GCSE(F)

**Mixed Numbers** consist of an **integer part** and a **fraction part**. They are written with the integer part first, then the fraction part.

Mixed numbers can be re-written as **top-heavy**, or **improper**, fractions. An improper fraction includes the integer part of the number in the numerator: when this happens, the numerator becomes larger than the denominator.

When calculating with fractions, it is normally easier to turn a mixed number into an improper fraction, carry out the calculation, and then turn the answer back into a mixed number.

To turn a mixed number into an improper fraction, multiply the integer part by the denominator and add this value to the numerator. The denominator stays the same:

`3frac(2)(5)=frac((3times5) + 2)(5) = frac(17)(5)`

To turn an improper fraction into a mixed number, divide the numerator by the denominator. The answer is the integer part; the remainder is the new numerator and the denominator remains the same.

1. Simplify `frac(26)(8)`

Answer: 3`frac(1)(4)`

`frac(26)(8) = frac(3 xx 8+2)(8) = 3frac(2)(8) = 3frac(1)(4)`

2. Calculate 1`frac(3)(8)` x 5.

Answer: 6`frac(7)(8)`

`1frac(3)(8) xx frac(5)(1)`

`= frac([1 xx 8] + 3)(8) xx frac(5)(1)`

`= frac(11)(8) xx frac(5)(1)`

`= frac(55)(8)`

`= frac(6 xx 8 + 7)(8)`

`= 6frac(7)(8)`

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