3.01 Simplifying expressions
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
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.