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AQA GCSE Maths Decimals, fractions and percentages

Decimals, fractions and percentages

This page covers the following topics:

1. Decimals
2. Fractions
3. Percentages
4. 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, Β²/β‚ˆ and ΒΉ/β‚„. 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

A percentage is denoted by the β€˜%’ symbol and refers to a part of a whole number in terms of parts per hundred. 17%, for example, means 17 parts out of every 100. A percentage can, therefore, be used to standardise quantities such as, for instance, 20 pencils out of a 200-pencil set which refer to 10% of the set.

Percentages

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.

Convert 23% into a decimal number.

2

Calculate 436 Γ· 10.

Calculate 436 Γ· 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.

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 ΒΉΒ²/₇ as a mixed number.

Express ΒΉΒ²/₇ 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.

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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