IB MYP 3 2021 Edition
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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+16xy30yz9yz $=$= $\frac{24xy}{30yz-9yz}$24xy30yz9yz

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.

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