Free Worksheets Maths: four rules

Resource of the Week: Long division

If there is one thing which really proves to be tricky for primary school children it is long division. In fact there have been calls for it to be abandoned with the calculator taking over. However, if children do grasp the method they can get great satisfaction from working their way carefully through the method to reach a correct answer.

Long division is hard because it requires a good knowledge of tables, the ability to multiply, estimate, use trial and improvement and go through several steps to reach the answer. These steps include:

e.g. 789 divided by 36

First carry out an estimate of the answer. I think 789 divided by 36 is about 20.

a. How many 36s in 78?

b. 2 x 36 is 72. 3 x 36 is 108 which is too many, so it must be 2.

c. Put the 2 in the tens column above the question.

d. Place the 72 below the 78 and subtract.

e. 78 – 72 is 6.

f. ‘Bring down’ the 9 to make 69.

g. How many 36s in 69.

h. By trial and improvement and some rough work multiplying 36 by my estimated numbers I find that 36 x 1 = 36.

i. Put the 1 in the units column above the question.

j. Place the 36 under the 69 and subtract.

k. The remainder (33) must be less than the original number you are dividing by.

I would suggest that only those children who have really mastered the basics of times tables and written methods for addition, subtraction and multiplication try these.

Division 3 by 2

More long division: 3-digits divided by 2-digits

One of the hardest things children try to do in primary school is long division. It is hard because it requires a good knowledge of tables, the ability to multiply, estimate, use trial and improvement and go through several steps to reach the answer. These steps include:

e.g. 789 divided by 36

First carry out an estimate of the answer. I think 789 divided by 36 is about 20.

a. How many 36s in 78?

b. 2 x 36 is 72. 3 x 36 is 108 which is too many, so it must be 2.

c. Put the 2 in the tens column above the question.

d. Place the 72 below the 78 and subtract.

e. 78 – 72 is 6.

f. ‘Bring down’ the 9 to make 69.

g. How many 36s in 69.

h. By trial and improvement and some rough work multiplying 36 by my estimated numbers I find that 36 x 1 = 36.

i. Put the 1 in the units column above the question.

j. Place the 36 under the 69 and subtract.

k. The remainder (33) must be less than the original number you are dividing by.

Good luck with these, but many year 6 children will find them too tricky! When I was at school I used to like doing pages of these because I had learnt the method ‘off by heart’ and it was just a matter of repeating it.

Division 3 by 2

Resource of the Week: How to do written multiplication

Some of our most popular resouces are to do with written methods of addition, subtraction, multiplication and division. This is just one of our worksheets that show how to use the standard or efficient method to multiply a 3-digit number by a single digit. There are other methods equally good, but it is important that children keep to one method that they become confident with. It presumes a good knowledge of tables before starting.

For example: 436 x 7.

First, do an estimate of the answer.
436 x 7 is approximately 400 x 7 which is 2800. The answer will be over 2800.
Then set the sum out in a vertical layout:
436
x 7

Start with the units.
6 x 7 is 42. Put the 2 in the units and carry the 4 tens into the tens column, under the answer line.
Then multiply the tens.
3 (tens) x 7 is 21(tens). Add the 4 (tens). to make 25(tens).
Place the 5 in the tens column and carry the 2 (hundreds) into the hundreds column.

Finally the hundreds.
4 (hundreds) x 7 is 28 (hundreds). Add the 2 (hundreds) to make 30 (hundreds).
Place the zero in the hundreds column and the 3 in the thousands column.
The answer is 3052.
A clearer layout of this is available on the worksheet explanation.

Further written multiplication worksheets can be found in the Year 5 and Year 6 Calculations sections.

Standard written multiplication: 3-digits by 1-digit

More addition of money

I am often asked to provide more pages of addition ‘sums’ so here is another look at using the standard method of addition for money.

The first eight questions are laid out in the correct way. The next seven need to be written in the same way, with the decimal points lining up in a vertical line.

With these questions there is ‘carrying’ from both the hundredths to the tenths and from the tenths to the whole pounds.

If this page is sent as homework look for clues that the answers have been done on a calculator. All working should be shown, including the smaller ‘1’ below the answer line. Also question 10 should be answered as £10.00 rather than just £10.

There is no harm in using a calculator to check that the answers are correct, but the main purpose of pages like these is to give practice and reinforcement of the written method.

This page and other similar pages can be found in the Four Rules category, under Addition.

Standard money addition (p3)

Long multiplication worksheets

Here is a page of practice questions for long multiplication using the standard written method. Each question is laid out so that the answer can be completed in three parts.

Looking at 67 x 23, the three stages would be:

1. multiply 67 by 20. The easiest way to do this is to place a zero in the units column of the answer and then multiply by 2. Placing the zero has the effect of moving each digit one place to the left, hence ten times bigger.

2. multiply by the units (3) and place the answer below, making sure the units go in the units column etc.

3. add the two products.

Of course the units could be multiplied first, followed by the tens, but it is important to find one standard method and stick to it. Of course, tables to to be known to make this a quick process.

This worksheet, and others, similar can be found in the Four Rules section of the site, under Multiplication.

Long multiplication 2-digits by 2-digits

Maths worksheet: Division of money

I have had several requests to produce another division of money worksheet as it seems this is quite hard and children need plenty of practice with it – so here it is. Dividing money by 2-digit numbers requires a very good knowledge of multiplication, tables and subtraction. The long division method can be found in other worksheets in this category but as a reminder the question should be started as follows:

eg £3.64 divided by 26.

1. ask how many 26s go into 3.

The answer is zero, so put the zero in the pounds column of the answer.

3. remember the decimal point.

4. Ask how many 26s go into 36 and continue with the long division method.

Money division (2)

Long multiplication: 3-digits by 2-digits

A standard page of long multiplication questions here. For children to be successful with these they need to have a good knowledge of ‘times tables’. Without this knowledge the whole process becomes quite tedious and errors can slip in even if the method is correct.

The standard method of long multiplication is one which most adults will be familiar with. It does not really matter if the number is multiplied by the tens first or the units first, as long as it is remembered to place a zero in the units column when multiplying by the tens digit. It is also important to line up the answer so that hundreds, tens and units are directly under each other: adding the final total can be very difficult if this is not done.

Long multiplication 3 digits by 2 digits

Resource of the Week: Written multiplication of money

Multiplication of money by a single digit is very much like multiplying a 3-digit number by a single digit, but, of course, the decimal point needs to be included. It would normally be expected to answer these types of question using the standard written method.

The first 8 questions are set out in the standard way but it is important that the second set of questions, from 9 to 15 should be set out in the correct way and not attempted as shown.

When marking these check that the working is shown, especially that the numbers have been carried across. It is often a good idea for children to check the answers to this type of question by using a calculator. (If they just use the calculator to find the answer this is quite obvious as there is no working shown!)

This page any many others can be found in our Four Rules section.

Multiplication of money (pg 1)

9x table space challenge

Continuing with my series of tables space challenges, we reach the 9x table. because there is a regular pattern to the answers to the 9x table it is one of the easier tables to learn. Of course, the digits of the answers always add up to 9 and the tens go up one at a time whilst the units decrease one at a time (only up to 90).

This worksheet can be used as a fun test to see how well knowledge of the times table can be put into practice. Because the table is jumbled up it becomes slightly harder and takes longer to do, especially if the table is not known ‘off by heart’. Remember, when learning the table say the whole of it (eg one times 9 is 9) and not just the answers, which is counting up in nines, not saying the table.

9x tables space challenge

Maths Resources: Written Addition

One of the most popular parts of the site for parents is our Free Maths Worksheets: Four Rules pages on written addition.

Many parents think that the methods they were taught at school (and for many this would be in the mid 1990s) are different from today. This is only partly true. Since the onset of the Numeracy Strategy and later the Primary Framework for Maths the emphasis has been on preparing children properly so that they understand the written methods they use. So there is a lot of preparation work and methods often called, ‘Moving towards the standard written method’ that may not be familiar to parents, but the end result is pretty much the same. It is these intermediate stages which some parents find puzzling.

The standard written method is to lay out the sum vertically, with the numbers to be added under each other. The units are added first, then the tens and so on. We have several worksheets which explain this method in full.

Go to Written Methods of Addition