite number because it is even.

It can be written as 2 × 4.

8 is a composite number not prime

Because 8 is composite, it is not prime.

9 is a composite number and is not prime.

9 can be written as 3 × 3.

9 is not a prime number it is 3 times 3

It is a common mistake to include 9 as a prime number because it is odd. It is our first odd number that is not prime. 9 is 3 times 3 and so, it can be broken down into smaller whole numbers.

10 is a composite number because it is even.

10 is in the 2 times table and the 5 times table.

10 is a composite number

10 is not a prime number.

11 is a prime number. 11 can only be written as 1 × 11.

11 is a prime number

12 is a composite number.

12 can be written as 1 × 12, 2 × 6 and 3 × 4.

12 is an example of a composite number

12 is not prime.

Finding Prime Numbers using the Sieve of Eratosthenes

Finding prime numbers is very difficult because there is no real pattern to them.

There is no quick way to find prime numbers. We must check to see if any smaller numbers divide into our number.

One way to find prime numbers is using the Sieve of Eratosthenes.

The Sieve of Eratosthenes is named after a Greek mathematician, Eratosthenes, who it is attributed to.

It uses the fact that a prime number will not be in the times table of any smaller number.

‘Prime’ is another word for ‘first’ and a prime number will be the first number in a times table as long as it does not appear in any other times table.

We start with a number grid and cross off the numbers in each times table.

We know that 1 is neither prime nor composite and so we will mark this in green to show this.

We then start with the two times table.

marking the 2 times table on the sieve of eratosthenes

We mark the first number in this times table as prime and cross off the numbers in the two times table that come after.

Any number in the two times table that is larger than 2 will not be prime. This is because they can be divided exactly by 2.

Once we have marked the two times table, we look at the next times table.

We mark the first number in the three times table, 3, as prime and then cross off the remaining numbers in the three times table.

crossing off the 3 times table on the sieve of eratosthenes

Some numbers in the 3 times table are already crossed off because they were in the 2 times table but we cross off the rest.

Next is the 4 times table, however all numbers in the 4 times table are also in the two times table.

marking the 4 times table on the sieve of eratosthenes

Next we mark 5 as prime and then every other number in this times table is marked as composite.

the 5 times table on the sieve of eratosthenes

All of the numbers in the 6 times table have already been marked.

This is because 6 is in the 2 times table and the 3 times table.

the 6 times table on the sieve of eratosthenes

We now mark the 7 times table. 7 is prime and we cross the next numbers as composite.

7 times table on the sieve of eratosthenes

The numbers that have been crossed off in blue on this grid are composite numbers.

All of the remaining numbers that are not crossed off on this grid are prime numbers. We will shade them in red.

Prime Numbers to 100 shown using the sieve of eratosthenes

Below are the prime numbers to 20.

Prime Numbers to 20

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Now try our lesson on Negative Numbers on a Number Line where we learn about negative numbers.

Negative Numbers on a Number Line

negative numbers

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Counting in Tenths

Counting in Tenths
Example Video Lesson

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Example Video Lesson

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what are tenths

  • The fraction one tenth is written as   1 / 10  .

  • This means 1 divided by 10.

  • We take one whole and divide it into ten equal parts.

  • Ten tenths make   10 / 10  .

  • Ten tenths make a whole.

One tenth is written as   1 / 10  .

Ten tenths make one whole.

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Counting in Tenths on a number line

  • The number on the top of the fraction tells us how many tenths we have.

  •   5 / 10   is half way between 0 and 1.

  •   10 / 10   is one whole.

Counting in Tenths

What are Tenths?

A tenth is a fraction written as   1 / 10  .

The 1 on the top of the fraction means to start with one whole.

The line in the fraction means to divide.

Then we have a 10 on the bottom of the fraction so we divide by 10.

What is a tenth?

One tenth means one whole divide into 10 equal parts.

Here we have 2 tenths, which is written as   2 / 10  .

It means to take 2 wholes and divide them both by 10.

two tenths

When we divide each whole by 10, we get a tenth.

We have 2 tenths.

Counting in Tenths

We can count up in tenths by increasing the number on the top of the fraction.

The number on the bottom of these fractions tells us how many tenths we have.

As the number goes up, we add another tenth.

Counting in Tenths from 0 to 1

10 tenths is written as   10 / 10  , which is one whole.

10 / 10   means 10 divided by 10, which equals one.

We can count up in tenths on a number line from 0 until we reach 1.

Counting in Tenths on a number line

We can see that   5 / 10   is half way and so   5 / 10   is one half.

10 / 10   is 10 tenths, which is the same as 1 on the number line.

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Now try our lesson on Shading Fractions of Shapes where we learn how to shade a fraction.

Shading Fractions of Shapes

shading fractions

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Right Angles

Right Angles
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Example Video Questions Lesson

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what are right angles

  • Right angles are exactly 90
    degreesThe measurements on a protractor used to measure the size of angles.
    .

  • This means that the two lines that form a right angle will meet to form a capital ‘L’ shape.

  • The lines that form the angle will line up directly with the sides of a ruler.

  • To identify a right angle, place a ruler or set-square in the corner of the angle and see if the sides line up.

  • If the angle doesn’t line up with the sides of the ruler or the set square then it is not a right angle.

  • We draw a square in the corner of the angle to show that it is a right angle.

  • We look out for
    horizontalLines that go from left to right, like the horizon.
    and
    verticalLines that go from up to down.
    lines that may meet at right angles.

Identifying Right Angles on a right angled triangle

  • We will test the angles of this triangle with a ruler to see if any of them are right angles.

  • The sides of the ruler line up perfectly with the angle in the bottom left corner and so, it is a right-angle.

  • We mark right angles with a square.

  • We place the ruler along the sides of the other angles but neither of them line up.

  • We only have one right angle.

  • We call a triangle that contains a right angle a right-angled triangle.

The lines that make right angles line up with the sides of a ruler or set square.

We mark right angles with a small square in the corner of the angle.

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Example of Identifying Right Angles on a trapezium

  • We line the ruler up with each angle in our trapezium.

  • We can see that the two base angles are right angles because the sides line up with the sides of the ruler.

  • We mark the two right angles with a square in each angle.

  • The other two angles in this shape are not right angles because the ruler does not line up with both sides of each angle.

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Identifying Right Angles Worksheets and Answers

identifying right angles on shapes worksheet pdf
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identifying right angles on shapes worksheet answers pdf
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Right Angles

What are Right Angles?

A right angle is a special type of angle that contains exactly 90 degrees. It is one quarter of a full turn. Right angles are found in all four corners of a square. We mark right angles with a square in the corner of the angle.

Right angles are always formed by any two horizontal and vertical lines.

forming right angles with horizontal and vertical lines

We mark the right angle with a square in the corner of the angle. Any time we see this square, we know we have a right angle.

Here is a right angle shown on a protractor. We can see that the lines are horizontal and vertical.

a right angle of 90 degrees shown on a protractor

Right angles are the angles found in the corners of squares or rectangles. Right angles look like capital ‘L’ shapes.

Here are some examples of right angles found in real life.

right angles on bricks
right angles on a table
right angle on a ruler

In shapes, right angles are often made up of one

horizontalLines that go from left to right, like the horizon.
line and one
verticalLines that go from up to down.
line.

How to Check if an Angle is a Right Angle

To test if an angle is right angle, place a protractor over one line of the angle and read the number that is in line with the other line of the angle. If the angle is 90 degrees, then it is a right angle.

It can be easier to place the corner of a ruler or set-square in the corner of an angle and check if both sides of the angle line up with the sides of the ruler or the set square.

The angle in the corner of a ruler is a right angle so if the sides of the ruler line up exactly with both sides of the angle, then the angle itself is a right angle.

If both sides of the angle do not line up with the sides of the ruler, then the angle is not a right angle.

Here are some examples of right angles made from horizontal and vertical lines.

We have a vertical line going up along with a horizontal line going right.

Identifying Right Angles in two lines

We can see that putting the corner of the ruler in the corner of the angle, the sides of the angle line up with the sides of the ruler.

We have a right angle.

To show that we have a right angle, we draw a square in the corner of the angle. This is an easy way to show that we have a right angle without writing 90 degrees next to it.

Here we have a vertical line going up and a horizontal line going left.

testing if an angle is a right angle

We can see that the ruler fits exactly in this angle, with the two sides of the angle lining up with the sides of the ruler.

This too is a right angle, so we mark it with a square.

In this example we have a vertical line down and a horizontal line right.

Whenever a vertical line meets a horizontal line, a right angle is formed.

Vertical lines and horizontal lines always meet at right angles.

Identifying Right Angles between two lines using a ruler

We mark the angle with a square to show that it is a right angle.

Here we have a vertical line down and a horizontal line left.

Again because we have a vertical line meeting a horizontal line, we have another right angle.

Identifying Right Angles 4

The sides of the ruler line up exactly with the two sides of the angle.

In this next example we have a vertical down line but the other line is not horizontal.

We can place on side of the ruler along one of the lines.

The other line does not line up with any of the other sides of the ruler.

These two lines do not form a right angle. We do not mark it with a square box.

example that is not a right angle

This angle was too small to be a right angle.

In this next example we have a horizontal line going right and another line.

We can line up one side of the ruler with the horizontal line. We can see that the other line does not line up with the other side of the ruler.

an example of an angle that is not a right angle

Because the sides of the angle do not line up with the sides of the ruler, this is not a right angle. We do not mark it with a square box.

The angle is too large to be a right angle. This means that the angle is too open.

We can see that horizontal and vertical lines are at right angles to each other. If one line is vertical, then the other line must be horizontal to make a right angle. If one line is horizontal, then the other line must be vertical to make a right angle with it.

Right angles do not have to be formed from horizontal and vertical lines. Right angles can face in any direction.

Examples of Right Angles

Right angles look like capital L shapes. Some common examples of right angles include corners of tables, windows and doors. In the home, some examples of right angles include the corners of dice, books and paper sheets. The corners of a square are all right angles.

Here are some examples of right angles shown going in different directions.

examples of right angles

Here are some examples of right angles found in real life.

Examples of right angles in real life include the corners of a road sign, the corners of a desk, the corners of a soccer pitch, the corners of a building and crossroads.

example of a real life right angle on a sign
right angles in real life example on a desk
right angle in real life example of a soccer pitch

example of a real life right angle on a sports pitch
right angles on a building in real life
a road intersection meeting at right angles

Here we can see how these right angles are marked.

marking a right angle on a sports pitch

how to show right angles

right angles on a building

Examples of Right Angles in Nature

Examples of right angles in nature include the angle between trees and the ground, rock formations and the angles between stalactites in caves and the ceiling of the cave.

example of right angles in nature with trees going into the ground
right angles in nature rock formation
stalactites are examples of right angles in nature

Right angles often form in nature due to the effects of gravity. Gravity acts at right angles to the ground. It pulls things down vertically to make a right angle with the horizontal ground.

We can see the right angles formed in this rock formation.

right angles in nature on a rock formation

Examples of Right Angles at Home

Examples of right angles are found all around the home wherever there are horizontal and vertical corners. Examples of right angles around the home include the corners of tables, mats, doors, bricks, windows, television screens, books, folders, boxes and dice.

examples of right angles in the home
right angles at home on a television screen
lots of examples of right angles on the home with windows doors

Most objects with corners can be tested for right angles. Many objects around the home contain right angles for their corners.

Here are examples of testing corners for right angles.

testing angles for right angles in the home

marking right angles on a house

the corners of a television are right angles

Right Angles in Shapes

Common shapes that contain right angles are squares, rectangles, right-angled triangles and right trapeziums. The angles of a rhombus and a kite do not typically have right angles but their diagonals will always cross at right angles.

Right angles are often identified as capital L shapes.

Here are some right angles, which can be used to create shapes.

right angles creating a square

Here we can see that four right angles can be used to create a square shape.

To identify right angles in shapes we look for two sides which form a capital L shape. We can line up our ruler to check.

If the sides of the shape line up with the sides of the ruler, the angle is a right angle.

We also look out for horizontal lines meeting vertical lines.

Right angles on a Square

All four angles on a square are always right angles, meeting at 90 degrees. The four right angles add to make a total of 360 degrees, so the angles in a square add up to 360 degrees.

Below is a square.

Identifying Right Angles on a square

We can line the ruler up with the sides of the shape to test for right angles.

We can see that the ruler lines up with the sides at every angle and so, all of the angles in a square are right angles.

A square has 4 right angles and we mark them with a square box.

Right Angles on a Rectangle

A rectangle always contains 4 right angles. Every angle on a rectangle is 90 degrees. A square is a special type of rectangle that has the same length sides and it also contains 4 right angles.

Below is a rectangle.

We can see that a rectangle also has 4 right angles.

Identifying Right Angles on a rectangle

Right Angles on a Triangle

Not all triangles contain right angles. A triangle can contain at most only one right angle and if it does, it is called a right angled triangle. The right angle is shown with a small square in the corner of the angle.

Below is a right-angled triangle.

Only one angle has sides that line up with the sides of the ruler.

This triangle has 1 right angle. The other two angles are too small to be right angles.

Identifying Right Angles on a right angled triangle

We call any triangle that contains a right angle a right-angled triangle.

A triangle can only contain at most one right angle.

Sometimes we don’t have any right angles in a triangle.

The triangle below does not have any right angles.

a triangle with no right angles

Right Angles on a Trapezoid

Not all trapezoids contain right angles. Isosceles trapezoids are symmetrical and do not contain any right angles. If a trapezoid contains a right angle, it is called a right trapezoid. In this case, it will have two adjacent right angles connecting the 2 parallel sides.

Below is a trapezoid.

We can see that the two base angles are both right angles. The base is horizontal and the left and right sides are both vertical. Vertical lines that meet horizontal lines create right angles.

The other two angles are not right angles. One angle is too large and the other is too small.

Identifying Right Angles on a trapezium

Shapes that do not have a Right Angle

Common shapes that do not contain any right angles include equilateral triangles, regular pentagons, hexagons, octogons. Kites do not always contain right angles, although they can do. Parallelograms do not have to contain right angles, although if they do, they are called rectangles.

Below is a regular pentagon.

All of this pentagon’s angles are the same size.

None of the angles are right angles. no right angles on a regular pentagon

Although it is close, the sides of each angle do not line up with the sides of the ruler. The angles are all slightly too large.

Other shapes that don’t have right angles can include kites and parallelograms.

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Now try our lesson on Parallel Sides where we learn how to identify parallel sides on shapes.

Parallel Sides

Parallel Lines

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Division Word Problems: Interactive Questions

Division Word Problems: Interactive Questions Return to video lesson on Division Word Problems

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Multiplying by Multiples of 10 and 100

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Multiplication Word Problems: Interactive Questions

Multiplication Word Problems: Interactive Questions Return to video lesson on Multiplication Word Problems

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Division Word Problems

Division Word Problems
Example Video Questions Lesson

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Example Video Questions Lesson

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Division Word Problems example involving packets of matches

  • I have 80 matches and I will put 8 into each packet.

  • There are two numbers in this question: 80 and 8.

  • We identify the total number, which is 80.

  • We identify the number in each group, which is 8.

  • We divide the total by the number in each group to find the number of groups.

  • 80 ÷ 8 = 10 and so, we can make 10 packets.

Divide the total by the number of groups to find the amount in each group.

Divide the total by the amount in each group to find the number of groups.

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Division Word Problems example involving money

  • Each shirt costs $11 and I have $66.

  • We identify $66 as the total.

  • $11 is the cost of each shirt.

  • We want to know how many times 11 can go into 66.

  • 66 ÷ 11 = 6 and so, 11 goes into 66 six times.

  • We can spend $11 six times.

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Simple Division Word Problems: Interactive Questions

Simple Division Word Problems: Interactive Question Generator

Simple Division Word Problems Decimals Worksheets and Answers

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Simple division word problems worksheet answers pdf
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Division Word Problems

How to Identify Division Word Problems

When an amount is shared into equal parts and we are asked for how many parts, or the number in each part, then we have a division.

To identify a division word problem, we need to read the question carefully and try to understand the context.

If we have been told the total and are sharing this total into equally sized parts, then a division is taking place.

Division keywords can also help to give us a clue that we have a division.

Here are some division keywords:

  • Share
  • Between
  • Evenly
  • Equally
  • Per
  • Shared
  • Split

However it is always worth reading the question carefully to make sure that we are sharing a total into an equally sized parts.

Simple Division Word Problems

To solve a division word problem, we can use the following steps:

  1. Identify the numbers given in the question.
  2. Identify which number is the total quantity.
  3. Identify how many groups we are sharing between or how many need to go in each group.
  4. Divide the total by the number of groups to find the amount in each group.
  5. Or divide the total by how many needed in each group to find out how many groups can be made.

    6. In this example, ‘I have 10 sweets to share evenly between 5 children. How many sweets do they each get?’

    We are trying to find how many sweets each child gets, so we want to know how many sweets will be in each group.

    We first identify the total, which is 10 sweets.

    Now we identify how many groups we have, which is 5. We are sharing equally between 5 children.

    We divide the total amount by the number of groups.

    Division Word Problems example

    We are sharing 10 sweets between 5 people.

    10 ÷ 5 = 2 and so, each child gets 2 sweets each.

    When teaching division word problems, we can draw 10 sweets and group them equally by drawing circles around them to help visualise this. We could also get 10 counters and share them out equally, one at a time.

    We can see in this example that we had the keywords of share evenly and each, which can give us a clue that we have a division.

    The division also tells us how many times 5 goes into 10.

    Division to see how many times does 5 go into 10

    In this next example, ‘I have 80 matches. I will put 8 into each packet. How any packets will I fill?’

    We want to see how many packets we will fill. We want to see how many groups we will create.

    We first identify the total number of matches, which is 80.

    We then identify the number in each packet, which is 8.

    To find the total number of packets, we will divide.

    example of a division word problem to see how many groups we can make

    80 ÷ 8 = 10 and so, we can make 10 packets.

    We can think of this as working out how many times 8 goes into 80 or how many packets can be made from 80 matches.

    In this next example, ‘I need 30 crayons. Each pack contains 5 crayons. How many packs should I buy?’

    The total number is the larger number, which is is 30.

    We are buying the crayons in equal groups of 5.

    We need to work out how many groups we need. How many fives make 30?

    We need to work out how many fives go into 30.

    Division Word Problem example

    30 ÷ 5 = 6 and so, we need 6 packs.

    We can check out answer. 6 lots of 5 make the 30 crayons needed because 6 × 5 = 30.

    In this example we needed to find the number of groups required. So we divided the total by the number in each group.

    In this example, ‘I have 21 chairs. I will arrange the chairs in rows of 7.How many rows should I make?’

    Here we have the total number of chairs, which is 21.

    We are arranging them into rows of 7, so each group contains 7 chairs.

    We want to find the number of rows that we can make. We want to work out how many rows of 7 can be made from 21 chairs. This is how many times 7 goes into 21.

    Division Word Problem using 21 chairs in rows of 7

    21 ÷ 7 = 3 and so, we can make 3 rows.

    We can see that each row is the same size. We can teach this by taking 21 counters and sharing them into 3 equal rows.

    In this example involving money, ‘Shirts cost $11 and I have $66. How many shirts can I buy?’

    We want to know how many elevens go into 66.

    The total is $66 and we are dividing by 11.

    Division Word Problems involving money

    We want to know how many times we can spend $11.

    66 ÷ 11 = 6 and so, we can spend $11 six times.

    We can buy six shirts.

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Now try our lesson on Short Division without Remainders where we learn how to use the short division method to divide numbers.

Short Division without Remainders

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Multiplication Word Problems

Multiplication Word Problems
Example Video Questions Lesson

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Example Video Questions Lesson

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simple multiplication Word Problem example

  • There are 3 tables and there are 6 children on each table.

  • The children are in equal groups of 6.

  • There a 3 groups.

  • We have 3 lots of 6, which we can write as a multiplication.

  • 3 ×6 = 18 and so we have 18 children.

  • We multiplied the number of groups by the number in each group to find the total.

When we have equal groups of the same number, we multiply to find the total.

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Simple Multiplication Word Problem example with eggs

  • There are 6 eggs in each box and I have 5 boxes.

  • I have 5 lots of 6 eggs.

  • When we have the same amount in each group we have a multiplication.

  • We multiply the number of groups by the amount in each group to find the total.

  • We have 5 groups of 6 and 5 × 6 = 30.

  • There are 30 eggs in total.

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Simple Multiplication Word Problems: Question Generator

Simple Multiplication Word Problems: Interactice Question Generator

Simple Multiplication Word Problems Decimals Worksheets and Answers

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Multiplication Word Problems

How to Identify Multiplication Word Problems

When we have equal groups of of the same amount, we can use multiplication to find the total.

The number of groups multiplied by the amount in each group gives us the total.

The best way to identify a multiplication word problem is to read the question fully and try to understand the context.

If we have multiple groups with an equal number of items in and we need a total, then we have a multiplication problem.

Keywords may help identify a multiplication. Some multiplication keywords are:

  • Lots of
  • Groups of
  • Each
  • Altogether
  • Total
  • In all

However, these keywords are only a clue to multiplication and we should always check the context of the question. For example, words such as ‘altogether’ and ‘in all’ may indicate addition instead.

Simple Multiplication Word Problems

To solve multiplication word problems follow these steps:

  1. Identify the numbers in the question.
  2. Identify which of these numbers tells us how many there are in each group.
  3. Identify which of these numbers tells us how many groups there are.
  4. Multiply these two numbers using times tables or long multiplication.

    5. In these examples we will look at simple multiplication word problems in which there is not a large paragraph of text and the numbers to multiply will be less than 12.

    In this question ‘There are 3 tables and there are 6 children on each table.’ We are asked, ‘How many children are there in total?’

    We have 6 children on each table, so there are 6 in each group.

    We have 3 tables, so 3 groups of children.

    We are asked for the total. To find the total, we multiply the number of groups by the amount in each group.

    Simple multiplication word problem example of children in groups

    We have 3 groups of 6, or 3 lots of 6 children.

    The word ‘lots of’ can be replaced with a multiplication sign.

    3 times 6 shown as a diagram of a real life situation

    3 × 6 = 18 and so, there are 18 children in total.

    As long as we have an equal number in each group then we can multiply to see how many there are in total. We had 6 children on every table.

    The words each and total together in this question could have given us a clue that we may have had a multiplication.

    When teaching multiplication word problems, it is very important to understand the context. To do so, we try to imagine what is actually happening in real life.

    Encourage children to draw the situation or model it using cubes or counters.

    In these examples we have drawn out the situation to help visualise what is going on.

    In this next example, ‘There are 6 eggs in a box. I have 5 boxes. How many eggs are there in total?’

    There are 6 eggs in each group.

    We have 5 boxes, so 5 lots of 6.

    We have an equal number of items in each group and so, to find the total, we multiply the number of groups by the number of items in each group.

    Multiplication Word Problems example with 5 times 6 eggs

    We have 5 boxes of 6, or 5 lots of 6 eggs.

    5 × 6 = 30 and so, there are 30 eggs in total in the 5 boxes.

    We could multiply in this word problem because there were the same number of eggs in each box.

    Again, when explaining these multiplication word problems, it is helpful to draw or model the situation if it is difficult to conceptualise.

    Here instead of drawing egg boxes, you could draw a circle to represent each egg, or use 5 pile of 6 counters.

    In this example, ‘There are 10 berries in each bag and there are 6 bags. How many berries are there in total?’

    We have 10 berries in each bag.

    There are 6 bags.

    We have the same number of berries in each bag and so we multiply to find the total.

    simple multiplication Word Problems example of berries in a bag

    We have 6 lots of 10.

    6 × 10 = 60 and so, there are 60 berries in total.

    With larger numbers, it is not a good idea to use 60 counters or draw 60 berries.

    Instead we can use multiplication as repeated addition to help us.

    We can draw the 6 bags and label a 10 by each.

    We can then count on in tens 6 times to reach our answer.

    In this example, ‘Each lollipop costs $2. I buy 8 lollipops. How much do they cost in total?’

    With multiplication word problems involving money, we multiply the number of items by the amount each costs.

    We are spending $2 for each lollipop.

    We spend $2 eight times.

    simple multiplication Word Problems with money

    8 × $2 = $16 and so, the 8 lollipops cost $16.

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Now try our lesson on Grid Method Multiplication where we learn how to work out larger multiplications using the grid method.

Grid Method Multiplication

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Multiplying Decimals

Multiplying Decimals
Example Video Questions Lesson

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Example Video Questions Lesson

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how to multiply decimals example of 0.3 times 0.5

  • We ignore the decimal points and any zeros in front of them and then multiply.

  • So 0.3 × 0.5 can be thought of as 3 × 5, which equals 15.

  • 3 is ten times larger than 0.3 and 5 is ten times larger than 0.5, so our answer is 100 times too big.

  • We divide 15 by 100 by moving the decimal point two places.

  • We then write a zero in front of the decimal point if there is no digit in front of it.

  • 3 × 5 = 15 and so, 0.3 × 0.5 = 0.15 .

  • 0.3 has one decimal place and 0.5 has one decimal place, which is two decimal places in total.

  • Our answer of 0.15 also has two decimal places.

Multiply the decimals like whole numbers.

Move the decimal point so that the answer has the same number of decimal places as the numbers in the question combined.

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Multiplying Larger Decimal numbers example

  • We ignore the decimal points and the zeros in front for the decimal numbers.

  • We think of 2.1 as 21 and 0.3 as 3.

  • We multiply each digit in 21 by 3 to get 63.

  • Now we correct the answer by counting the decimal places in the question.

  • 2.1 has one decimal place and 0.3 has one decimal place.

  • There are 2 decimal places in the question so there will be 2 decimal places in the answer.

  • We put 2 decimal places after the decimal point and fill in our answer from right to left.

  • We put a zero in front of the decimal point.

  • 2.1 × 0.3 = 0.63.

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Supporting Lessons

Introduction to Multiplying Decimals

Multiplying Decimals using Long Multiplication

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Multiplying by Decimals Interactive Question Generator

Multiplying Decimals with Times Tables: Interactive Questions

Multiplying by Decimals by Decimals Worksheets and Answers

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Multiplying by Decimals using Long Multiplication Worksheets and Answers

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How to Multiply Decimals

To multiply decimals use the following steps:

  1. Ignore the decimal points then multiply the numbers that remain.
  2. Count the number of decimal places in all of the numbers of the question combined.
  3. Place the decimal point so that there are the same number of decimal places in the answer and the question.
  4. Add a zero in front of the decimal point if there are no digits there.

Here is an example of how to use these steps to multiply two decimal numbers.

We have 1.1 × 0.8.

Step 1: Ignore the decimal points then multiply the numbers that remain.

Ignoring the decimal point in 1.1, we have 11.

Ignoring the decimal point and the zero before it in 0.8, we have 8.

We multiply 11 × 8.

step 1 multiplying decimals

From our times tables, we know that 11 × 8 = 88.

Step 2: Count the number of decimal places in all of the numbers of the question combined.

The number of decimal places in each number is equal to the number of digits to the right of the decimal point. The decimal places are shown underlined in each number below.

1.1 has one decimal place.

0.8 has one decimal place.

In total, the question has two decimal places. One from 1.1 and one from 0.8.

step 2 multiplying decimals.png

The number of decimal places in each number is also equal to the number of digits that the decimal point must jump over to get to the right end of the number.

We can see that we have one jump shown in each number and that there are 2 jumps in total in both numbers of our question. There are 2 decimal places in total in our question.

Step 3: Place the decimal point so that there are the same number of decimal places in the answer and the question.

We know that there are 2 decimal places in the question and so, there must be 2 decimal places in our answer.

It is easiest to first write the decimal point and then count the 2 decimal places to the right of this.

step 3 multiplying decimals

We work from right to left placing the digits of our answer in.

We place the two 8 digits in the two decimal places to the right of the decimal point.

Step 4: Add a zero in front of the decimal point if there are no digits there.

We have .88 and so, there are no digits in front of the decimal point.

We must write a zero in front of the decimal point to show that there are no units there.

step 4 multiplying decimals

The answer to 1.1 × 8 = 0.88.

Multiplying Decimals example of 1.1 multiplied by 0.8

Why the Trick for Multiplying Decimals Works

In this example we have 0.4 × 0.3.

We think of it as 4 × 3, which equals 12.

Multiplying two decimals example 0.3 times 0.4

We have made 0.4 ten times bigger to get 4 and 0.3 ten times bigger to get 3.

The answer of 12 is 100 times too big and so we need to make it 100 times smaller by moving the decimal point two places left.

We get .12 and we write a zero in front to get 0.12 as our answer.

To make each decimal in the question into a whole number, the decimal point must move past each decimal place.

Each decimal place in the question is an extra division by 10.

We can simply count the number of decimal places in all numbers of the question and make sure that there are the same in the answer.

0.4 has 1 decimal place and 0.3 has 1 decimal place.

Multiplying decimals using the decimal place trick

Our answer has 2 decimal places and so, we can put two lines as decimal places after the decimal point. We then fill these places with the answer to 4 × 3.

We work from right to left, so 2 goes in on the rightmost decimal place and 1 goes in the left one.

There are no more digits left so we just write a zero in front of the decimal point.

Examples of Multiplying Decimals by Decimals

In this example we have 0.2 × 4.

We think of the multiplication as 2 × 4, which is equal to 8.

Multiplying Decimals 0.2 times 4

However this answer is ten times too big because we had 0.2 rather than 2. We made 0.2 ten times larger to get this answer.

We have to divide by ten to undo this. We move the decimal point one place left and write a zero in front of it.

0.2 × 4 = 0.8

We can see that 0.2 has 1 decimal place and so does our answer of 0.8.

In this next example of multiplying decimals we have 0.3 × 0.5.

We ignore the decimal points and the zeros in front of them and work out 3 × 5.

Multiplying Decimals by decimals example of 0.3 times 0.5

3 × 5 = 15, however we multiplied 0.3 by ten to get 3 and we multiplied 0.5 by ten to get 5.

So we must divide 15 by ten and then by ten again to get our correct answer.

We can see that there is one decimal place in 0.3 and one decimal place in 0.5. This makes 2 decimal places in total in our question.

We know that our answer must have two decimal places after the decimal point.

0.3 × 0.5 = 0.15

Multiplying Decimals with Zeros in the Product

If the product in a decimal multiplication ends in any zeros, then remove the zeros before writing the final answer.

Here is an example of a decimal multiplication in which we must remove zeros from our final answer.

We have 0.25 × 0.04.

We first work out 25 × 4, which equals 100.

Multiplying Decimals with zeros example of 0.25 times 0.04

We have 2 decimal places in 0.25 and 2 decimal places in 0.04

Our answer will have a total of 4 decimal places.

We have 0.0100, which has 4 decimal digits: 0100.

However, we do not need to write the last two zeros that follow the 1.

0.0100 is the same as 0.01.

0.25 × 0.04 = 0.01

In this example we have 3.4 × 7.5.

We ignore the decimal points and work out 34 × 75.

This is quite a large calculation and so we can use long multiplication to work out the answer on grid paper.

First we multiply the digits in 34 by 5.

Multiplying Decimals on grid paper

4 × 5 = 20, so we write the 0 and carry the 2.

3 × 5 = 15 and we add the 2 that we carried to make 17.

34 × 5 = 170.

We now multiply the digits in 34 by 70.

To do this we write a zero to multiply by ten and then multiply by 7.

Multiplying Larger Decimals example using grid paper

4 × 7 = 28, so we write the 8 and carry the 2.

3 × 7 = 21 and we add the 2 that we carried to make 23.

34 × 70 = 2380

We now add the digits to get the answer to 34 × 75.

using graph paper to multiply decimals in steps

34 × 75 = 2550

We now correct our answer to obtain the correct answer to the decimal multiplication of 3.4 × 7.5.

We have 1 decimal place in 3.4 and 1 decimal place in 7.5. There are 2 decimal places in total in the question and so we will have 2 decimal places in the answer.

3.4 × 7.5 = 25.50

Multiplying Decimals using graph paper

Now that we have got our answer, we can see that there is a zero at the end of the answer. Remember that we can remove any zeros at the end of a decimal number.

25.50 is the same as 25.5 and so, our answer is 25.5.

Multiplying Larger Decimals using Grid Paper

In these examples we must use long multiplication on grid paper to work out the answers to the decimal multiplications.

In this example we have 5.2 × 1.6.

We first multiply 52 and 16. We multiply the digits in 52 by 6.

Multiplying Larger Decimals using grid paper long multiplication

2 × 6 = 12 so we write the 2 and carry the 1 ten.

Next we multiply 5 by 6 which equals 30. We add the 1 that we carried to make 31.

52 × 6 = 312

We now multiply the digits in 52 by 10. 52 × 10 = 520.

Multiplying Larger Decimals example using graph paper

We now add the digits in each column to get our answer .

Multiplying Larger Decimals using long multiplication

52 × 16 = 832

Finally, we make sure that our answer has the same number of decimal places as in the question.

5.2 has 1 decimal place and 1.6 has 1 decimal place. The question has 2 decimal places so our answer will have 2 decimal places.

Multiplying Larger Decimals using the decimal place trick

We write the ‘3’ and the ‘2’ of 832 in the two decimal places of the answer and the ‘8’ must go on the left of the decimal point.

The digits in our answer of 8.32 must be in the same order as in 832.

In this example we have 6.3 × 7.02.

We multiply 63 by 702 using long multiplication.

63 × 2 = 126

Multiplying Larger Decimals in steps using long multiplication

Next we multiply 63 by 0.

Anything times zero equals zero and so, we do not need to write anything for this.

Multiplying Larger Decimals example

Next we multiply the digits in 63 by 700. We first multiply by 100 by writing two zeros and then we can simply multiply by 7.

Multiplying Larger Decimals

3 × 7 = 21, so we write the 1 and carry the 2 tens.

6 × 7 = 42, plus the 2 we carried equals 44.

63 × 700 = 44100

Multiplying Larger Decimals 7d

We add the digits to get our answer to 63 × 702, which is 44226.

Multiplying Larger Decimals using the decimal place trick

We now use our decimal place trick to convert our answer to 63 × 702 into the correct answer for 6.3 × 7.02.

6.3 has 1 decimal place and 7.02 has 2 decimal places.

This is three decimal places in total and so, our answer must have three decimal places.

We put the digits of 226 in the three decimal place spots and then the 44 goes in front of the decimal point.

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Now try our lesson on Finding Simple Percentages of Amounts: 10%, 25%, 50% and 100% where we learn how to find simple percentages of amounts.

Finding Simple Percentages of Amounts: 10%, 25%, 50% and 100%

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Multiplying by 0 and 1

Dividing Fractions
Example Video Questions Lesson

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Example Video Questions Lesson

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Multiplying by Zero

rule for multiplying by 0

  • Here are 4 empty egg cartons, each with zero eggs in.

  • We have 4 lots of zero eggs.

  • There are still zero eggs in total.

  • 4 lots of zero is zero.

  • 4 × 0 = 0.

  • Any number multiplied by zero always equals zero.

  • It does not matter how many numbers there are or how large they are, if we have a multiplication by 0, the answer will always be zero.

  • Even if zero was written first, the answer is still zero.

  • For example, 0 × 4 = 0.

Multiplying by One

Rule for multiplying by 1

  • We have 3 cartons of eggs, each containing one egg.

  • We have 3 lots of 1, which is 3 eggs in total.

  • We write this as 3 × 1 = 3.

  • Multiplying by 1 did not make 3 any larger, it just remained the same.

  • One multiplied by a given number equals the given number.

  • The number multiplied by 1 is 3 and so, 3 is the answer.

  • Even written the other way around, we have 1 × 3 = 3.

When we multiply by zero the answer is always zero.

When we multiply a number by one it remains the same size.

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Examples of Multiplying by 0

Example of multiplying by 0

  • If there is a zero in a multiplication then the answer to a multiplication will always by zero.

  • It does not matter if the zero comes first, such as in 0 × 5 = 0.

  • 0 × 0 = 0 because we have zero lots of nothing.

  • Even large numbers equal zero when multiplied by zero, such as 57 × 0 = 0.

  • It does not matter how many numbers there are. If there is only multiplication happening and there is a zero, then the answer is zero.

  • 6 × 0 × 9 = 0, we don’t need to do any calculations in this example.

Examples of Multiplying by 1

Examples of Multiplying by 1

  • If we multiply by 1, then the other number stays the same.

  • It does not matter if the one comes first, such as in 1 × 8 = 8.

  • It does not matter if the one comes second, such as in 7 × 1 = 7.

  • Even large numbers remain the same size when multiplied by one, such as 94 × 1 = 94.

  • Even zero remains as zero when we multiply it by 1, such as in 0 × 1 = 0

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Supporting Lessons

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Multiplying by 0 and 1 Interactive Question Generator

Multiplying by 0 and 1: Interactive Questions

Multiplying by 0 and 1 Worksheets and Answers

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How to Multiply by Zero and One

How to Multiply by 0

The rule for multiplying any number by 0 is that we always get a result of 0. Any number times zero equals zero.

It does not matter where the zero appears in the multiplication. If the only operation is multiplication, then the answer will be zero if we multiply by 0.

To understand why this is the case, we will look at some examples of multiplication.

Here are three boxes of eggs. Each box has ten eggs. We have 3 lots of 10.

We write ‘lots of’ as a multiplication sign.

3 lots of 10 is written as 3 × 10.

3 lots of 10 eggs

3 × 10 = 30 and so, there are 30 eggs in total.

If we remove a box, we now have 2 lots of 10 eggs, written as 2 × 10.

2 lots of ten eggs

2 × 10 = 20, we have 20 eggs in total.

If we remove another box, we have one lot of ten eggs, written as 1 × 10.

one lot of ten eggs

If we remove our final box, there are no eggs left.

The number that is used to represent nothing is zero. We write zero as 0.

zero eggs

We have no more boxes, so we have no lots of 10.

We write this as 0 × 10, which is pronounced zero times ten.

There are no eggs in total so 0 × 10 = 0.

Multiplying by 0

We say that zero lots of any number always equals zero.

It does not matter what the number is, if it is multiplied by zero, then the answer is zero.

In this example we have 3 empty boxes.

Each box contains zero eggs so in three boxes we say we have 3 lots of 0.

Multiplying by 0 equals 0

3 × 0 = 0 because there are no eggs in total.

Even if we add another empty box, we are not adding any eggs. We still have zero in total.

We have 4 lots of zero, written as 4 × 0.

Multiplying by 0 equals 0

4 × 0 = 0

We say that any number multiplied by zero always equals zero.

‘× 0’ means ‘lots of nothing’. It does not matter how much of nothing you have, it is still nothing.

Here are some examples of multiplying by zero.

Remember that it does not matter what the other numbers are, as long as we are multiplying by zero, then the answer is zero.

We can see that the simple example of 0 × 5 = 0 because no lots of 5 is nothing.

examples of multiplying by 0

0 × 0 = 0 because this means no lots of nothing. It total we have nothing.

57 × 0 = 0. It does not matter how large the other number is, 57 lots of nothing is still nothing. This is like having 57 empty boxes of eggs. There are still no eggs in any of them.

Even if there are many numbers multiplied together, the answer is still zero if we are multiplying by zero.

6 × 0 × 9 = 0, which is like 9 people who each have 6 empty boxes of eggs. There are still no eggs in total because all of the boxes are empty.

How to Multiply by 1

The rule for multiplying any number by 1 is that the number remains the same size. When multiplying a given number by one, the answer is simply the given number.

To understand why this rule works we will look at some examples of multiplication.

Here is a single box of 10 eggs. It is just one box so we say we have one lot of ten.

We write one lot of ten as 1 × 10.

Multiplying by 1 real life example with eggs

1 × 10 = 10 because there are 10 eggs in total.

Here is a box of 6 eggs.

Again we have one lot of 6, which we write as 1 × 6.

example of Multiplying by 1

1 × 6 = 6.

We can see in both of these cases, the answer shown after the equals sign is simply the other number that is multiplied by 1.

We say that a given number multiplied by one equals the given number.

We can also look at examples where 1 comes second in the multiplication calculation.

Here we have 3 boxes, which each contain 1 egg.

We have 3 lots of 1.

3 lots of 1 is written as 3 × 1.

Multiplying 3 by 1 shown visually

3 × 1 = 3 because there are three eggs in total.

Again the answer is simply the other number in the calculation that we multiply by 1.

We say that one multiplied by a given number equals the given number.

Here are some example questions of multiplying by 1.

1 × 8 = 8. We are multiplying by 1 and the other number is 8, so the answer is 8.

It does not matter if 1 comes second in the multiplication. For example 7 × 1 = 7. We are multiplying by 1 and so, the answer is simply the other number of 7.

multiplying by 1 example questions

It does not matter if the other number is large, we do not need to do any working out, we simply write the other number as our answer.

94 × 1 = 94. The answer is simply the number we are multiplying by 1.

In the last example we have 0 × 1 = 0. Even the number ‘0’ remains the same. We are multiplying by 1 and so the answer is the number that is being multiplied by 1, which is 0.

We can also solve this last example with our rule for multiplying by 0.

Any number multiplied by 0 is 0 and here we have 0 × 1 = 0. One is being multiplied by zero and so, the answer is zero.

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Now try our lesson on Multiplication by Partitioning where we learn how to multiply larger numbers.

Multiplication by Partitioning

multiplication by partitioning

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