division | Maths Blog

Year 5 Maths Worksheet: Solving division problems (pg 1)

Year 5 Maths Worksheet: solving division problems

By year 5 solving division problems ‘in your head’ get quite tricky and a very good understanding of the relationship between multiplication and division is needed. Questions involving sharing with remainders need to be solved which need both working out ‘tables’ and calculating the number left over.

It is always a good idea to ask children how they reached their answers as this can reveal a great deal about their mathematical thinking as well as their knowledge of ‘times tables’.

Here we have a page of division problems, all of which should be answered mentally, although ‘jottings’ may help.

Division problems to calculate mentally (pg 1)

Year 4 Maths Worksheet: division problems (pg 1)

Division problems worksheet

Solving division problems ‘in your head’ can often prove to be tricky and a good knowledge of tables and multiplication facts is needed.

Here we have a set of questions all involving mental division.

There are a number of different skills which can be used to answer them. For example, dividing by 4 can be achieved by halving and halving again. Dividing £1 between 5 involves converting the £1 into 00p first.

Perhaps the trickiest question asks how many 10 cm lengths of wire can be cut from 156 cm of wire; of course there will be some left over, which in the context of the question can be ignored.

Division problems to calculate mentally (pg 1)

Mental arithmetic: divide by 6

Being successful with mental arithmetic is all about making use of the knowledge you have. For example, once the 6 times table has been learned it needs to be put to good use. This worksheet looks at how the six times table can be used to answer division questions.

Because division is the inverse of multiplication knowing tables means that the inverse can be quickly worked out eg knowing that 6 x 10 = 60 means that 60 divided by 6 is 10 and 60 divided by 10 is 6 can be quickly worked out.

This page could be tackled in a variety of ways. A child might ask themselves what 60 divided by 6 is, or they might ask what number times 6 makes 60? Either way, responses should be quick!

Divide by 6

Resource of the Week: Divide by 5 mentally

Learning tables is considered an essential to maths progress, and indeed, it is vital. But knowing tables is only a starting point: these facts then need to be used. The most obvious use other than to multiply numbers is to do the reverse; to divide numbers. We have a number of resources which look dividing ‘in your head’ including this one on divide by 5 mentally.

Essentially it is the reverse of a times table sheet and highlights that if 4 x 5 = 20 is known then 20 divided by 4 = 5 should come quickly after it.

Mental arithmetic: divide mentally

Year 5 number worksheet: Tests of divisibility for multiples of 3 and 6

This page continues with our series on tests of divisibility.

To find out whether a number is exactly divisible by 3:

Add up the digits of the number.

If the total is divisible by 3 then so is the number.

Eg: 345

3 + 4+ 5 = 12.

12 is divisible by 3 so 345 is also divisible by 3.

To find out if a number is exactly divisible by 6:

Check that it is even.

If it is even, apply the test of divisibility for 3. If the total of the digits is divisible by 3 and the number is even, it is also divisible by 6.

Eg 348

348 is even.

3 + 4+ 8 = 15.

15 is divisible by 3 so 348 is divisible by 6.

Divisible by 3 and 6

Year 5 number worksheet: recognise tests of divisibility for multiples of 9 and 10

This maths worksheet is another in our set on rules of divisibility. Knowing these rules will really help children in their maths up to the end of High School and beyond.

The rule for dividing by 10 is the easiest of them all:

If the whole number ends in a 0 then the number is divisible by 10.

The rule for 9 is also easy, but it does require a little adding up:

Add up all the digits. If the total of the digits is divisible by 9 then the whole number will be.

Example: 2304

2 + 3 + 0 + 4 = 9

So 2304 is divisible by 9.

Example: 9630

9 + 6 + 3 + 0 = 18

18 is divisible by 9 therefore 9630 is also divisible by 9.

The second part of the worksheet asks which numbers are divisible by both 9 and 10. Probably the best way to do this is to ignore any numbers that do not end in a zero, then add up the digits of the rest and see if they come to a multiple of 9.

If they do, and the last digit is a zero, then they are multiples of both 9 and 10. Easy!!

Divisible by 9 and 10

Maths worksheet: Long division p2

The second in our series of long division pages. These are very hard for primary school children and should not be attempted until they have a good knowledge of tables, multiplying and subtraction.

Example: 789 divided by 36.

First carry out an estimate of the answer. I think 789 divided by 36 is about 20.
Then proceed using these steps:
1. How many 36s in 78?
2. 2 x 36 is 72. 3 x 36 is 108 which is too many, so it must be 2.
3. Put the 2 in the tens column above the answer.
4. Place the 72 below the 78 and subtract.
5. 78 – 72 is 6.
6. ‘Bring down’ the 9 to make 69.
7. How many 36s in 69.
8. By trial and improvement and some rough work multiplying 36 by my estimated numbers I find that 36 x 1 = 36.
9. Place the 36 under the 69 and subtract.
10. The remainder (33) must be less than the original number you are dividing by.

Long division (pg 2)

Maths worksheet: Long division

Perhaps the hardest thing that children are asked to do in primary school is long division – and many children never master it, not even later in life. The main reason it is so difficult is that involves a number of stages, a good knowledge of tables and multiplication as well as subtraction. Looking at a problem such as 867 divided by 34, there are at least ten distinctive stages to go through:

34)867
First carry out an estimate of the answer. I think 867 divided by 34 is over 20 but under 30.

Then proceed using these steps:
1. How many 34s in 86?
2. 2 x 34 is 68. 3 x 34 is 102 which is too many, so it must be 2.
3. Put the 2 in the tens column above the answer.
4. Place the 68 below the 86 and subtract.
5. 86 – 68 is 18.
6. ‘Bring down’ the 7 to make 187.
7. How many 34s in 187.
8. By trial and improvement and some rough work multiplying 34 by my estimated numbers I find that 34 x 5 = 170.
9. Place the 170 under the 187 and subtract.
10. The remainder must be less than the original number you are dividing by.

Long division (pg 1)

Year 4 number worksheet: recognising tests of divisibility for 4 and 5

There are some things which children can learn which can really help them later at High School. Tests of divisibility are a great set of ‘tricks’ to know and will certainly help any child with their maths in the future. This page looks at divisibility by 4 and 5. Being divisible by 5 means that there is no remainder when a number is divided by 5; in other words it divides exactly.

Recognising when a number is divisible by 5 is easy: only whole numbers ending in 5 or 0 are divisible by 5.

Recognising a number which is divisible by 4 is harder: are the last two digits divisible by 4? If so then the number is too. eg 156344 is divisible by 4. (try it with a calculator.)

This worksheet only uses 2-digit numbers which by year 4 children should be able to divide by 4 in their heads. (Halve and halve again: if the answer is a whole number it is divisible by 4).

Divisible by 4 and 5

Mental arithmetic: Dividing by 4

A nifty way of dividing a number by 4 is to halve the number and then halve again. This method is much easier with even numbers and, of course, whole multiples of 4, but can be used for most 2-digit numbers – just the remainders become tricky. All these questions are multiples of 4 so should be relatively straightforward. Knowing these ‘tricks’ can give children a lot of confidence and can also be a useful way of checking answers which have been calculated on paper, or even on a calculator, to ensure that the answer is sensible.

Divide by 4 mentally