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Level 5-6 Numbers - Long Multiplication and Division
Farmer O'Nions sells his carrots in sacks of 120.

Level 5-6 Numbers - Long Multiplication and Division

Master long multiplication and division with neat steps. Break big problems into parts, estimate first, then check your answer.

Fascinating Fact:

Long division can test estimation, 975 ÷ 25 = 39, which means 25 goes into 975 thirty nine times exactly.

In KS3 Maths, you practise efficient written methods for multiplying and dividing larger numbers. Setting work out clearly and estimating first helps you spot mistakes and explain your reasoning.

  • Long multiplication: A step-by-step written method to multiply larger numbers accurately.
  • Long division: A written method that divides numbers by repeated subtraction in organised steps.
  • Estimation: A quick, sensible guess used to check if an answer is reasonable.
How do I set out long multiplication?

Write numbers in columns with units lined up, multiply each digit, write partial products underneath, then add them to get the final answer.

What is an easy way to check a long division answer?

Multiply the quotient by the divisor and add any remainder. If it equals the original dividend, your division is correct.

Why should I estimate before using long methods?

Estimation gives a target size for the answer, helping you spot place-value slips or arithmetic errors quickly.

1 .
The latest best-selling novel is 314 pages long. A bookstore orders 840 copies. How many pages will there be?
240,650
256,781
261,009
263,760
That's a lot of pages!
2 .
What is 1,000 / 8?
120
125
130
135
10 ÷ 8 = 1r2, 20 ÷ 8 = 2r4 and 40 ÷ 8 = 5 so the answer is 125
3 .
A train carries 107 seated passengers. At Waterloo station there are 33 trains. If the trains are full, how many seated passengers will there be?
3,531
3,786
3,855
4,000
Remember to check your answer by dividing it by 107 (to get 33) or 33 (to get 107)
4 .
Anne has a collection of 483 stamps. Two friends want the same hobby so Anne shares her stamps between the three of them. How many does each person get?
151
155
157
161
483 / 3 = 161
5 .
Pens are sold in boxes of 85. A shop orders 63 boxes. How many pens does the shop receive?
4,800
4,863
5,355
5,638
63 boxes of 85 pens. The calculation is 63 x 85
6 .
What is the remainder when 550 is divided by 9?
1
2
5
7
550 divided by 9 equals 61.1111... Ignore the decimal part and calculate 9 x 61 = 549. Thus, 550 - 549 =1. This method will always give you the whole number remainder in problems like this
7 .
What is 1,445 / 17?
80
85
90
95
You can also multiply your answer by 17 to check it's correct. 85 x 17 = 1,445
8 .
What is 234 x 87?
20,358
20,538
20,583
20,835
4 x 7 = 28 so you know that the correct answer will end in 8
9 .
Farmer O'Nions sells his carrots in sacks of 120. A restaurant is doing a carrot soup special and requires 1,000 carrots. How many sacks will they order?
8
9
10
11
1,000 / 120 is more than 8, therefore 9 sacks are needed
10 .
Mr Picasso buys 287 paintbrushes for his 41 art students. How many paintbrushes does each student get?
4
7
9
11
7 x 41 = 287
You can find more about this topic by visiting BBC Bitesize - Operations - Calculations

Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)

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