To divide a number by 1000 we move each digit in that number three place value columns to the right.

Dividing a whole number that ends in three zeros by 1000 has the same effect as removing the three zeros.

This trick only works for whole numbers that end in three zeros (or numbers that are multiples of 1000). Here is an example of dividing such a number by 1000.

In the example above, each digit in the number 9000 has been moved three places to the right.

The digit of ‘9’ in the thousands column moves into the units column.

When dividing by one thousand, any digit in the thousands column will always move into the units column to the left of the decimal point.

The ‘0’ in the hundreds column moves three places into the tenths column, immediately after the decimal point.

The ‘0’ in the tens column moves three places into the hundredths column.

Finally, the ‘0’ in the units column moves into the thousandths column.

So, 9000 becomes 9.000, which is the same as 9.

If a number only has the digit of ‘0’ after its decimal point, then it is a whole number and we do not write the zeros or the decimal point.

It is easier to write 9 than 9.000.

You may also know that when we divide a whole number ending in three zeros by 1000, that we can simply “remove the zeros” from the end of this number.

This trick will not work if we have a decimal number.

It is important to understand how dividing by 1000 works because not all numbers that we divide by 1000 will end in three zeros.

For example:

To divide 604 by 1000, we move each digit in 604 three places to the right.

We begin by moving the ‘6’ from the hundreds column three places to the right into the tenths column.

The ‘0’ and the ‘4’ will then follow the 6 in the same order. The ‘0’ moves from the tens column into the hundredths column and the ‘4’ moves from the units column into the thousandths column.

Because there are no longer any digits in the units column, we write in a zero.

And so, 604 ÷ 1000 = 0.604.

We always write a single ‘0’ digit in the units column before the decimal point if there is no other digit remaining to write there. It is not correct to start a number with a decimal point and so we write ‘0.604’ rather than ‘.604’. This avoids confusion in written text involving numbers. It avoids confusion between commas, full stops and decimal points.

A decimal point is small and sometimes not noticed. By including the zero before the decimal point, it helps to identify to the reader that there is likely to be a decimal point after the zero. This is because whole numbers do not start with a zero and the only way for a zero to be the first digit in a number is if it is a decimal number.

In the following example we are dividing a decimal number by 1000.

We begin by moving the digit of ‘1’ three places to the right. It moves from the tens column to the hundredths column. The 2 and the 8 will then follow. We move the 2 from the units column to the thousandths column and we move the 8 from the tenths column to the ten-thousandths column.

As there are no longer any digits in either the units column or the tenths column, we write a zero in each of these spaces.

Therefore, 12.8 ÷ 1000 = 0.0128

In the following example we are dividing a decimal number that is less than 1 by 1000.

To do this, we move the digit of ‘5’ three places to the right, from the tenths column to the ten-thousandths column.

Because there are no digits in either the tenths column, the hundredths column or the thousandths column, we write a zero in each of these columns to show that their values are zero.

Therefore, 0.5 ÷ 1000 = 0.0005.

To divide a number by 10 we move each digit in that number one place value column to the right.

If a number has a zero in its units column, then dividing this number by ten has the effect of removing this zero.

In the example above, each digit in the number 30 has been moved one place to the right. So, 30 becomes 3.0.

If the only digit after a decimal point of a number are zero then there is no need to write these zeros or the decimal point.

Instead of writing ‘3.0’, it is better to write ‘3’.

We also know from our times tables that 30 ÷ 10 = 3.

The number 30 is an example of a number that has a ‘0’ in its units column (or a number that ends in a zero).

We can see that if the number ends in a zero then dividing it by ten has the same effect as removing this zero digit.

30 became 3.

This is a trick that will only work for numbers with a zero in the units column.

It is important to understand how dividing by 10 works because not all numbers that we divide by 10 will end in a zero in their units column.

For example:

To divide 4 by 10, we move the 4 one place to the right. So, it moves from the units column into the tenths column. Because there is no longer a digit in the units column, we write in a zero.

Therefore 4 ÷ 10 = 0.4.

If there are no digits before the decimal point of a number, one zero digit it always written in the units column to show this.

It is important to make sure that when we are dividing a number with more than one significant digit that we move every digit one place to the right.

For example:

To divide 91 by 10, we move both digits one place to the right. We can move them one at a time to make sure that we don’t make any mistakes.

We start by moving the 9 from the tens column into the units column. The ‘1’ will then follow, remaining to the right of the ‘9’.

We move the ‘1’ from the units column into the tenths column. Therefore 91 ÷ 10 = 9.1.

We can see that the digits of ‘9’ and ‘1’ remain in this order, with the ‘9’ directly to the left of the ‘1’.

Now we will divide a decimal number by 10. For example:

In this example we still follow the same place value rules. Each digit in 4.6 must move one place to the right. We start by moving the 4 from the units column into the tenths column and then the 6 will follow.

The 6 is moved from the tenths column into the hundredths column.

4.6 divided by 10 is 0.46

Remember that because there are no digits in the units column or anywhere before the decimal point, we must write a single zero digit in the units column to show this.

We follow the same rules when dividing a decimal number that is less than 1 by 10.

For example:

We begin by moving the 7 one place to the right, from the tenths column into the hundredths column. The 2 will then follow. It moves from the hundredths column into the thousandths column.

As there are no digits in either the units column or the tenths column, we must make sure that we write zeros in here to show that their values are zero.

Alternatively, we can move the zero from the units column into the tenths column.

And so, 0.72 ÷ 10 = 0.072.

We always leave a single zero digit in the units column before the decimal point for numbers that have no more digits remaining before the decimal point.

We also put zeros between the decimal point and the first non-zero decimal digit.

We need to be more careful when dealing with numbers where there is a zero between two other digits.

For example:

We must make sure that we move every digit in 80.5 one place to the right, including the zero.

We move the 8 from the tens column into the units column, we move the 0 from the units column into the tenths column and we move the 5 from the tenths column into the hundredths column.

And so, 80.5 ÷ 10 = 8.05.

We can see that there are three digits ‘8’, ‘0’ and ‘5’ in this order in the original question.

We can see that these three digits remain in this order, immediately next to each other in the answer as well.

When teaching dividing by ten, it is worth making sure that the answer is sensible by comparing it to an easier example.

In this example we know that 80 divided by 10 is 8 and so we know that when we divide 80.5 by 10, we will have an 8 in the units column as well.

The digits of ‘0’ and ‘5’ will then follow the ‘8’.

Number bonds to 20 are the pairs of numbers that add together to make twenty.

There are ten number bonds to 20, which are:

• 1 + 19
• 2 + 18
• 3 + 17
• 4 + 16
• 5 + 15
• 6 + 14
• 7 + 13
• 8 + 12
• 9 + 11
• 10 + 10

To learn the number bonds to 20, learn the number bonds to ten and add a 10 to one of the numbers in the pair.

It helps to remember the pairs of digits that make a ten, which are 1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5.

Below is the full display list of the number bonds to 20.

We can see that the order of the numbers being added does not matter.

For example: 2 + 18 and 18 + 2 are the same numbers just in a different order. When teaching number bonds to 20, it is important to point this out to children who may not otherwise consciously think of this.

It is easier to memorise the pair of numbers in the sum than memorising the two sums with the numbers in a different order. Instead of remembering both 3 + 17 and 17 + 3, just focus on remembering that 3 and 17 go together.

We can show the number bonds to 20 with a visual aid in the form of counters or cubes. This is a useful practical activity for introducing the number bonds and showing the number size and decomposition.

Number bonds are typically taught to children from kindergarten to first grade (KS1). When teaching number bonds to 20, it is first important to teach the number bonds to 10. The number bonds to 20 are very similar to the number bonds to 10.

The pairs of numbers that add to make 10 are:

• 1 and 9
• 2 and 8
• 3 and 7
• 4 and 6
• 5 and 5

This is only 5 pairs of numbers. If we remember these, then we can remember the number bonds to 20.

We simply put a ‘1’ tens digit in front of one of the numbers in each pair. This is because the number bonds to 20 are just 10 larger than the number bonds to 10.

Below we can see the number bonds to 20 compared to the number bonds to 10.

Removing the ‘1’ tens digit from the number bonds to 20, we can see that we are left with the number bonds to 10.

Whilst visual aids are the best teaching tool for introducing the idea of number bonds, the best way to actually learn the number bonds to 20 is by first learning the number bonds to 10. We just add a ‘1’ tens digit to one of the numbers in the pair.

When teaching number bonds to 20, it is useful to point out the pattern of increasing and decreasing numbers.

As we increase one number by one, the number that pairs with it decreases by one.

This can help memorise and learn the number bonds to 20.

For example if we remember that 10 + 10 = 20, then we can increase the first number by 1 and decrease the second number by 1 to get another number bonds to 20. We get 11 + 9. We can continue to increase one number and decrease the other to get 12 + 8 and so on.

Number bonds require practise to learn and memorise. We recommend using our online number bonds to 20 activity to help learn them.

Alternatively, we have part part whole model worksheets. The part part whole teaching model is made up of three circles. The larger number goes in the largest circle and two smaller circles contain the two numbers that add to make this number.

Here are all of the number bonds to 20, shown as part part whole models.

The entire list of number bonds to 20 are shown as a display poster below.

If you are teaching number bonds to 20, please feel free to download and print this list.

To divide a number by 100, move each digit in that number two place value columns to the right.

If the number ends with two zero digits in the tens and units column, then dividing by 100 has the same effect as removing these two zero digits.

This trick only works for whole numbers that are in the 100 times table (ending in two zeros).

In the example above, we have 400 ÷ 100 = 4.

To divide a number by 100, move all of its digits two place value columns to the right.

The digit of ‘4’ moves from the hundreds column to the units column.

The digit of ‘0’ in the tens column moves to the tenths column, immediately after the decimal point.

The digit of ‘0’ in the units column moves to the hundredths column.

400 ÷ 100 is 4.00.

If a number only has zeros after its decimal point, then it is a whole number and there is no need to write these zeros.

It is better to write: 400 ÷ 100 = 4.

It can bee seen that we have simply “removed the two zeros”.

This trick only works for whole numbers that actually have two zeros in the tens an units columns to remove.

It is important to understand how dividing any number by 100 works because not all numbers that we divide by 100 will end in two zeros.

For example:

To divide 527 by 100, we move each digit in 527 two places to the right.

We start by moving the ‘5’ from the hundreds column two places along into the units column.

The ‘2’ and the ‘7’ will then follow the ‘5’.

The 2 moves from the tens column into the tenths column and the 7 moves from the units column into the hundredths column.

Each digit has moved two places to the right and therefore 527 ÷ 100 = 5.27.

If the number’s largest digit is in the hundreds column, then this digit will move to the units column when it is divided by 100.

The remaining digits to the right will then appear in the same order to the right of the decimal point.

So in this example, the ‘5’ is the digit to the left of the decimal point and then the ‘2’ and the ‘7’ will be in the same order, immediately after the decimal point.

In the following example we are given a number that is less than 100 and has only two digits. We still follow the same rules for dividing by 100 and move each digit two places to the right.

We begin by moving the ‘1’ two places to the right, from the tens column into the tenths column. The ‘9’ will then follow. We move it from the units column into the hundredths column.

Whenever there are no digits remaining to the left of the decimal point, a single ‘0’ digit is written in the units column.

Therefore, 19 ÷ 100 = 0.19.

We may be asked to divide a single-digit number by 100.

For example:

Although 6 has only one digit, we still follow the same rule for dividing by 100. We move the 6 two places to the right. It moves from the units column into the tenths column.

Because there is no longer a digit in the units column and there is a space in the tenths column, we write a zero in both columns to show that their values are zero.

Therefore 6 ÷ 100 = 0.06.

We need to be careful when dealing with numbers where there is a zero between two other non-zero digits.

For example:

To divide by 100, we must make sure that we move every digit in 30.2 two places to the right, including the zero. We move the 3 from the tens column into the tenths column, we move the zero from the units column into the hundredths column and we move the 2 from the tenths column into the thousandths column.

The digits remain in the same order. And so, 30.2 ÷ 100 = 0.302.

Number bonds to 10 are pairs of numbers that add together to equal 10.

The poster below shows the complete list of number bonds to 10.

Number bonds to 10 are usually one of the first set of number facts that are taught.

Number Bonds to 10 are usually taught to primary school children in their first or second year (KS1 or First Grade).

Number bonds are important for developing further skills such as addition and subtraction. Learning number bonds to 10 then lead on to learning number bonds to 20 and further number facts up to 100. Number bonds also help children to visualise the size of numbers.

It is important to teach number bonds to 10 visually, with practical activities when first introducing them. This can be done with counters as shown below.

Tens frames can be used as a guide to put the counters in. Tens frames are simple blank rectangles that are 2 by 5 in size.

To use a tens frame, simply shade in some of the boxes (or put counters in) and then see how many more filled boxes are required to fill the complete frame of 10.

For example, here is a tens frame already containing 2 counters.

It is used to work out which number bond pairs with 2 to make 10.

To use a tens frame, add a counter to each blank box and then count how many counters have been added.

8 more counters are needed to fill the frame.

When introducing the idea of number bonds, further practical activities can be used, such as multi-link cubes or dominoes.

It can help to give time to practise with physical models in order to develop a good understanding of how the number 10 can be broken down into different sums.

However to memorise number bonds to 10, we can see that there are only five pairs of numbers to remember.

The pairs of numbers that add to make 10 are:

• 1 and 9
• 2 and 8
• 3 and 7
• 4 and 6
• 5 and 5

Remembering 5 pairs of numbers is easier than remembering 10 separate addition facts.

For example: 1 + 9 contains the same pair of numbers as the number bond of 9 + 1.

We simply swap the positions of the two numbers.

When teaching number bonds to 10, it is useful to break it down into the task of remembering the 5 pairs of numbers that add to make 10.

If you remember one of the number bonds to 10, then you can use this to work out some of the others.

The pairs of numbers that add to make 10 are shown again below and we can see a pattern with the numbers.

As the first number increases from 1 to 5, the second number decreases from 9 to 5.

• 1 and 9
• 2 and 8
• 3 and 7
• 4 and 6
• 5 and 5

We can get to another number bond by adding 1 to one of the numbers and subtracting one from the other number.

For example if we remember 5 + 5 , then we can add 1 to one number and subtract 1 from the other to make 6 + 4.

If we remember 1 + 9, we can add 1 to the first number and subtract 1 from the second number to make 2 + 8.

In order to move swiftly on to learning the number bonds to 20 and further addition facts, it is important to know the number bonds to 10 with quick recall.

Part, part whole models are often used for practising number bonds to 10.

Part, part whole models contain 3 circles with a larger circle connected to two smaller circles.

The larger circle contains the number bond we are making, which in this case is 10.

One of the smaller circles contains one part of the number bond and the other smaller circle is blank, ready to be filled in.

We have part part whole model worksheets for download with which you can practise this.

Here are the complete set of number bonds to 10 shown with the part part whole model.

Games, competitions and quick tests are very useful ways to practise and we have Interactive Questions that you can use.

In this lesson we will be learning how to use the column subtraction method when we need to borrow from zero. These examples will be of column subtraction with zero in the middle of a three digit number.

We will look at how to calculate 604 – 328. Here we are subtracting from a three-digit number with zero in the middle.

We begin by lining up the digits in their place value columns. We want to subtract the digits in the units column. However, 8 is greater than 4, so we can’t.

We would normally borrow (regroup) from the tens column. However, we have a zero written here, which means that there aren’t any tens.

Therefore, before we can borrow some units from the tens, we need to borrow some tens from the hundreds column. We need to borrow from the 6 hundreds.

We move 1 hundred next to the zero to make 10 tens. We are left with 5 hundreds. This process is also known as regrouping.

Now that we have 10 tens, we can borrow some units from this column. We move 1 ten next to the 4 to make 14 units. We are now left with 9 tens in the tens column.

Now we can subtract the units.

14 – 8 = 6

Next, we subtract the tens.

9 – 2 = 7

Finally, we subtract the hundreds.

5 – 3 = 2

This is the process of three-digit subtraction borrowing from zero and the result is:

604 – 328 = 276.

We will look at how to calculate 346 – 178.

We begin by lining up the digits of each number in their place value columns. We start with the units column.

We want to subtract 8 from 6. However, 8 is greater than 6, so we can’t take it away.

We must therefore borrow some units from the tens column. We can borrow from the 4 tens.

We move 1 ten next to the 6. We have 16 units in total. We are left with 3 tens in the tens column.

We can now subtract the units.

16 – 8 = 8

Next, we look at the tens column.

We want to subtract the 7 from the 3. However, 7 is greater than 3, so we can’t.

We must therefore borrow from the hundreds column. We can borrow from the 3 hundreds.

We move 1 hundred next to the 3 in the tens column. This makes 13 in the tens column. We are left with 2 hundreds in the hundreds column.

We can now subtract the tens.

13 – 7 = 6

Finally, we look at the hundreds column.

Because we borrowed 1 hundred, we are left with 2 hundreds.

2 – 1 = 1

Therefore,

346 – 178 = 168.

In order to calculate the column subtraction of 592 – 226, we must begin by lining up the numbers so that their digits are in the correct place value columns.

We want to subtract 226, so this must be written below 592.

We begin with the units column. However, the 6 is larger than the 2, so we can’t subtract it without regrouping.

We must therefore borrow some units from the tens column. We can borrow from the 9 tens.

We regroup 1 ten to borrow and we carry it over into the units column, next to the 2. In total, we now have 12 units. This leaves us with 8 tens in the tens column.

Following this regrouping, we can now subtract the units.

12 – 6 = 6

Next, we look at the tens column.

Because we borrowed from the 9, we are now left with 8 tens.

8 – 2 = 6

Finally, we look at the hundreds column.

5 – 2 = 3

Therefore,

592 – 226 = 366.

Another column subtraction example that we will look at is 674 – 482.

Again, we line up the digits of each number according to their place value columns. We start by subtracting the digits in the units column.

4 – 2 = 2

Next, we look at the tens column.

The 8 is larger than the 7, so we can’t take it away without regrouping. We must therefore borrow from the 6 in the hundreds column.

We regroup 1 hundred for the tens column and write it next to the 7. This gives us 17 in the tens column. We are left with 5 in the hundreds column.

Following this borrowing, we can now subtract the tens column.

17 – 8 = 9

Finally, we look at the hundreds column.

Because we borrowed from the 6, we are now left with 5 hundreds.

5 – 4 = 1

Therefore,

674 – 482 = 192.

How to Convert a Percent to a Decimal

To convert a percent to a decimal, remove the percentage symbol and divide the number by 100. To divide by 100, move the decimal point 2 places to the left. For example, 92% as a decimal is 0.92.

Percent means to divide by 100.

This is because the word ‘per’ can mean ‘divide by’ and the word ‘cent’ means ‘100’. The percent symbol ‘%’ can mean ‘divide by 100’.

Here is an example of writing a percentage in decimal form. 92%, can be read to mean 92 ‘divided by 100’.

To divide a number by 100, we divide by 10 and then divide by 10 again.

When a number is divided by 10, the digits move one place value column to the right.

92 ÷ 10 = 9.2. We divide by 10 again.

9.2 ÷ 10 = 0.92. We write the 0 in front of the decimal point because there are no more digits. There is not a digit to put in the ones column, so we put a 0 to show this.

Dividing a number by 100 is the same as dividing it by 10 and then by 10 again.

When dividing a number by 100, the digits each moved 2 places right.

Rather than moving each of the digits, it is easier to move the decimal point the other way instead.

To divide by 100, simply move the decimal point to the left two places.

When teaching converting percents to decimals, it is easier to divide by 100 by moving the decimal point two places left instead of moving all of the digits two places right. Students are less likely to make a mistake if they only have the decimal point to move rather than every single digit. We can leave all the digits where they are and just focus on carefully moving the decimal point two places left.

92% written in decimal form is 0.92.

Here is another example of writing a percent in decimal form.

We will write 6% as a decimal number by removing the % sign and dividing by 100.

To divide by 100, move each digit two places to the right.

6 ÷ 10 = 0.6 and then 0.6 ÷ 10 = 0.06.

6 ÷ 100 = 0.06 and so, 6% as a decimal is 0.06.

Alternatively, we can divide 6 by 100 by moving the decimal point two places left.

The decimal point must move twice.

We move the decimal point once to go from 6. to .6 and now we need to move it once more.

We need to put a 0 in front of the 6 digit so that we can jump over that.

We go from 0.6 to .06 and we write a zero in front of the decimal point to get 0.06.

6 ÷ 100 = 0.06 and so 6% as a decimal is 0.06.

It is important to move the decimal point carefully when converting a percentage to a decimal.

It is a common mistake to write percentages such as 6% as 0.6 instead of 0.06. It is common to miss out the extra 0 after the decimal point.

When converting a single digit percentage to a decimal, there will always be a 0 between the decimal point and the digit. In general a% can be written as a decimal as 0.0a.

For example, 5% is 0.05, 3% is 0.03 and 9% is 0.09.

To converting a double digit percentage to a decimal, simply write the two digits immediately after the decimal point. In general ab% can be written as a decimal as 0.ab.

For example, 25% is 0.25, 37% is 0.37 and 99% is 0.99.

Converting a Decimal Percentage to a Decimal

No matter what the percentage is, divide it by 100 to write it as a decimal number. If the percentage is already a decimal number, then when it is written as a decimal, it will be 100 times smaller. For example 3.2% as a decimal is 0.032.

It is possible to have decimal percentages. For example 3.2%.

The rule remains the same. Remove the % sign and divide the number by 100.

To divide by 100, we divide by 10 twice.

3.2 ÷ 10 = 0.32 and then 0.32 ÷ 10 = 0.032.

3.2% is 0.032 as a decimal. Because the % sign has been removed, the number has now got 100 times smaller.

It can be easier to move the decimal point two places to the left.

Moving the decimal point two places we go from 3.2 to 0.32 to 0.032.

3.2% is 0.032.

Here are some examples of converting percentages to decimals.

Percentage	Decimal
48%	0.48
2%	0.02
0.6%	0.006
2.57%	0.0257
200%	2
354%	3.54

Simply divide the percentage by 100 to get it in decimal form.

How to Check Divisibility by 2, 5 or 10

To check if a number is divisible by 2, 5 or 10, follow these steps:

• Look at the last digit of the number.
• If the digit is a 2, 4, 6, 8 or 0, the number is divisible by 2.
• If the digit is a 5 or a 0, the number is divisible by 5.
• If the digit is a 0, the number is divisible by 10.

For example, here is 68. We will check if it is divisible by 2, 5 or 10.

Its last digit is 8.

If the digit is a 2, 4, 6, 8 or 0, the number is divisible by 2. Therefore 68 is divisible by 2.

The last digit must be a 5 or a 0 for the number to be divisible by 5. 8 is neither of these digits and so, 68 is not divisible by 5. It is not in the 5 times table. A number can be divisible by 2, 5 and 10. If a number is divisible by 10, it is also divisible by 2 and 5.

For example, here is 70.

70 ends with a digit of 0.

A number must end in a 0 to be divisible by 10. 70 is in the 10 times table. It is divisible by 10.

If the digit is a 2, 4, 6, 8 or 0, the number is divisible by 2. Since 70 has a final digit of 0, it is divisible by 2.

A number must end in a 5 or a 0 to be divisible by 5. 70 ends in a 0 and so, it is divisible by 5 too.

A number divisible by 10 is also divisible by 2 and 5 because 2 and 5 both divide into 10.

Which of the Following Numbers are Divisible by 2, 5 or 10?

If a number ends in 2, 4, 6, 8 or 0, it is divisible by 2. If it ends in 5 or 0, it is divisible by 5. If it ends in 0, it is divisible by 10. If it is divisible by 10, it is also divisible by 2 and 5.

Here is a table of examples of numbers that will be checked for divisibility by 2, 5 and 10 using this rule.

Number	Last Digit	Divisible by 2	Divisible by 5	Divisible by 10
42	2	✔	✖	✖
25	5	✖	✔	✖
80	0	✔	✔	✔
1908	8	✔	✖	✖
7540	0	✔	✔	✔
3895	5	✖	✔	✖

42 ends in a 2 and so, it is divisible by 2 but not 5 or 10.

25 ends in a 5 and so, it is divisible by 5 but not 2 or 10.

80 ends in a 0 and so, it is divisible by 2, 5 and 10.

1908 ends in an 8 and so, it is divisible by 2 but not 5 or 10.

7540 ends in a 0 and so, it is divisible by 2, 5 and 10.

3895 ends in a 5 and so, it is divisible by 5 but not 2 or 10.

Rule for Divisibilty by 2

A number is divisible by 2 only if its last digit is a 2, 4, 6, 8 or 0. For example, 426 is divisible by 2 because it ends in a 2. 327 is not divisible by 2 because it ends in a 7.

If a number is divisible by 2, it means that is can be divided by 2 exactly without a remainder. It is in the 2 times table.

All numbers in the 2 times table repeat the pattern of the last digit ending in 2, 4, 6, 8 and 0.

Every time we get to a number ending in 0, the pattern starts again.

This means that to check if a number is a multiple of 2, simply look at the last digit and ignore all preceding digits. If the number ends in 2, 4, 6, 8 or 0, the number is a multiple of 2.

For example, we will use the rule to test if 68 is divisible by 2.

68 ends in an 8, which is one of the digits 2, 4, 6, 8 or 0.

68 is divisible by 2 because it is an even number.

It does not matter how large the number is, only look at the last digit to decide if a number is divisible by 2. For example, here is 37,110.

37,100 ends in a 0. 0 is an even number and so, 37,100 is divisible by 2.

Here is 209, which ends in a 9.

A number must end in 2, 4, 6, 8 or 0 to be divisible by 2. If a number ends in 9 it is not divisible by 2.

209 is not divisible by 2.

Rule for Divisibilty by 5

A number is divisible by 5 only if its last digit is a 5 or a 0. For example, 935 is divisible by 5 because it ends in a 5. 732 is not divisible by 5 because it ends in a 2.

If a number is divisible by 5, this means it can be divided exactly by 5 with no remainder. It is in the 5 times table.

All numbers in the 5 times table repeat the pattern of ending in 5 or 0.

If a number ends in any other digit apart from 5 or 0, it is not in the 5 times table.

For example, here is 45.

45 ends in a 5. Numbers that end in 5 or 0 are divisible by 5 and so, 45 is divisible by 5.

It does not matter how large a number is. If a number ends in a 5 or a 0, it is in the 5 times table. We only need to look at the last digit.

Here is 17,760.

17,760 ends in a 0. If a number ends in a 5 or a 0, it is divisible by 5.

Therefore 17,760 is divisible by 5.

Here is 803.

803 ends in a 3. To be divisible by 5, a number can only end in a 5 or a 0.

803 is not divisible by 5.

Rule for Divisibilty by 10

A number is divisible by 10 only if it ends in a 0. For example, 770 is divisible by 10 because it ends in a 0. 565 is not divisible by 10 because it ends in a 5.

If a number is divisible by 10, this means that is can be divided exactly by 10 with no remainder. It is in the 10 times table.

All numbers in the 10 times table end in a 0.

If a number does not end in a 0, it is not in the 10 times table.

For example, here is 70.

70 ends in a 0. If a number ends in a 0, it is in the 10 times table and can be divided exactly by 10.

70 is divisible by 10.

It does not matter how large a number is, if it ends in a 0, it is divisible by 10.

For example, here is 2,070,420.

2,070,420 ends in a 0. We do not need to look at the digits in front of the last digit to decide.

2,070,420 is divisible by 10 because it ends in a 0.

Here is the example of 177.

177 ends in a 7. For a number to be divisible by 10, it must end in a 0.

177 is not divisible by 10.