Topics
5. Fractions
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AustraliaNSW
Stage 2

5.02 Mixed numbers and improper fractions

Lesson
Practice
Lesson

Are you ready?

Let's review how to  identify a fraction  using the shaded area of a shape.

Examples

Example 1

Which of the following shows \dfrac{1}{10} of the area of the shape shaded?

A
A rectangle divided into 10 equal parts. 2 parts are shaded.
B
A rectangle divided into 11 equal parts. 1 part is shaded.
C
A rectangle divided into 10 equal parts. 1 parts are shaded.
D
A rectangle divided into 9 equal parts. 1 part is shaded.
Worked Solution
Create a strategy

The numerator tells us how many parts should be shaded. The denominator tells us how many parts to divide the shape into.

Apply the idea

The fraction \dfrac{1}{10} is asking for one part of the shape to be shaded out of 10 total parts. The shape in option C has 10 total parts with 1 shaded part.

The answer is option C.

Idea summary

  • The numerator (top number) is the number of parts shaded to represent the fraction.

  • The denominator (bottom number) is the number of equal parts the shape is divided into.

Mixed numbers

How to write and read mixed numbers.

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Examples

Example 2

Write 2 and 2 thirds as a mixed number.

Worked Solution
Create a strategy

We can write a mixed number as: \,a\,\dfrac{b}{c} where a is the whole number, b is the number of parts we have, and c is the total number of parts.

Apply the idea

Two thirds is the same as \dfrac{2}{3} and the whole number is 2.

The mixed number is: 2\dfrac{2}{3}

Idea summary

We can write a mixed number as: \,a\,\dfrac{b}{c} where a is the whole number, b is the number of parts we have, and c is the total number of parts.

Mixed and improper fractions

This video looks at how to change a mixed number into an improper fraction, or an improper fraction to a mixed number.

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Examples

Example 3

Rewrite 4\dfrac{1}{2} as an improper fraction.

Worked Solution
Create a strategy

To find the improper fraction, multiply the whole number by the denominator, then add the numerator.

Apply the idea
\displaystyle 4\dfrac{1}{2}\displaystyle =\displaystyle \dfrac{4\times 2 + 1}{2}Multiply the denominator and whole number
\displaystyle =\displaystyle \dfrac{8+1}{2}Add the numerator
\displaystyle =\displaystyle \dfrac{9}{2}
Reflect and check
The image shows 5 rows and 2 columns of squares. 9 squares are shaded with blue and 1 square is shaded yellow.

We could also draw an array for 4\dfrac{1}{2} where each part represents \dfrac{1}{2}.

We can see that there are 9 shaded parts.

So the improper fraction is \dfrac{9}{2}.

Example 4

Rewrite \dfrac{11}{3} as a mixed number.

Worked Solution
Create a strategy

Divide the numerator by the denominator. The remainder will be the numerator of the mixed fraction.

Apply the idea

11 divided by 3 is 3 remainder 2.

So, \dfrac{11}{3} is made up of 3 wholes and 2 out of 3 remaining.\dfrac{11}{3}=3\dfrac{2}{3}

Idea summary

The whole number component of a mixed number tells you how many wholes there are.

Outcomes

MA2-7NA

represents, models and compares commonly used fractions and decimals

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