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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.

Picture of a pencil case plus three pencils

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?


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?


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?

3 boxes containing x number of marbles


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


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.)