Foundation - Fractions - GCSE Mathematics

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Foundation - Fractions

infoWhy this? This unit develops pupils’ fluency in converting, ordering and calculating with fractions, decimals and percentages, including the four operations, mixed numbers, reciprocals and finding fractions of amounts. It deepens understanding of equivalence and number structure, so pupils can solve more complex numerical and contextual problems accurately.

scheduleWhy now? Pupils are ready for this unit because they have already studied numerical properties, rounding, numerical operations, ratio and proportion, and percentages, which provide the foundations for working confidently with fractional and decimal forms. Teaching it here also prepares them for later work involving decimal calculations and interpretation, including averages and measures of spread.

A fraction, a decimal and a percentage can represent the same proportion, such as `\frac{1}{2}=0.5=50\%`.
Percent means “out of 100”, so `37\%` means `\frac{37}{100}` or `0.37`.
To convert a fraction to a decimal, divide the numerator by the denominator.
To convert a decimal to a percentage, multiply by 100; to convert a percentage to a decimal, divide by 100.
Equivalent fractions have the same value because the numerator and denominator have been multiplied or divided by the same non-zero number.
Fractions can be compared and ordered by converting them to equivalent fractions with a common denominator or by converting them to decimals or percentages.
To add or subtract fractions with different denominators, the fractions must first be written with a common denominator.
When multiplying fractions, multiply the numerators together and multiply the denominators together.
Dividing by a fraction is the same as multiplying by its reciprocal, such as `3 \div \frac{2}{5}=3 \times \frac{5}{2}`.
The reciprocal of a non-zero number is the number that multiplies by it to make 1, such as the reciprocal of `\frac{3}{4}` being `\frac{4}{3}`.
A mixed number is made of an integer part and a proper fraction part, such as `2\frac{1}{3}`.
A mixed number can be converted to an improper fraction by multiplying the whole number by the denominator, adding the numerator, and keeping the same denominator.
To multiply a fraction by an integer, write the integer as a fraction over 1 or multiply the numerator by the integer.
To divide a fraction by an integer, write the integer as a fraction over 1 and multiply by its reciprocal.
The place value of digits after the decimal point is tenths, hundredths, thousandths, and so on.
When multiplying decimals, the number of decimal places in the answer equals the total number of decimal places in the factors.
When dividing by a decimal, multiplying both numbers by the same power of 10 can change the calculation into an equivalent division by an integer.
To find a fraction of an amount, divide the amount by the denominator and multiply by the numerator.
If a fraction of an original amount is known, the original amount can be found by dividing by the numerator and multiplying by the denominator.
Adding, subtracting, multiplying and dividing decimals follow the same operation rules as whole numbers, but place value and decimal point position must be handled accurately.

rocket_launchYou must be able to

Convert between fractions, decimals and percentages accurately, using division by the denominator and multiplication or division by 100 as appropriate.
Order fractions, decimals and percentages by converting them to a common form and comparing their values from smallest to largest or largest to smallest.
Add and subtract fractions with different denominators by finding a common denominator, creating equivalent fractions, calculating the numerators, and simplifying the answer where possible.
Multiply and divide fractions, integers and mixed numbers by converting to improper fractions where needed, using reciprocals for division, and simplifying the result.
Calculate with decimals using written methods for addition, subtraction, multiplication and division, aligning place value correctly and placing the decimal point accurately.
Multiply and divide decimal numbers by decimal numbers by scaling the calculation to use whole numbers, then adjusting the answer using place value.
Find a fraction of an amount by dividing by the denominator and multiplying by the numerator, including cases where the answer is not a whole number.
Find the original quantity when given a fraction of it by using the known fractional part to find one unit fraction and then the whole amount.
Find the reciprocal of a fraction, integer, mixed number or decimal by first writing it as a fraction and then inverting the numerator and denominator.

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