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
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