We simplify algebraic expressions following the same order of operations as for numeric expressions. That is,
- Simplify any expression in brackets first.
- Simplify any powers.
- Simplify any multiplication or division from left to right.
- Simplify any addition or subtraction from left to right.
Worked example
example 1
Simplify $\frac{8xy+16xy}{30yz-9yz}$8xy+16xy30yz−9yz.
Think: The numerator and denominator count as being inside brackets, so we want to simplify each of them before we simplify the fraction.
Do:
| $\frac{8xy+16xy}{30yz-9yz}$8xy+16xy30yz−9yz | $=$= | $\frac{24xy}{30yz-9yz}$24xy30yz−9yz |
Simplify the addition in the numerator |
| $=$= | $\frac{24xy}{21yz}$24xy21yz |
Simplify the subtraction in the denominator |
|
| $=$= | $\frac{8x}{7z}$8x7z |
Simplify the fraction by cancelling the common factor of $3y$3y |
Reflect: The order of operations was the same as for a numerical expression.
We simplify algebraic expressions following the same order of operations as for numeric expressions. That is,
- Simplify any expression in brackets first.
- Simplify any powers.
- Simplify any multiplication or division from left to right.
- Simplify any addition or subtraction from left to right.
Practice questions
Question 1
Simplify the expression $2t+4\times8t$2t+4×8t.
Question 2
Simplify the expression $12u\div3-2u$12u÷3−2u.
Question 3
Simplify the expression $\left(13a+15a\right)\div7$(13a+15a)÷7.
Equivalent expressions
Simplified expressions are equivalent to the original expression. But there are many ways to write an equivalent expression.
Worked example
example 2
Write three equivalent expressions to the expression: $4(2x-6)+8x.$4(2x−6)+8x.
Think: One way we could find an equivalent expression is just by separating the $8x$8x into two terms.
Do: So an equivalent expression would be: $4(2x-6)+3x+5x$4(2x−6)+3x+5x.
Think: Another way we could find an equivalent expression is just by expanding the brackets.
Do:
| $4(2x-6)+8x$4(2x−6)+8x | $=$= | $8x-24+8x$8x−24+8x |
Think: To get a third equivalent expression we can just simplify the previous expression.
Do: $8x-24+8x=16x-24$8x−24+8x=16x−24.
So an equivalent expression does not have to be in simplest form.