Mixed Number

# Mixed Number

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.

## Examples

1. Simplify frac(26)(8)

Answer: 3frac(1)(4)

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

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

Answer: 6frac(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)