Not all mathematics questions come in the form of an equation. Sometimes we are presented with a real world problem and we want to translate the words into mathematics, so that we can solve the problem

Part of solving word problems comes from understanding the information we are given by reading it carefully, and correctly deciding which mathematical operations to perform. In this lesson we will look at how to turn word problems into a mathematical statement.

Following on from writing mathematical statements with whole numbers , we can see that the arithmetic operations we use can be expressed with words.

An image showing different ways we can refer to the four basic operations. Ask your teacher for more information.

Examples

Example 1

On Grace's farm, there are 6 cows and 9 goats. How many animals are there altogether?

Worked Solution

Create a strategy

The word "altogether" here indicates addition.

Apply the idea

\displaystyle \text{Number of animals}	\displaystyle =	\displaystyle 6+9	Add the number of cows and goats
	\displaystyle =	\displaystyle 15	Evaluate

There are 15 animals altogether.

Example 2

I scored 7 goals in my netball match. Eileen scored twice as many as me. How many goals did Eileen score?

Worked Solution

Create a strategy

The phrase "twice as many" indicates multipication by 2.

Apply the idea

\displaystyle \text{Eileen's score}	\displaystyle =	\displaystyle 7\times2	Multiply by 2
	\displaystyle =	\displaystyle 14	Evaluate

Ellen scored 14 goals.

Example 3

The number of motor accidents at a particular intersection was reported by traffic police to be 45 last year. The local council then decided to put up warning signs for motorists approaching this intersection. The following year the police reported only 29 accidents there.

How many fewer accidents were there after the signs were introduced?

Worked Solution

Create a strategy

The phrase "How many fewer" indicates subtraction. Find the difference in the number of accidents between last year and the following year using the subtraction vertical algorithm method.

Apply the idea

Write the subtraction in a vertical algorithm.\begin{array}{c} & &4 &5 \\ &- &2 &9 \\ \hline & \\ \hline \end{array}

Subtract the numbers using trading where necessary:\begin{array}{c} & &3 & \text{}^1 5 \\ &- &2 &9 \\ \hline & &1 & 6 \\ \hline \end{array}

There were 16 fewer accidents after the signs were introduced.

Idea summary

To help determine what arithmetic operations should be used to solve a problem, we should look for key words that correspond to the basic operations.

1.06 Solving contextual problems with whole numbers

Ideas

Contextual problems with whole numbers

Examples

Example 1

Example 2

Example 3

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