Tag: division

Short division of decimals (1)

Here is a page of practice on using the short method of division of decimals. The numbers being divided are just units and tenths which helps with getting the method correct.

There are arguments for and against putting the decimal point in before you start, or leaving it until you have reached that point in the question. it does not matter as long as it is inserted correctly.

One of the best ways to be fluent with this method is to talk it through out loud. If we look at question 2 which is 4.5 divided by 3, the verbal stages are:

a. How many 3s in 4?

b. 1 times 3 is 3 so there is 1 with a remainder of 1.

c. Place the 1 on the answer line, immediately above the 3.

d. Place the decimal point just above the answer line so it can be clearly seen.

e. The remainder 1 is placed just in front of the 5 (usually written smaller).

f. How many 3s in 15?

g. 3 x 5 is 15 so the answer is 5.

h. Place the 5 on the answer line, immediately above the 5 (tenths).

i. Answer 1.5

This page can be found in our Four Rules, Division category.

Division of decimals (1)

Written methods of dividing

Today we have a straightforward page of division questions, using the standard method of written division. There are several stages in this process if the correct answer is to be reached.

For example: 74 divided by 3

1. Make a rough estimate of the answer; this can be along the lines of, “It will be over 20 but not as many as 30”.

2. Ask the question, “How many threes in 7?”

There are 2 threes in 7 with a remainder of 1.

3. Place the 2 above the 7 on the answer line and place the one remainder in front of the 4 (making 14).

4. Ask the question, “How many threes in 14?”

There are 4 threes in 14 with 2 remainder.

5. Place the 4 on the answer line.

6. The 2 remainder can be shown as 2/3 on the answer line: making the answer 24 and 2/3.

Remember to set out the last few questions just as the earlier ones have been set out.

Division_2_by_1_p3

Mental arithmetic: dividing by 100

It’s January, and the beginning of a new year, but the sharp brains may have been dulled a little over the last week, so why not satart the new year with a little mental arithmetic? Here we our highlighting the next worksheet in our series of dividing mentally. This page looks at dividing larger numbers by 100. All the numbers are multiples of 100 so there will be no decimals involved with the answers. As has been said before, but the idea has to be repeated many times for children to fully understand; to divide by 10, move each digit one place to the right. To divide by 100 move each digit two places to the right.

So 1200 divided by 10 is 12.00. There is nothing wrong with leaving the two zeros after the decimal point, but we usually don’t worry with the decimal point or zeros if the answer is a whole number. Whatever you do, don’t tell your children to take away the noughts!!

This, and many other division worksheets, can be found in our Four Rules section as well as in the year group sections under calculating.

Divide by 100 (pg1)

Year 3 maths worksheet: more division practice

Here is a follow up page to that published earlier, giving more practice with simple division. If children have a good knowledge of the 2x, 4x, 5x and 10x tables they should find these quite straightforward. The only potentially tricky ones are where the missing number is in the middle of the number sentence

eg 24 divided by ? = 6

This requires a good understanding of what the number sentence means, but all that is required to answer is a knowledge of ‘what multiplied by 6 makes 24’.

This worksheet can be found in our Year 3 Knowing Number Facts section.

Division practice (2)

Year 3 maths worksheet: division practice

Once children have learnt the 2x, 4x, 5x and 10x tables they can put their knowledge to good use by working out division questions. Because division is the inverse of multiplication the only knowledge needed to work out 14 divided by 2 is that 2 x 7 = 14.

This is a more abstract way of working with division and children should have had a great deal of practical work sharing out coins, cubes, sweets etc before moving onto this type of question.

Division practice (1)

Year 3 maths worksheet: division and multiplication

This is the second page that looks at the relationship between division and multiplication and how knowledge of one fact can lead to knowing several other facts.

Some children fail to realise that division and multiplication are related, so when it comes to long division later, which involves mostly multiplication, they are lost.

This sheet shows clearly that if you know one multiplication fact then you can instantly work out two division facts. The only issue is that they use the numbers correctly ie if they know that 79 x 5 = 45 they alos know that 45 divided by 5 is 9 and that 45 divided by 9 is 5 (but it is obviously not true to say that 9 divided by 5 is 45!)

Division as the inverse of  multiplication (2)

Year 4 maths worksheet: More dividing by 10 and 100

This page looks for a rapid response from children to show that they clearly understand what is happening when numbers become 10 times or 100 times smaller.

The process is simple: to divide by 10 move each digit one place to the right. To divide by 100 move each digit 2 places to the right.

All the numbers are multiples of 10 so there is no need to get involved with decimal points, but some children might ask what happens to the zero. For example 500 divided by 10: move each digit one place to the right gives 50.0; this is correct but it can be written as 50.

Divide by 10 and 100 (2)

Year 6 maths worksheet: Division with decimals (2)

This is the second of our pages on dividing decimals mentally. Concentrating on just one decimal place it is a good test of how well children know their tables and understand place value.

This is published in our Year 6 maths worksheets, under Knowing Number Facts. As well as these resources further number worksheets can also be found in or Four Rules section.

Divide decimals (2)

Year 3 maths worksheet: division and multiplication

It is important to show children the relationship between multiplication and division as this makes division so much easier.

Here we have a page which shows that if you know one multiplication fact you can quickly work out two division facts.

For example:

if you know that 5 times 7 is 35

then you can instantly work out that

35 divided by 7 is 5 and

35 divided by 5 is 7.

Knowing that you can do this greatly increases speed of calculating and it is speed, as well as accuracy that we are looking for. This page can be found in ourYear 3 Calculations section.

Division as the inverse of multiplication 1

Year 4 maths worksheet: Remainders

By year 4 most children will be confident with the concept of remainders after dividing. The next step is to ‘neaten up’ the division so that there is no remainder. What is left becomes part of the answer as a fraction.

It is easy to write the remainder as a fraction as is shown on this worksheet. The top number is the number or remainder that is left when the whole number has been divided. The bottom number is the number that you have been dividing by.

So 54 divided by 5 is 10 remainder 4 which can be written as 10 and 4 fifths (4/5).

Divide with fraction remainders (3)