Category: Uncategorized

Number Grid: Adding and Subtracting Ten

Number Grid adding Single Digits Example

Every time we add 1, we move one place to the right on our number grid.

When we reach the end of a
rowHere each row is a line of numbers that goes across from left to right.
, to add one more, we start at the beginning of the next row.

38 + 4 means that we find 38 and move to the right 4 places.

We move one place to the right to get to 39.

We move a second place to the right to get to 40.

We are now at the end of the row so to add one a third time we start at the beginning of the next row at 41.

We add one a fourth time to get to 42.

We have added 4 in total by moving 4 places.

38 + 4 = 42.

Supporting Lessons

Number Grid: Adding and Subtracting One

Adding and Subtracting Single Digit Numbers Worksheets and Answers

adding single digit numbers pdf worksheet

How do we Add or Subtract Single-Digit Numbers using a 100 Number Grid?

When we add 1 to a number using the number grid, we move one place to the rightand when we subtract 1 from a number, we move one place to the left.

In this lesson, we will look at adding and subtracting multiples of 1 using the number grid.

Multiples of 1 up to 9 shown as the one times table

Above are the first nine multiples of 1.

We can see that:

1 is 1 lot of 1

2 is 2lots of 1

3 is >3 lots of 1

4 is 4 lots of 1

5 is 5 lots of 1

6 is 6 lots of 1

7 is 7 lots of 1

8 is 8 lots of 1

9 is 9lots of 1

This tells us how many places we move left or right on the number grid.

For example, if we are adding 3, we move 3 places to the right on the number grid, or if we are subtracting 5, we move 5 places to the left on the number grid.

Here is an example of addition using the number grid:

moving right on the number grid calculating 14 + 5

We are asked: what is 14 + 5?

When we add 1, we move 1 place to the right on the number grid.

5 is 5 lots of 1, so we move 5 places to the right.

showing 14 + 5 = 19 by moving right on the number grid

We start at 14 and we move 5 places to the right on the number grid.

We stop at 19.

Therefore,

14 + 5 = 19.

Here is another example of addition using the number grid:

38 + 4 on the number grid by moving right for addition

We are asked: what is 38 + 4?

When we add 1, we move 1 place to the right on the number grid.

4 is 4 lots of 1, so we move 4 places to the right.

38 + 4 shown on the number grid by moving right

We start at 38 and want to move 4 places to the right.

After moving 2 places, we land on 40, which is at the end of the row.

So, we can’t move any further to the right.

Our next step is to move to the beginning of the next row.

We have now moved 3 places. We now move 1 more place to the right.

In total, we have moved 4 places.

Therefore,

38 + 4 = 42.

Here is an example of subtraction using the number grid:

showing subtraction on the number grid by calculating 28 - 6

We are asked: what is 28 – 6?

When we subtract 1, we move 1 place to the left on the number grid.

6 is 6 lots of 1, so we move 6 places to the left.

28 - 6 on the number grid

We start at 28 and we move 6 places to the left on the number grid.

We stop at 22.

Therefore,

28 – 6 = 22.

Here is another example of subtraction using the number grid:

91 - 8 showing subtraction on the number grid

We are asked: what is 91 – 8?

When we subtract 1, we move 1 place to the left on the number grid.

8 is 8 lots of 1, so we move 8 places to the left.

91 - 8 showing subtraction on the number grid

We start at 91 and want to move 8 places to the left.

We are starting at the beginning of the row, so we can’t move any further to the left.

Therefore, our first step is to move to the end of the previous row.

We have moved 1 place, so we now need to move 7 more places to the left.

We stop at 83.

Therefore,

91 – 8 = 83.

Now try our lesson Number Grid: Adding and Subtracting Ten, where we learn how to add and subtract ten using a 100 number grid.

adding 10 using a 100 number grid

Number Grid: Adding and Subtracting Multiples of Ten

Adding and Subtracting Multiples of Ten: Video Lesson – Maths with Mum Download the Number Grid to 100 below:

Supporting Lessons

Adding and Subtracting Multiples of 10: Worksheets and Answers

Lesson: Adding 2-Digit Numbers

How to Add or Subtract Multiples of 10

When we add 10 to a number using the number grid, we move one place down and when we subtract 10 from a number, we move one place up.

In this lesson, we will look at adding and subtracting multiples of 10 using the number grid.

10 times table or multiples of ten poster

Above are the first nine multiples of 10.

We can see that: 10 is 1 lot of 10

20 is 2 lots of 10

30 is 3 lots of 10

40 is 4 lots of 10

50 is 5 lots of 10

60 is 6 lots of 10

70 is 7 lots of 10

80 is 8 lots of 10

90 is 9 lots of 10

This tells us how many places we move up or down the number grid.

For example, if we are adding 40, we move 4 places down the number grid, or if we are subtracting 50, we move 5 places up the number grid.

Here is an example of addition using the number grid:

adding 30 to 24 on the number grid

We are asked: what is 24 + 30?

When we add 10, we move 1 place down the number grid.

30 is 3 lots of 10, so we move 3 places down the number grid.

24 + 30 = 54 shown on the number grid

We start at 24 and we move 3 places down the number grid.

We stop at 54. Therefore,

24 + 30 = 54.

Here is an example of subtraction using the number grid:

82 - 60 shown on the number grid

We are asked: what is 82 – 60?

When we subtract 10, we move 1 place up the number grid.

60 is 6 lots of 10, so we move 6 places up the number grid.

82 - 60 = 22 shown on the number grid

We start at 82 and we move 6 places up the number grid.

We stop at 22. Therefore,

82 – 60 = 22.

Inverse Operations: Addition and Subtraction

Inverse Operations: Multiplication and Division

The Inverse of Addition is Subtraction

subtraction is the inverse of addition example of 10 + 5 = 15

In maths, inverse means opposite.

Subtraction is the inverse of addition, which means that subtraction “undoes” addition.

We can rearrange the numbers in an addition sentence to make two different subtraction sentences.

10 + 5 = 15 can be written as 15 – 10 = 5 or 15 – 5 = 10.

The answer to an addition can be written at the start of a subtraction sentence.

The two numbers that are added together in an addition go after the subtraction sign and after the equals sign in either order.

If you know an addition, then you can simply use this rule to rearrange the numbers to form a subtraction.

The Inverse of Subtraction is Addition

the inverse of subtraction is addition example of 10 - 6 = 4

Addition is the inverse of addition, which means that addition “undoes” subtraction.

We can rearrange the numbers in a subtraction sentence to make two different addition sentences.

10 – 6 = 4 can be written as 6 + 4 = 10 or 4 + 6 = 10.

The number at the start of a subtraction that we are subtracting from becomes the answer of an addition sentence.

The two other numbers in the subtraction are the two numbers that get added together in an addition sentence.

If you know a subtraction, then you can simply use this rule to rearrange the numbers to form an addition.

Addition and subtraction are inverse operations.

The numbers can be rearranged in an addition to form a subtraction and vice versa.

example of inverse operations writing an addition as a subtraction

We will use inverse operations to write the addition of 25 + 8 = 33 as a subtration.

If you know an addition fact, there is no need to do any calculations, simply rearrange the numbers to write it as a subtraction.

To write an addition as a subtraction, write the answer of the addition at the start of the subtraction.

33 is the answer to the addition and so, we write the 33 at the start of the subtraction.

The two numbers being added together in an addition are then placed after the subtraction sign and the equals sign in any order.

The two numbers being added together are 25 and 8.

We can write the 25 after the subtraction sign and the 8 after the equals sign.

25 + 8 = 33 can be written as 33 – 25 = 8.

We can also write 25 + 8 = 33 as 33 – 8 = 25.

Supporting Lessons

Number Bonds to Ten

Writing Additions as Subtractions

Writing Additions as Subtractions: Further Examples

Writing Subtractions as Additions

Writing Subtractions as Additions; Further Examples

Inverse Operations of Addition and Subtraction

What is the Inverse of Addition?

The inverse of addition is subtraction. This means that subtraction is the opposite of addition. Adding and subtracting the same number cancel each other out. For example, adding 2 and then subtracting 2 results in no change to the original number.

Subtraction is the inverse of addition.

addition is the inverse of subtraction

An inverse operation is a calculation which has the effect of ‘undoing’ another calculation.

Here is the addition of 10 + 2 = 12.

rewriting the addition number sentence of 10 + 2 = 12 written as a subtraction number sentence using inverse operations

We started with the number 10 and added 2 to it to get 12.

We can subtract 2 from 12 to get back to 10.

the addition sentence 10 + 2 = 12 written as the subtraction 12 - 2 = 10 using inverse operations

Adding and subtracting 2 have the effect of cancelling each other out. We started with 10 and after adding 2 and then subtracting 2, we ended up back at 10.

Adding and subtracting the same number have the effect of cancelling each other out. They are inverse operations. This is true only if the number being subtracted is the same as the number being added.

How to Write Addition as Subtraction

To write an addition as subtraction, follow these steps:

Write the answer of the addition as the number at the start of the subtraction, before the subtraction sign.

Write the two numbers being added in the addition after the subtraction sign and the equals sign of the subtraction sentence in either order.

For example, here is 10 + 5 = 15. We will write this addition sentence as a subtraction sentence.

how to write addition as subtraction 10 + 5 = 15

Step 1 is to write the answer of the addition as the number at the start of the subtraction, before the subtraction sign.

The answer of the addition in 10 + 5 = 15 is the number 15. We write this number first, before the subtraction sign.

Step 2 is to write the two numbers being added in the addition after the subtraction sign and the equals sign of the subtraction sentence in either order.

The two numbers being added in the addition are 10 and 5.

We write these numbers after the subtraction sign and the equals sign in either order.

For every addition sentence, we can write two different subtraction sentences.

10 + 5 = 15 can be written as 15 – 10 = 5 or 15 – 5 = 10. The numbers of 5 and 10 can be written in either order to make two different subtractions.

A subtraction sentence can be written by simply rearranging the numbers in an addition sentence. If the numbers in the addition sentence are known, there is no need to do any calculations to turn it into a subtraction. Simply rearrange the numbers.

For example, here is the addition of 39 + 26 = 65.

The subtraction sentence can be written without any need to do a calculation.

The first step is to write the answer to the addition as the first number of the subtraction, before the subtraction sign.

We write 65 at the start of the subtraction.

how to write an addition as a subtraction example

The second step is to write the two numbers being added after the subtraction sign and after the equals sign respectively.

We write 39 after the subtraction sign and 26 after the equals sign.

39 + 26 = 65 can be rewritten as a subtraction as 65 – 39 = 26.

The numbers of 39 and 26 can be switched to create the second subtraction sentence.

writing an addition as a subtraction sentence example of 39 + 26 = 65

39 + 26 = 65 can be rewritten as a subtraction as 65 – 26 = 39.

We did perform any calculations to write these subtractions. We simply rearranged the numbers in the known addition sentence that we were given.

two alternative subtraction sentences

When teaching the writing of subtraction sentences from addition sentences, it is important to show the two different subtractions that can be made, comparing the positions of the numbers.

What is the Inverse of Subtraction?

The inverse of subtraction is addition. This means that subtraction is the opposite of addition. Subtracting and adding the same number have the effect of cancelling each other out. For example, subtracting 5 and adding 5 to a number does not change the size of that number.

inverse means opposite and the inverse operation of addition is subtraction

Here is 10 – 2 = 8.

We started with 10 and subtracted 2 to get to 8.

10 - 2 = 8

The opposite of subtracting 2 is to add 2.

We can add 2 to 8 to get back to 10.

10 -2 = 8 as an addition 8 + 2 = 10

Subtracting 2 and adding 2 are inverse operations. We started at 10 and when we subtracted 2 and then added 2, we arrived back at 10.

Subtracting and adding the same number are inverse operations.

How to Write Subtraction as Addition

To write a subtraction as an addition, follow these steps:

Write the number before the subtraction sign as the answer at the end of the addition, after the equals sign.

Write the other two numbers in the subtraction as the two numbers added together, either side of the addition sign.

For example, here is the subtraction of 20 – 5 = 15. We will use the steps shown to write it as an addition.

The first step is to write the number before the subtraction sign as the answer at the end of the addition, after the equals sign.

The number before the subtraction sign is 20. We will write this as the answer of our addition.

how to write a subtraction as an addition example of 20 - 5 = 15

The second step is to write the other two numbers in the subtraction as the two numbers added together, either side of the addition sign.

The other two numbers are 5 and 15. We write this on either side of the addition sign.

The subtraction of 20 – 5 = 15 can be rewritten as an addition as 5 + 15 = 20.

The numbers of 5 and 15 can be written in the other order to create another addition sentence.

writing a subtraction as an addition

The subtraction of 20 – 5 = 15 can be rewritten as an addition as 15 + 5 = 20.

two different addition sentences 5 + 15 = 20 and 15 + 5 = 20

It does not matter how large the numbers are in the addition or subtraction because there is no need to perform any calculations if the original subtraction sentence is known. We simply need to rearrange the numbers

For example, here is 53 – 17 = 36. We will rearrange the numbers to form two different addition sentences.

The first step is to write the number at the start of the subtraction at the end of the addition sentence after the equals sign.

We write 53 as the answer to the addition.

example of rewriting a subtraction as an addition 53 - 17 = 36

The other two numbers in the subtraction are written either side of the addition sign in the addition sentence.

The subtraction of 53 – 17 = 36 is written as an addition as 17 + 36 = 53.

We can switch the places of these these two numbers to create another addition sentence.

subtraction and addition are inverse operations example

The subtraction of 53 – 17 = 36 is written as an addition as 36 + 17 = 53.

two different addition sentences for 36 + 17 = 53 and 17 + 36 = 53

Now try our lesson on Inverse Operations: Multiplication and Division where we learn the relationship between multiplication and division.

multiplication and division inverse

Converting Decimals to Percentages

How to write a decimal as a percentage

The percentage sign is %.

‘Per’ means ‘divide’ and ‘cent’ means ‘100’.

25% means 25 divided by 100.

25 ÷ 100 = 0.25 and so, 25% is the same as 0.25.

A percentage is simply another way to write a decimal number.

0.25 and 25% are the same number.

To write 0.25 as a percentage, multiply it by 100 and write the % sign afterwards.

0.25 × 100 = 25 and so, 0.25 is 25%

how to multiply 25 by 100

To multiply a decimal by 100, simply move each digit two places left while keeping the decimal point still.

We can see this method above.

It can be easier to move the decimal point two places right such as in the method below.

This method may be easier as we only move the one point rather than moving every digit.

multipying the decimal 0.25 by 100 by moving the decimal point

To write a decimal as a percentage, multiply it by 100 and write the percentage sign, %.

writing the decimal 0.43 as a percentage 43%

To write 0.43 as a percentage, we multiply it by 100 and put a % sign afterwards.

0.43 × 100 = 43.

We can work this out by moving the decimal point two places right.

We write the percentage sign afterwards to show that it is a percentage.

0.43 is the same as 43%.

We can see that we removed the 0 from the front of 0.43 when we multiplied it by 100.

This is because we don’t write zeros in front of whole numbers.

We write 43% rather than 043%.

Supporting Lessons

Writing Decimals as Percentages: Interactive Activity

Converting Decimals to Percentages Worksheets and Answers

converting decimals to percents worksheet pdf

converting decimals to percents worksheet anwers pdf

Converting Fractions to Decimals

Converting Decimals to Percentages

How to Write a Decimal as a Percent

To write a decimal number as a percentage, multiply it by 100 and then write a % sign afterwards.

To multiply a decimal by 100, use one of the following two methods:

Move each digit in the number two places to the left, keeping the decimal point in place.
Or alternatively, move the decimal point two places to the right.

Both methods multiply by 100 by multiplying the number by ten and then multiplying it by 10 again.

This is because 10 × 10 = 100.

For example, to write the decimal 0.43 as a percentage, we multiply 0.43 by 100 to get 43 and then write a percentage sign afterwards.

0.43 = 43%

converting the decimal 0.43 into a percentage by multiplying by 100 to get 43%

We can work out the calculation of 0.43 × 100 using either of the two methods.

In the first method, we keep the decimal point in the same place and move each digit in the number two places to the left.

converting 0.43 to a percentage as 43%

We move the 4 into the tens column and the 3 into the units column.

0.43 = 43%

Notice that the 0 at the beginning of 0.43 has been removed because we do not write zeros at the start of whole numbers. We write 43%, not 043%. Otherwise, the digits in 0.43 are in the same order as in 43%.

Moving each digit is a longer process than simply moving the decimal point instead.

When introducing multiplying by 100, it is best to teach it using the method above, as we can see the numbers getting larger.

However, once this process is understood, the most efficient method to teach is the method below, where we only move the decimal point.

Moving the decimal point two places right has the same effect as moving each digit two places left. It is easier to do mentally because we are only moving a single point rather than moving each digit.

Decimal to Percentage by moving the decimal point in 0.43

Again, moving the decimal point two places right, we can see that

0.43 = 43%

We can see that:

A decimal number that has two non-zero decimal digits is written as a percentage by writing both non-zero digits in front of the % sign.

We simply wrote the 4 and the 3 in 0.43 as 43%.

However, it is important to multiply smaller decimals by 100 carefully.

For example, below is the decimal 0.09.

0.09 multiplied by 100 is 9.

0.09 = 9%

converting 0.09 into a percentage by multiplying by 100 to get 9%

Remember to multiply by 100, we move each digit in the number two places left, whilst keeping the decimal point fixed in place.

The 9 moves from the hundredths column into the tenths column and then into the units colum.

We move from 0.09 to 0.9 to 9.

multiplying 0.09 by 100 to get 9 when converting decimals to percentages

0.09 = 9%

We can see that the digit in the hundredths column is the percentage in this example.

Here is another example of converting decimals to percentages.

Here we have 0.2.

To convert a decimal into a percentage, multiply it by 100 and write a percentage sign after it.

The decimal 0.2 written as a percentage is 20%

converting 0.2 into a percentage by multiplying by 100 to get 20%

We multiply 0.2 by 100 by moving each digit two places left and keeping the decimal point fixed in place.

The 2 is the only non-zero digit and so, it is the digit we move.

The 2 moves from the tenths column into the units column and then into the tens column.

We go from 0.2 to 2 to 20.

Converting the decimal 0.2 into the percentage 20%

We can see that once we move from 0.2 to 2 to 20, we have to put a zero after the 2 to turn it into 20.

To multiply by 100, we multiply by 10 and then 10 again. We move the 2 two places to do this.

Teaching Converting Decimals to Percentages

When teaching decimals to percentages, it is first important to understand what a percentage is and secondly, to understand how to multiply by 10 and 100.

If these concepts are understood well, then we can use shortcuts to help us multiply by 100.

We can see that 0.25 has a 2 in the tenths column and a 5 in the hundredths column.

0.25 shown in its place value columns

The digits to the right of the decimal point represent numbers that are smaller than 1.

0.25 is 25 hundredths because the 5 is in the hundredths column.

0.25 is the same as ²⁵ / ₁₀₀

$0.25 shown in its place value columns and as a fraction out of 100$

This fraction is 25 out of 100.

Instead of writing 25 out of 100, we can use the word ‘percent’ to replace ‘out of 100’.

‘Per’ means out of and ‘cent’ means ‘100’.

25 out of 100 can be written as 25 percent and we can even shorten this further by using the percent sign, %, to mean percent.

0.25 is 25 percent, which can be written as 25%.

0.25 is 25 out of 100 or 25%

25% is said as 25 percent, which means 25 out of 100 parts.

Converting decimals to percentages example of 25%

It can be helpful to introduce decimals and percentages using a place value grid but it is a slow procedure to do.

We can see that we simply multiply 0.25 by 100 to get the answer of 25%.

Once place value is well understood, we can teach converting decimals to percentages by simply multiplying by 100.

converting 0.25 into a percentage by multiplying by 100 to get 25%

We can easily see the comparison between the digits of 2 and 5 in 0.25 and 25%.

comparing decimals to percents

When first teaching multiplying by 100, we show the digits getting larger on a place value grid.

When multiplying by 100, the digits get larger and the decimal point does not actually move.

100 is the same as 10 × 10.

To multiply by 100, we multiply by 10 and then multiply by 10 again.

Each time we multiply by 10, we move each digit one place left on the place value grid.

To multiply by 100, move each non-zero digit separately two places to the left.

converting the decimal 0.25 into a percentage of 25%

0.25 becomes 2.5 when we multiply it by 10 and then it becomes 25 when we multiply by 10 again.

However, we can see that it can be quicker to move the decimal point two places right instead of moving every digit two places left.

Whilst the decimal point does not actually ever move, this is a trick that we can use as it will give us the correct answer.

It is easier to move the decimal point rather than every digit because we only need to move one point. This makes this method the quickest and easiest method to use as well as being the best mental method to use.

multiplying by 100 on a place value grid to write 0.25 as a percentage

Now try our lesson on Converting Fractions to Decimals where we learn how to write a fraction as a decimal.

$writing fractions as decimals example of 3 tenths$

Multiplication by Partitioning

Multiplication by Partitioning method example of partitioning 14 into tens and units then multiplying

In maths, partitioning means that we will split a number into smaller numbers, such as its tens and units.

We can partition 14 into 10 + 4.

14 multiplied by 5 is the same as multiplying 10 and 4 by 5 separately and then adding the answers together.

10 multiplied by 5 is 50.

4 multiplied by 5 is 20.

We add 40 and 20 to make 70.

Therefore 14 multiplied by 5 is 70.

We partition our number into tens and units. We then multiply these values separately and add the values at the end.

Multiplication by Partitioning method Example

We have 27 multiplied by 6.

We can partition 27 into 20 + 7.

20 x 6 = 120.

7 x 6 = 42.

120 + 42 = 162.

Therefore 27 x 6 = 162.

Supporting Lessons

Multiplication by Partitioning: Interactive Question Generator

Multiplication by Partitioning Worksheets and Answers

multiplication by partitioning worksheet and answers

Grid Method of Multiplication

What is the Multiplication by Partitioning Method?

The multiplication by partitioning method is a multiplication strategy that may be taught in primary schools to help work out larger multiplication calculations.

Multiplication by partitioning involves breaking a number into the values of its

, which we multiply separately and then add at the end.

In maths, partitioning means to break a larger number down into the sum of two or more numbers added together.

The most common way to partition numbers is to break them down into their hundreds, tens and units. We partition a number into the values of its individual digits.

This method is the most common multiplication strategy that we would teach a child to use to multiply a larger number

Here is an example of using the multiplication by partitioning method:

we will multiply 14 x 5 using the multiplication by partitioning method

To multiply 14 by 5, we could begin by partitioning 14. We partition our larger,

14 x 5 multiplied by partitioning 14 into 10 and 4

The digits in ’14’ represent ‘1’ ten and ‘4’ units.

Therefore, 14 can be partitioned into 10 + 4.

Our method is to then multiply 5 by 10 and then multiply 5 by 4.

We multiply our partitioned parts separately.

14 x 5 approached by partitioning 14 into 10 and 4

We begin by multiplying 10 by 5.

14 x 5 multiplied by partitioning 14 into 10 and 4 and 10 x 5 = 50

5 x 10 = 50

an example of 14 x 5 multiplied by partitioning method 14 into 10 and 4 and 10 x 5 = 50

Next, we multiply 5 by 4.

14 x 5 = 70 approached by partitioning 14 into 10 and 4 and 10 x 5 = 50

5 x 4 = 20

Now that we have multiplied the parts separately, we must add the answers together.

14 x 5 = 70 approached by partitioning 14 into 10 and 4 and 10 x 5 = 50

50 + 20 = 70

Therefore,

14 x 5 = 70.

The method of partitioning works because 10 lots of 5 plus 4 lots of 5 is the same as 14 lots of 5.

Here’s another example of using this method:

27 x 6

To multiply 27 by 6, we can begin by partitioning 27.

27 x 6 with 27 partitioned into 20 + 7

27 can be partitioned into 20 and 7.

We want to find 27 lots of 6 and we know that we can make 27 lots of 6 by adding 20 lots of 6 to 7 lots of 6.

We will therefore multiply 6 by both 20 and 7 separately.

We will find 6 x 20 and then 6 x 7.

27 x 6 with 27 partitioned into 20 + 7

We begin by multiplying 6 by 20.

27 x 6 with 27 partitioned into 20 + 7 and 20 x 6 = 120 shown

6 x 2 = 12

Therefore,

6 x 20 = 120

We can just multiply the digit ‘2’ by 6 and then times this by ten afterwards. When teaching this process, it is always easiest to multiply by the digit in the tens column using times tables and then multiply this by 10 afterwards.

27 x 6 with 27 partitioned into 20 + 7 and 20 x 6 = 120 shown

Next, we multiply 6 by 7.

example of multiplication by partitioning with 27 x 6 with 27 partitioned into 20 + 7 and 7 x 6 = 42 shown

6 x 7 = 42

example of multiplication by partitioning with 27 x 6 = 162 with 27 partitioned into 20 + 7

Now that we have multiplied the parts separately, we must add the answers together.

120 + 42 = 162

Therefore,

27 x 6 = 162.

We found 27 lots of 6 by finding 20 lots of 6, 7 lots of 6 and then adding them together.

When teaching the multiplication by partitioning strategy, you should write down the result of the two multiplications and these values can be added with column addition.

However this method does lend itself to mental multiplication since there is unlikely to be much

involved when adding the numbers.

Now try our lesson on Grid Method of Multiplication where we learn another multiplication strategy, the grid method.

grid method of multiplication

Partitioning Numbers into Hundreds, Tens and Units

Partitioning a number into hundreds, tens and units example of 285

Partitioning a number is splitting it up into the sum of smaller numbers.

Partitioning a number into its hundreds, tens and units will separate the number into the values represented by each digit.

The ‘2’ in 285 represents 200.

The ‘8’ in 285 represents 80.

The ‘5’ is in the ones column and is just worth 5.

We write the larger number in expanded form as a sum of the partitioned values.

285 = 200 + 80 + 5.

Writing a number in expanded form means to write the number as the sum of the values of each digit.

We write the number as the sum of the values represented by each digit.

example of partitioning a number into hundreds, tens and units in expanded form

We will partition the number 574 into its hundreds, tens and units and write it in expanded form.

The ‘4’ in in the units (or ones) column and is just worth 4.

The ‘7’ is in the tens column and so, 7 tens are worth 70.

The ‘5’ is in the hundreds column and 5 hundreds are worth 500.

574 is written in expanded form as 500 + 70 + 4.

We have partitioned the larger number into the sum of its hundreds, tens and ones.

Supporting Lessons

Partitioning Numbers Worksheets and Answers

partitioning numbers into tens and units worksheet pdf

Partitioning Numbers Interactive Arrow Cards

Partitioning Arrow Cards (2-Digit Numbers): Interactive Questions

Partitioning Arrow Cards (3-Digit Numbers): Interactive Questions

Partitioning Numbers into Hundreds, Tens and Units and Writing them in Expanded Form

Partitioning a number means to write it as the sum of smaller numbers.

Partitioning is an important method because breaking down larger numbers into smaller numbers means that they are easier to work with when performing calculations.

To partition a number into its hundreds, tens and units, we write the number as the sum of the values of its digits.

Writing a number in expanded form means to write the number as the sum of the values of its digits.

We will start by looking at an example of partitioning a number with only 2 digits.

The number 12 has 2 digits which are ‘1’ in the tens column and ‘2’ in the units column.

The ‘1’ ten is worth 10 and the ‘2’ units are just worth 2.

Partitioning 12 into tens and units 10 plus 2 in expanded form

12 can be partitioned into its tens and units as 10 + 2.

10 is the value of the digit ‘1’ and 2 is the value of the digit ‘2’. Writing a number as the sum of the value of its digits is called writing the number in expanded form.

writing 12 in expanded form by partitioning it into its tens and units

We will now partition the number of 25 into its tens and units, writing it in expanded form.

The digit of ‘5’ is in the units column as it is the rightmost digit. It is just worth 5.

The digit of ‘2’ is in the tens column. 2 tens are worth 20.

We can also see that the ‘2’ in 25 is worth 20 by writing 25 with a zero in the place of the 5.

Partitioning 25 into tens and units and writing it in expanded form s 20 + 5

We can write 25 in expanded form as 20 + 5.

We can write 25 = 20 + 5. partitoning a number into tens and ones example of 25 = 20 + 5

Here is another example of partitioning into tens and ones.

Example of partitioning 48 into 40 + 8

48 contains two digits, which are a ‘4’ in the tens column and an ‘8’ in the ones column.

4 tens are worth 40 and 8 ones are worth 8.

48 = 40 + 8

We have partitioned 48 its expanded form notation.

example of writing a number in expanded form notation

We will now partition 93 into its tens and units.

Partitioning a two digit number 93 into tens and units in expanded form

9 tens are worth 90 and 3 units are worth 3.

We can partition 93 into its tens and units and write it in expanded form as:

93 = 90 + 3

partitioning a 2-digit number into tens and units example

We have looked at partitioning two-digit numbers into tens and units.

We will now look at partitioning three-digit numbers into their hundreds, tens and units.

The first example of partitioning a 3-digit number will be to partition the number 123.

The ‘1’ in 123 is in the hundreds column and 1 hundred is worth 100.

The ‘2’ in the tens column is worth 2 tens, which is 20.

The’3′ is in the ones column and so it is just worth 3.

Partitioning a number into hundreds tens and units

We write the number in expanded form as the sum of the values of these digits above.

123 = 100 + 20 + 3

example of writing a three digit number in expanded form

The digit of ‘1’ in 123 is worth 100 and this can be seen by replacing the other digits after the ‘1’ in 123 with zeros.

The digit of ‘2’ is worth 20 and this can be seen by replacing the digit after ‘2’ in 123 with a zero.

Here is another example of writing a three-digit number in expanded form using the partitioning method.

We will partition 286 into hundreds, tens and units.

Partitioning 286 into its hundreds tens and units place value digits

The digit of ‘2’ in 286 is in the hundreds column.

2 hundreds = 200.

The digit of ‘8’ in 286 is in the tens column.

8 tens = 80.

The digit of ‘6’ in 286 is in the units column.

6 units = 6.

example of partitioning 286 into expanded form writing it as a sum of its hundreds tens and units

We will partition the 3-digit number of 574 into expanded form as the sum of its hundreds, tens and units.

Partitioning 574 into its hundred tens and units

The digit of ‘5’ is worth 500.

The digit of ‘7’ is worth 70.

The digit of ‘4’ is just worth 4.

writing the number of 574 in expanded form using the partitioning method

In expanded form, 574 = 500 + 70 + 4.

It has been partitioned into the hundreds, tens and units place value columns.

In this next example we look at the number 305.

305 is a three-digit number which has the three digits of ‘3’, ‘0’ and ‘5’.

The ‘3’ is in the hundreds column and is worth 300.

The ‘0’ is in the tens column and is worth 0.

The ‘5’ is in the ones column and so is worth 5.

In this example we have a ‘0’ in the tens and because this digit holds no value, we do not write it.

Partitioning 305 into expanded form as 300 + 5

We partition 305 into the sum of 300 and 5.

We do not write the tens column in this sum because it is worth zero. We simply skip it.

In expanded form we can write:

305 = 300 + 5

We do not write 300 + 0 + 5 as there is no need to write the tens place value column in this example.

We never include digits with a ‘0’ in our expanded form answer.

writing 305 = 300 + 5 having partitioned it into hundreds and units

When teaching partitioning it can be useful to use partitioning arrow cards to help visualise the value of each digit.

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

Multiplication by Partitioning

multiplication by partitioning

Division with Remainders as Fractions

Division with Remainders as Fractions Interactive Question Generator

$how to write remainders as fractions in division$

The remainder is the amount left over after a division has shared an amount equally.

Here we are sharing 5 carrots between 2 people with the division 5 ÷ 2.

The people get 2 carrots each with 1 remaining.

We can write 5 ÷ 2 = 2 remainder 1.

We can divide this remainder of 1 by 2 to share it equally.

1 ÷ 2 is written as as a fraction as ¹ / ₂ .

The two people each get 2 ¹ / ₂ carrots each.

5 ÷ 2 = 2 ¹ / ₂ .

$writing remainders as a fraction. 1 divided by 2 or one half.$

The remainder is written as the numerator of the fraction and the denominator is the number we are dividing by.

$Short Division writing remainders as fractons example of 465 divided by 2$

465 ÷ 2 is set out with the short division method.

4 ÷ 2 = 2 and so we write 2 above.

6 ÷ 2 = 3 and so we write 3 above.

5 ÷ 2 = 2 remainder 1.

This is because 2 goes into 5 twice with 1 left over to get from 4 to 5.

The remainder of 1 is now divided by 2 as well.

We write 1 ÷ 2 as a fraction as ¹ / ₂

465 ÷ 2 = 132 ¹ / ₂

Supporting Lessons

Division with Remainders as Fractions Interactive Questions

Division with Remainders as Fractions Worksheets and Answers

$division with remainders as fractions worksheet pdf$

$division with remainders as fractions worksheet answers pdf$

Short Division with Decimal Remainders

Division with Remainders Written as Fractions

Remainders as Fractions

A remainder is the number left over after a division. It has not been divided.

To write a remainder as a fraction, divide it by the number being divided by. The remainder becomes the numerator, on top of the fraction and the number being divided by becomes the denominator on the bottom of the fraction.

In this example below, we have 5 ÷ 2. We are sharing 5 carrots between 2 people.

We can give each person 2 carrots with one left over as a remainder.

We can write 5 ÷ 2 = 2 r1.

$How to write remainders as fractions in short division$

However we can divide this remainder by 2 and give half to each person. They each have 2 ¹ / ₂ .

We can write the remainder of 1 as a fraction.

5 ÷ 2 = 2 ¹ / ₂ .

The remainder was 1 and we were dividing by 2. We wrote the remainder of 1 on top of the fraction and the 2 on the bottom of the fraction.

one half shown as 1 divided by 2 in short division with remainders

The horizontal line that separates the numbers in a fraction is a division.

So, the fraction ¹⁄₂ means 1 divided by 2.

Short Division Method with Remainders as Fractions

Here is an example of using the short division method. We have 465 ÷ 2.

465 divided by 2 shown as a short division

We set out the short division calculation as shown above. We want to divide each digit in 465 by 2.

We work from left to right, starting with the 4.

4 ÷ 2 = 2

We write the 2 above the 4.

465 divided by 2 using the short division method

6 ÷ 2 = 3

We write the 3 above the 6 in our division.

465 divided by 2 shown as a short division

2 divides into 5 twice, with 1 left over.

We write the 2 above the 5. There is a remainder of 1.

465 divided by 2 = 232 remainder 1 shown as a short division

We are going to write this remainder as a fraction.

To write a remainder as a fraction it is written as the numerator, with the number we are dividing by written below it as the denominator.

We have ¹ / ₂ .

465 divided by 2 = 232 and a half shown as a short division

Therefore,

465 ÷ 2 = 232 ¹ / ₂ .

example question of short division with Remainders as Fractions 465 divided by 2

Here is another example of using the short division method, writing the remainder as a fraction:

We have 517 ÷ 3.

517 divided by 3 shown as a short division with a remainder

We set out the short division calculation as shown above. We want to divide each digit in 517 by 3.

We work from left to right, starting with the 5.

3 divides into 5 once, with 2 left over.

517 divided by 3 shown as a short division

We write the 1 above the 5 and we carry the 2 to meet the next digit along.

We now have 21 ÷ 3.

21 ÷ 3 = 7

We write the 7 above the 21.

517 divided by 3 shown as a short division

3 divides into 7 twice, with 1 left over. We write the 2 above the 7.

517 divided by 3 = 172 remainder 1 shown as a short division

We have a remainder of 1, which we want to write as a fraction.

We divide the 1 by 3.

The fraction is ¹ / ₃ .

517 divided by 3 = 172 and a third shown as a short division

Therefore,

517 ÷ 3 = 172 ¹ ⁄ ₃ .

Short Division Remainder written as a Fraction example of 517 divided by 3

In this next example we have 854 ÷ 4.

4 divides exactly twice into 8 and so, we write a 2 above 8.

5 ÷ 4 = 1 r1 so we carry the remainder of 1 over to meet the 4.

14 ÷ 4 = 3 remainder 2. This is because 4 times 3 equals 12.

$Example of 854 divided by 4 with the short division method writing the remainder as a fraction$

We divide this remainder of 2 by 4 and write it as a fraction as ² / ₄ .

² / ₄ can be simplified to ¹ / ₂ because 2 is half of 4; .

854 ÷ 4 = 213 r ¹ / ₂ .

In this next example of short division with fractional remainders we have 789 ÷ 5.

7 ÷ 5 = 1 r2 and so we carry the 2 over to the 8 to make ’28’.

28 ÷ 5 = 5 r3 because 5 times 5 equals 25. We carry the remainder of 3 over to make 39.

39 ÷ 5 = 7 r4 because 5 times 7 = 35.

$Short Division Remainders as fractions 789 divided by 5$

The remainder of 4 is written as a fraction by also dividing it by 5. As a fraction it is written ⁴ / ₅ .

And so 789 ÷ 5 = 157 ⁴ / ₅ .

Now try our lesson on Short Division with Decimal Remainders where we learn how to write remainders as decimals.

How to Calculate a Ratio of 3 Numbers

calculating a Ratio of 3 numbers Summary and example

There are three numbers in the ratio: ‘2’, ‘5’ and ‘3’. This means that the amount is shared between three people.

2 + 5 + 3 equals a total of 10 parts in the ratio.

To find the value of each part, we divide the amount of £20 by the total number of parts.

£20 ÷ 10 = £2.

Finally we multiply each of the three numbers in our ratio by the value of each part.

2:5:3 multiplied by £2 gives the final answer of £4:£10:£6.

The value of each part is found by dividing the given amount by the sum of the parts in the ratio.

We then multiply each number in the ratio by the value of each part.

calculating a ratio of three numbers example

We are sharing $48 between three people in the ratio 3:1:2.

The total number of parts in the ratio is 3 + 1 + 2 = 6 parts.

To find the value of each part in the ratio we divide $48 by the total number of parts.

$48 ÷ 6 = $8.

To find how much each person receives we multiply the ratio by the value of each part.

13:1:2 multiplied by $8 is $24:$8:$16.

The first person receives $24, the second person receives $8 and the third person receives $16.

Supporting Lessons

Calculating a Ratio of 3 Numbers: Interactive Questions

Sharing in a Ratio: Random Question Generator

Sharing in a Ratio of 3 Numbers: Worksheets and Answers

calculating a ratio of 3 numbers worksheet pdf

calculating a ratio of 3 numbers worksheet answers pdf