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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?

  1. Give your answer as an improper fraction.

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

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