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4.07 Story problems with mixed operations


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Let's try this problem to practice reading a story problem and then  writing the number sentence  that we would use to solve it.


Example 1

Dylan has 120 chocolates to give out to 10 guests at his birthday party and wants to make sure each guest gets the same amount.

Write a number sentence for this story problem to find how much each guest would get.

Worked Solution
Create a strategy

Dylan needs to equally share the chocolates, so we need to use division.

Apply the idea

Dylan needs to share or divide 120 chocolates into 10 equal groups. So he needs to divide 120 by 10.

Number sentence =120\div 10

Idea summary

If we know our total and want to find out how many groups we have, or how many are in each group, we need to divide.

Story problems with multiplication and division

We can use numbers, pictures and symbols to solve number problems. Let's see how we can solve multiplication and division in this video.

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Example 2

Sally and her mum were at home. Her grandma came around to visit, then her dad and brother came home together.


Which number sentence matches the number of people in the house?

Worked Solution
Create a strategy

We need to add the number of people who came home.

Apply the idea

There are two people in the house at the start, Sally and here mum.

Then one more person arrived, grandma.

Then two more people arrived, Sally's dad and brother.

We can say that the correct number sentence is 2+1+2, so the correct option is C.


How many people are in the house altogether?

Worked Solution
Create a strategy

Use the number sentence in part (a).

Apply the idea
\displaystyle \text{Number of people}\displaystyle =\displaystyle 2+1+2Use the number sentence
\displaystyle =\displaystyle 5Add the numbers
Idea summary

Mathematical problems can be represented with words, pictures and symbols.

Story problems with mixed operations

Sometimes we need more than one step to solve a number problem, so it helps to look at how to work through each step.

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Example 3

Charlie has 50 cm of ribbon, which he cuts into 10 equal pieces.

He then selects one of these pieces, and cuts 2 cm off it.

How long is this piece of ribbon now?

Worked Solution
Create a strategy

For the first sentence, the ribbon is being shared so we will use division. For the second sentence a length is being taken away so we will use subrtraction.

Apply the idea

Divide 50 into 10 equal shares.

\displaystyle \text{Length of pieces}\displaystyle =\displaystyle 50\div 10Write the number sentence
\displaystyle =\displaystyle 5Divide by 10

So the length of each of the 5 pieces is 5 cm.

Now we need to subtract 2 cm from this 5 cm length.

\displaystyle \text{Cut length}\displaystyle =\displaystyle 5-2Write the number sentence
\displaystyle =\displaystyle 3\text{ cm}Subtract 2 from 5
Idea summary
  • If our problem has equal groups and we need to find a total, we use multiplication.

  • If we have to share our total into equal groups, we use division.



uses mental and written strategies for addition and subtraction involving two-, three-, four and five-digit numbers


uses mental and informal written strategies for multiplication and division

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