Example 1

Joe has a pencil case that contains an unknown number of pencils. He has three other pencils. Let x be the number of pencils in the pencil case. Then Joe has x + 3 pencils altogether.

Example 2

Theresa takes 5 chocolates from a box with a large number of chocolates in it. How many chocolates are left in the box?

Solution

Let z be the original number of chocolates in the box.

Theresa takes 5 chocolates so there are z – 5 chocolates left in the box.

Example 3

There are n oranges to be divided equally among 5 people. How many oranges does each person get?

Solution

Each person receives n ÷ 5 oranges.

Example 4

There are three boxes each with the same number of marbles in them. If there are \(x\) marbles in each box, how many marbles are there in total?

Solution

There are 3 × x = 3x marbles in total.

Summary

The following table gives the meanings of some commonly occurring algebraic expressions.

Common algebraic expressions

\(x\) + 3	The sum of \(x\) and 3 3 added to \(x\), or \(x\) added to 3 3 more than \(x\), or \(x\) more than 3
\(x\) – 3	The difference of \(x\) and 3, where \(x\) is greater than or equal to 3 3 is subtracted from \(x\) 3 less than \(x\) \(x\) minus 3
3 × \(x\)	The product of \(x\) and 3 \(x\) multiplied by 3, or 3 multiplied by \(x\)
\(x\) ÷ 3	\(x\) divided by 3 The quotient when \(x\) is divided by 3
2 × \(x\) – 3	\(x\) is first multiplied by 2 and then 3 is subtracted
\(x\) ÷ 3 − 2	\(x\) is first divided by 3 and then 2 is subtracted

Expressions with zeros and ones

Zeros and ones can often be eliminated. For example:

\(x + 0 = x\) (Adding zero does not change the number.)

\(x × 1 = x\) (Multiplying by 1 does not change the number.)