Grade 6

2.05 Problem solving with fractions

Ideas

Problem solving with fractions

Problem solving 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.

We can use keywords to help us work out which operation we need to use to solve the problem. Some keywords in the story could be:

addition	subtraction	multiplication	division
more	less	product	equally shared
add	subtract	by	in each
all together	how many left	times	per
total	difference	groups of	divided by

Examples

Example 1

At a party, Bill makes a drink by combining 5 \, \dfrac{1}{3} \text{ L} of water with 1 \, \dfrac{1}{2} \text{ L} juice concentrate.

What is the total amount of the drink?

Worked Solution

Create a strategy

Identify the keyword in the story. The word "total" tells us we need to add the amounts for each part of the drink.

Apply the idea

\displaystyle \text{Total}	\displaystyle =	\displaystyle 5 \, \dfrac{1}{3} + 1 \, \dfrac{1}{2}	Add the values
	\displaystyle =	\displaystyle 5 + \dfrac{1}{3} + 1 + \dfrac{1}{2}	Split the mixed numbers into whole and fraction parts
	\displaystyle =	\displaystyle 6 + \dfrac{1}{3} + \dfrac{1}{2}	Evaluate
	\displaystyle =	\displaystyle 6 + \dfrac{1 \times 2}{3 \times 2} + \dfrac{1 \times 3}{2 \times 3}	Multiply to have the same denominator
	\displaystyle =	\displaystyle 6 + \dfrac{2}{6} + \dfrac{3}{6}	Evaluate
	\displaystyle =	\displaystyle 6 + \dfrac{2 + 3}{6}	Add the numerators over the common denominator
	\displaystyle =	\displaystyle 6 + \dfrac{5}{6}	Evaluate
	\displaystyle =	\displaystyle 6 \, \dfrac{5}{6} \text{ L}	Simplify

Example 2

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?

Express your answer as an improper fraction.

Worked Solution

Create a strategy

Identify the keyword in the story. The word "each" tells us we need to divide the length of fabric by the amount needed for each bag.

Apply the idea

\displaystyle \text{Number}	\displaystyle =	\displaystyle \dfrac{7}{2} \div \dfrac{2}{5}	Divide the values
	\displaystyle =	\displaystyle \dfrac{7}{2} \times \dfrac{5}{2}	Rewerite as multiplication using the reciprocal
	\displaystyle =	\displaystyle \dfrac{7 \times 5}{2 \times 2}	Multiply the numerators and denominators separately
	\displaystyle =	\displaystyle \dfrac{35}{4}	Simplify

Idea summary

Use keywords to help you identify which operation to use:

addition	subtraction	multiplication	division
more	less	product	equally shared
add	subtract	by	in each
all together	how many left	times	per
total	difference	groups of	divided by

Outcomes

6.NS.A.1

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g. By using visual fraction models and equations to represent the problem.