Middle Years

# 2.03 Simplifying expressions

Lesson

We simplify algebraic expressions following the same order of operations as for numeric expressions. That is,

1. Simplify any expression in brackets first.
2. Simplify any powers.
3. Simplify any multiplication or division from left to right.
4. Simplify any addition or subtraction from left to right.

#### Worked Example

Simplify $\frac{8xy+16xy}{30yz-9yz}$8xy+16xy30yz9yz.

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.

Summary

We simplify algebraic expressions following the same order of operations as for numeric expressions. That is,

1. Simplify any expression in brackets first.
2. Simplify any powers.
3. Simplify any multiplication or division from left to right.
4. 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÷​32u.

##### Question 3

Simplify the expression $\left(13a+15a\right)\div7$(13a+15a)÷​7.