topic badge
Middle Years

2.08 Solve contextual problems with fractions

Worksheet
Applications of fractions
1

Sharon walks \dfrac{2}{5} of a kilometre and runs \dfrac{1}{7} of a kilometre to get to school. How many kilometres does she travel?

2

Carl has \dfrac{3}{7}\text{ m} of ribbon. After he uses some ribbon for a present, he has \dfrac{1}{4}\text{ m} left.

How much ribbon did he use on the present?

3

For a project, Ivan needs to cut a metal rod such that the longer piece is three times the length of the shorter piece.

a

What fraction of the rod's total length will be made up of the shorter piece?

b

If the rod is \dfrac{3}{8}\text{ m} long, what is the length of the shorter piece?

4

Bianca has \dfrac{5}{6} \text{ kg} of beads. She shares the beads evenly between 3 friends. How many kilograms does each friend receive?

5

At a party, Bill makes a drink by combining 5\dfrac{1}{3} \text{ L} of water with 1\dfrac{1}{2} \text{ L} of cordial. What is the total amount of litres in the mixed drink?

6

Skye wants to decorate her window sill with fairy lights. The window sill is 3\dfrac{4}{9}\text{ m} wide. If she only has 2\dfrac{1}{8}\text{ m} of fairy lights, how much of the window sill will not be decorated?

7

Katrina takes 3\dfrac{2}{3} minutes to drive from her home to the local shopping centre. She spends \dfrac{1}{4} of this time waiting at traffic lights. Find the number of minutes she spends waiting.

8

Jack is making bags for his friends. He has 3\dfrac{1}{2}\text{ m} of fabric. If each bag requires \dfrac{2}{5}\text{ m} of fabric, how many bags can he make?

9

At the Easter Show, Tobias spends \dfrac{2}{4} of an hour visiting chickens and \dfrac{3}{9} of an hour visiting alpacas. How much time has he spent visiting animals?

10

Caitlin runs a cafe and is interested in the drink choices of her customers. She finds that 3 out of 4 customers order hot chocolate. If she has 4000 customers on a particular day, how many hot chocolates would she expect to sell?

11

A bag of oranges weighing \dfrac{8}{9} \text{ kg} was divided among 6 children. What was the mass of the oranges given to each child?

12

Tricia attends a 3-hour painting class. The instructor uses \dfrac{12}{14} of an hour to discuss colour mixing and then allows students to use the rest of class time to complete a painting. How much time does Tricia have left to finish her work?

13

Katrina and Luigi ordered a pizza to share. Katrina ate \dfrac{3}{7} of the pizza while Luigi ate \dfrac{1}{2}.

a

Who ate more pizza?

b

What fraction of the pizza did they eat together?

c

What fraction of pizza is left?

14

Luke has a dice tin that is \dfrac{1}{4} full. He puts 8 extra dice in and the tin is now \dfrac{1}{3} full.

a

What fraction of the tin do the 8 extra dice take up?

b

How many dice can fit inside the tin?

15

Victoria borrows a 360-page novel from the library. She reads \dfrac{3}{4} of the novel.

a

How many pages did she read?

b

How many more pages does she have to read to finish her novel?

16

Christa is creating a 3 minute slide show with pictures from her holiday. Each picture will be displayed for 4\dfrac{1}{2} seconds.

a

How many seconds are in 3 minutes?

b

How many pictures can she show in 3 minutes?

17

Danielle is studying for three tests. She studies science for 3\dfrac{1}{4} hours, English for \dfrac{2}{5} of an hour and visual arts for \dfrac{1}{4} of an hour. How many hours does she spend studying?

18

Homer works as an accountant and is at the office for 7\dfrac{1}{2} hours each day. He eats lunch with his colleagues for \dfrac{5}{6} hours each day. How much time does he spend working in one day?

19

In a school debate, each speaker was allowed 1\dfrac{6}{7} minutes. How many speakers participated if the debate went for 26 minutes?

20

Paul delivers online orders to customers for 6\dfrac{5}{8} hours each weekday.

a

Over the five weekdays, how many hours does he work?

b

On Saturdays he works half the time of a weekday. How many hours does he work on a Saturday?

c

How many hours in total does he work in one week if he does not work on Sundays?

21

Han spent \dfrac{1}{8} of his money on a printer and \dfrac{1}{5} of his money on a table.

a

What fraction of his total money did Han spend?

b

What fraction of Han's money does he still have?

22

In a survey of 270 people, \dfrac{1}{10} said their favourite sport was soccer, and \dfrac{1}{9} said their favourite sport was tennis.

a

Calculate the total fraction of people who said their favourite sport was soccer or tennis.

b

Calculate the fraction of people who did not put soccer or tennis as their favourite sport.

c

Calculate the number of people who did not put soccer or tennis as their favourite sport.

23

In a class with 40 students, \dfrac{2}{5} of the class are boys.

a

What fraction of the class are girls?

b

How many girls are in the class?

24

An engineer is estimating the length and width of a room using the length of his steps. The length of the room is \dfrac{4}{5} of the width. He determined that the width is about 27 steps and that one of his steps is \dfrac{2}{3} \text{ m} long. Find the length of the room.

25

Two cars leave home at the same time travelling south. Car A travels at the rate of 83 \dfrac{1}{4} \text{ km/h} while Car B is at 88 \dfrac{3}{4} \text{ km/h}. If both cars continue to travel at these speeds in the same direction, how far apart will the two cars be at the end of 4 hours?

26

About \dfrac{3}{10} of the cars in a city are less than 5 years old. About \dfrac{1}{5} of the cars are between 5 and 10 years old. If there is a total of 1200 cars registered in the city, find the number of cars that are greater than 10 years old.

27

The mall parking lot has 800 parking spaces. \dfrac{1}{4} of the parking spaces are for cars. On a particular day there were 200 cars and some trucks in the parking lot. The parking lot was \dfrac{5}{8} full. How many trucks were in the parking lot?

Sign up to access Worksheet
Get full access to our content with a Mathspace account

What is Mathspace

About Mathspace