NUMBERS • IMPROPER FRACTIONS AND MIXED NUMBERS 43
Changing a mixed number to an improper fraction
If we count the eighths in one
whole, then add the three-eighths
of our fraction, we have 11 eighths. We
write this as the improper fraction^11 / 8.
Let’s change 1^3 / 8 into an improper
fraction. First, we divide the whole
into eighths, because the denominator
of the fraction in our mixed number is 8.
To change a mixed number to an
improper fraction, we multiply the
whole number by the denominator,
then add it to the original numerator
to make the new numerator.
Proper
fraction
Numerator of the
improper fraction
Whole number
Denominator
Numerator
Denominator
of the improper
fraction
What would the improper
fraction^10 / 3 be as a mixed
number? The fraction tells us
that we have 10 lots of one
third (^1 / 3 ).
If we put the thirds
together, we can make
three wholes, with one third
left over. We can write this as
a mixed number: 3^1 /3.
To make an improper fraction a mixed number,
divide the numerator by the denominator. Write
down the whole number part of the answer. Then
write a fraction in which the numerator is the
remainder over the original denominator.
Changing an improper fraction to a mixed number
1
8
10 ÷ 3 = 3
10
3
3
1
3
10
3
3
8
1 × 8 + 3
8
1
3
11
8
1
(^81)
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
= =
1
3
8
1
3
1
3
1
3
1
3
1
3
1
3
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
8
1
3
1
3
1
3
1
3
1
3
=
1
11
8
One whole
Three eighths
1 1 1
042_043_Improper_fractions.indd 43 29/02/2016 14:22