Help your students prepare for their Maths GCSE with this free fraction worksheet of 43 questions and answers
Fractions represent a part of a whole. The denominator of a fraction represents how many equal parts the whole has been divided into and the numerator of the fraction represents how many of those fractional parts we have. For example, the fraction 3 fifths means the whole amount has been divided into 5 equal parts (fifths) and we have 3 of them. Unit fractions have a numerator of 1.
Some fractions are equivalent to each other – they represent the same proportion of a whole. For example, the fractions 1 over 2, 2 over 4, 3 over 6 and 50 over 100 are all equivalent. We may be asked to simplify a fraction and this means finding an equivalent fraction which is made up from smaller numbers (this is sometimes called reducing fractions). Equivalent fractions are useful when converting fractions to percents.
Proper fractions are greater than 0 and less than 1 and can be placed between 0 and 1 on a number line. We also sometimes work with improper fractions, where the numerator is bigger than the denominator, and with mixed numbers (also called mixed fractions) which consist of a whole number and a proper fraction. Improper fractions and mixed numbers are greater than 1 and we can convert between them.
We can find a given fraction of a whole number. To do this, we divide the number by the denominator and then multiply the answer by the numerator.
We can also add, subtract, multiply and divide fractions. When performing fraction addition or subtraction, we need to ensure the fractions have a common denominator. If the fractions have different denominators, we can find equivalent fractions to make the denominators the same. We can then add or subtract the numerators.
When performing fraction multiplication we need to multiply the numerators and multiply the denominators. When dividing fractions we need to turn the second fraction upside down and then multiply them together.
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