2.08 Solve contextual problems with fractions

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

Question 2

Question 3