We need a good technique for long division that will work every time no matter how difficult the numbers. Around the world there are various different techniques – ask your teacher to show you an example technique, and if you have an alternative technique, perhaps you could share it with the class too? Cambridge are happy for you to use any technique as long as you master a formal technique that consistently works.

Note that with the non-integer part of a number, a long division technique can give you the answer with a fractional part a with a decimal part. Both of these can be useful (in the exercise below we will write the answers with a decimal part, including no more than 2 decimal places)

Example

• Calculate
  • 981 ÷ 3
  • 637 ÷ 7
  • 600 ÷ 7
  • 241 ÷ 5

Exercise

Calculate the following without using a calculator:

(1.) 672 ÷ 21 (2.) 425 ÷ 17 (3.) 576 ÷ 32 (4.) 247 ÷19 (5.) 875 ÷ 25 (6.) 574 ÷26 (7.) 806 ÷ 34 (8.) 748 ÷ 41 (9.) 666 ÷ 24 (10.) 707 ÷ 52 (11.) 951 ÷ 27 (12.) 806 ÷ 34 (13.) 2917 ÷ 42 (14.) 2735 ÷ 18 (15.) 56274 ÷ 19

Solutions

(1.) 31, (2.) 25, (3.) 18, (4.) 13, (5.) 35, (6.) 22.08, (7.) 23.71, (8.) 18.24, (9.) 27.75, (10.) 13.6, (11.) 35.22, (12.) 23.71, (13.) 69.45, (14.) 151.94, (15.) 2961.79

Word Problems

In practice mathematics is useful because it can be applied to solve problems. Throughout our mathematics course we must develop our ability to quickly read questions, understand the way in which we can apply mathematics to answer them and then use the relevant mathematics.

Worked Examples

Let’s identify which types of arithmetic we need to use and then find the answer for each of the following questions:

Exercise

Let’s try this for the exercise below:

Solutions

(1.) $47.04, (2.) 46, (3.) 7592, (4.) 12 with 17c change, (5.) 8, (6.) $80.64, (7.) $14m, (8.) $85, (9.) $21,600