Translating a sentence into a multi-step equation

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Introduction

In word problems, the sentences are translated into multi-step equations for solving. This process can be best understood using examples given below.

Example 1

Translate the following sentence into an equation.

The sum of a number divided by 8 and 9 equals 3.

Solution

Step 1:

Let the number be x

Step 2:

Number divided by 8 is $\frac{x}{8}$

Step 3:

The word sum points to addition or + operation. The sum of a number divided by 8 and 9 translates to

$\frac{x}{8} + 9$

Step 4:

The word equals translates to = sign

So, The sum of a number divided by 8 and 9 equals 3 translates to

$\frac{x}{8} + 9 = 3$

Example 2

Translate the following sentence into an equation.

Nine times the difference of a number and 7 equals 4.

Solution

Step 1:

Let the number be x

Step 2:

The word difference points to subtraction or operation

So, Difference of the number and 7 is x 7

Step 3:

The word times points to multiplication or × operation

Nine times the difference of a number and 7 is 9 × (x 7) or 9(x 7)

Step 4:

The word equals translates to = sign

So, Nine times the difference of a number and 7 equals 4 translates to

9(x 7) = 4