Mixed Number

## Mixed Number

A Mixed Number consists of an integer part and a fraction part. They are written with the integer part first, then the fraction part.

A Mixed number can be re-written as a top-heavy fraction, or improper fraction.

When calculating with fractions, 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.

## Example 1

Simplify frac(26)(8)

26 ÷ 8 = 3 rem 2

The 3 is the integer part.

The 2 is the numerator.

The 8 is the denominator.

Then simplify the fraction part.

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

Answer: 3frac(1)(4)

## Example 2

Calculate 1frac(3)(8) xx 5.

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)

= 55÷8 = 6rem 7

= 6frac(7)(8)

Answer: 6frac(7)(8)