 Australia
Year 7

# 2.08 Solve contextual problems with fractions

Lesson

We use fractions to solve many everyday problems. For example, in recipes, ingredients are often measured in fractions of a cup. If we wanted to know the total volume of the ingredients, we could use fraction addition.

Here are some tips for applying fractions to real world problems:

• When we describe equal parts out of a whole, we can write the situation as a fraction. For example, if a prize was split $6$6 ways, each recipient would get $\frac{1}{6}$16 of the total.
• The denominator is the total number of parts. In some cases, we can find it by adding together all of the parts. For example, if Mick picked $4$4 strawberries and Rachel picked $5$5, then Mick picked $\frac{4}{4+5}=\frac{4}{9}$44+5=49 of the strawberries.
• If we want to find a fraction of a quantity, we can multiply the fraction by the quantity. This works if the quantity is a fraction as well. For example, if we want to find $\frac{2}{3}$23 of $\frac{1}{10}$110 of a minute in seconds, we would find $\frac{2}{3}\times\frac{1}{10}\times60$23×110×60.
• Fractions are also a way to write division. If a piece of timber was divided into $5$5 parts, each part would be $\frac{1}{5}$15 of the original piece.
• Improper fractions and mixed numbers can be used to represent more than one whole. For example, if Francisco ran one lap around a track and then ran another third of the track, he has run $\frac{4}{3}$43 or $1\frac{1}{3}$113 laps.

#### Practice questions

##### Question 1

Carl has $\frac{3}{7}$37m of ribbon. After he uses some ribbon for a present, he has $\frac{1}{4}$14m left.

How much ribbon did he use on the present?

##### Question 2

At a party, Bill makes a drink by combining $5\frac{1}{3}$513L of water with $1\frac{1}{2}$112L of cordial.

What is the total amount of the drink?

##### Question 3

Jack is making bags for his friends. He has $3\frac{1}{2}$312m of fabric.

If each bag requires $\frac{2}{5}$25m of fabric, how many bags can he make?

### Outcomes

#### ACMNA153

Solve problems involving addition and subtraction of fractions, including those with unrelated denominators

#### ACMNA154

Multiply and divide fractions and decimals using efficient written strategies and digital technologies

#### ACMNA155

Express one quantity as a fraction of another, with and without the use of digital technologies