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Decimals and fractions for AQA GCSE Maths

Decimals and fractions

This page covers the following topics:

1. Decimals
2. Fractions
3. Ordering

Decimal numbers are used to represent a part of a whole number. The decimal point separates the whole number part of a number from its complementary value that is smaller than one. These values that are smaller than one can be interchangeably represented with fractions, decimals, or percentages.

Decimals

Fractions are a way to represent parts of a whole number or mixed numbers. They are denoted by using a numerator and denominator. To add or subtract fractions, the denominators of the fractions must be made the same by multiplying the numerator and denominator by the same number to create equivalent fractions like, for instance, ยฒ/โ‚ˆ and ยน/โ‚„. To multiply fractions, find the product of their numerators and of their denominators. And to divide fractions, multiply a fraction with the inverse of the dividing fraction.

Fractions

Fraction, decimals, and percentages are interchangeable ways to represent parts of a whole number and each of the three can either be a positive value or a negative value. These quantities can, therefore, be compared and ordered by using the symbols provided.

Ordering

1

Convert 23% into a decimal number.

23% can be rewritten as 23/100.
This is equivalent to dividing by 100.
Then the decimal point will move two positions to the left.
Therefore, 23% can be written as a decimal number as 0.23.

0.23

Convert 23% into a decimal number.

2

Calculate 436 รท 10.

When dividing by 10, the decimal point will move one place to the left.
Therefore, 436/10 = 43.6.

43.6

Calculate 436 รท 10.

3

Niharika has one chocolate bar that she is willing to share equally between herself and her 4 friends. How much of the chocolate bar will each of them have after splitting it equally? Give your answer as a decimal.

The chocolate bar will be shared between 5 people, Niharika and her 4 friends. Therefore, each friend will get one part of the chocolate out of five equal parts. This is equivalent to 1/5 = 0.20.

0.2

Niharika has one chocolate bar that she is willing to share equally between herself and her 4 friends. How much of the chocolate bar will each of them have after splitting it equally? Give your answer as a decimal.

4

Express ยนยฒ/โ‚‡ as a mixed number.

7 goes into 12 fully only once, therefore the whole number part of the mixed number is 1.
The remainder is 5, so the fraction part of the mixed number will be 5/7.
Putting this together gives 1 โต/โ‚‡.

1 โต/โ‚‡

Express ยนยฒ/โ‚‡ as a mixed number.

5

Lester is conducting an experiment in his science lesson. He finds that adding 100 ml of vegetable oil to 10 ml of sodium hydroxide produces 10 g of soap and he has 1 litre of vegetable oil and 120 ml of sodium hydroxide available to make as much soap as he can. Find how much of sodium hydroxide Lester needs out of the total amount he has.

ยนโฐโฐ/โ‚โ‚‚โ‚€ = โต/โ‚†

โต/โ‚†

Lester is conducting an experiment in his science lesson. He finds that adding 100 ml of vegetable oil to 10 ml of sodium hydroxide produces 10 g of soap and he has 1 litre of vegetable oil and 120 ml of sodium hydroxide available to make as much soap as he can. Find how much of sodium hydroxide Lester needs out of the total amount he has.

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