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.
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.
There are n oranges to be divided equally among 5 people. How many oranges does each person get?
SolutionEach person receives n ÷ 5 oranges.
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?
There are 3 × x = 3x marbles in total.
The following table gives the meanings of some commonly occurring 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.)