Help your students prepare for their Maths GCSE with this free Mixed Numbers and Improper Fractions worksheet of 42 questions and answers
A mixed number (sometimes called a mixed fraction) has both a whole number part and a proper fraction part. An improper fraction is one where the numerator is greater than the denominator ; they are informally known as top-heavy fractions.
A proper fraction is one where the numerator is smaller than the denominator.
A mixed number cannot be composed of an integer and an improper fraction (more than one whole), such as 6 and 8⁄5. This would have to be corrected to a mixed number – in this case, it would be 7 and 3/5.
In order to carry out fraction arithmetic it is useful to be able to convert a mixed number to an improper fraction, and an improper fraction to a mixed number.
To convert mixed numbers into improper fractions, we consider how many of the denominators we have in total. For example, for the number 1 whole and 3 fifths we know that a whole has 5 fifths, so in total we have 5 fifths added to 3 fifths which is 8 fifths. For the number 2 1/4 we know that two whole numbers have 8 quarters (fourths), so in total we have 8 quarters added to 1 quarter which is 9 quarters.
In order to convert an improper fraction to a mixed number we need to divide the numerator by the denominator. For example, to convert 11/5 from an improper fraction to a mixed number, we need to divide 11 by 5. 5 goes into 11 twice leaving a remainder of 1 fifth. So the improper fraction of 11/5 is equivalent to the mixed number 1 and 1 fifth.
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