AI TutorHigh School
SAT
ACT
University
MCAT
LSAT
DAT
Wize High School Grade 9 Math Textbook > Rational Numbers

Review - Order of Operations

Intro to Rational NumbersNext Section
Popular Courses
Find My Course
0:00 / 0:00

Order of Operations - BEDMAS

When numbers are being added, subtracted, multiplied, and divided, we need to be careful with the order we do our calculations.

*Some teachers call this PEDMAS, where P is "Parentheses" , which is same as Brackets
  1. We always start by simplifying (calculating) whatever is inside brackets
  2. Then, we simplify any exponents AND SQUARE ROOTS (\sqrt{\boxed{}})
  3. Next, we go from left to right, and simplify anything that is being divided or multiplied
  4. Finally, we go from left to right, and simplify anything that is being added or subtracted
PAGE BREAK
Example
Simplify 15−3×4+2(3+2)2+6÷215-3\times4+2\left(3+2\right)^2+6\div2.

15−3×4+2(3+2)⏟Brackets2+6÷215-3\times4+2{\underbrace{\bco{\left(3+2\right)}}_{\text{Brackets}}}^2 +6\div2

=15−3×4+2(5)2+6÷2=15-3\times4+2(\bco{5})^2+6\div2

=15−3×4+2(5)2⏟Exponents+6÷2=15-3\times 4+2\underbrace{\bct{(5)^2}}_\text{Exponents}+6\div2

=15−3×4+2(25)+6÷2=15-3\times 4+2(\bct{25})+6\div2

=15−3×4⏟Multiplication+2(25)⏟Multiplication+6÷2⏟Division=15-\underbrace{\bcth{3\times4}}_\text{Multiplication}+\underbrace{\bcth{2(25)}}_\text{Multiplication}+\underbrace{\bcth{6\div2}}_\text{Division}

=15−12+50+3=15-\bcth{12}+\bcth{50}+\bcth{3}

=15−12+50+3⏟Do the Addition & Subtraction from left to right=\underbrace{\bcfi{15-12+50+3}}_\text{Do the Addition \& Subtraction from left to right}

=56=\boxed{56}
0:00 / 0:00

Example: Order of Operations

Simplify 5(2)+402−(4−1)(2×3−22)35(2)+\dfrac{40}{2}-(\sqrt4-1)(2\times3-2^2)^3.

5(2)+402−(4−1)⏟Brackets(2×3−22)3⏟Bracket5(2)+\dfrac{40}{2}-\underbrace{\bco{(\sqrt4-1)}}_\text{Brackets}{{\underbrace{\bco{(2\times 3-2^2)}^3}_\text{Bracket}}}

=5(2)+402−(4−1)⏟BracketsDeal with Square Roots first(2×3−22)3⏟BracketsDeal with Exponents first=5(2)+\dfrac{40}{2}-\underbrace{\bco{(\colorbox{yellow}{$\sqrt4$}-1)}}_{\begin{array}{c}\scriptsize\text{Brackets}\\\scriptsize\colorbox{yellow}{\text{Deal with Square Roots first}}\end{array}}{{\underbrace{\bco{(2\times 3-\colorbox{yellow}{$2^2$})}^3}_{\begin{array}{c}\scriptsize\text{Brackets}\\\scriptsize\colorbox{yellow}{\text{Deal with Exponents first}}\end{array}}}}

=5(2)+402−(2−1)⏟Brackets(2×3−4)3⏟BracketsDeal with Multiplication next=5(2)+\dfrac{40}{2}-\underbrace{\bco{(2-1)}}_\text{Brackets}{{\underbrace{\bco{(\colorbox{yellow}{$2\times 3$}-4)}^3}_{\begin{array}{c}\scriptsize\text{Brackets}\\\scriptsize\colorbox{yellow}{\text{Deal with Multiplication next}}\end{array}}}}

=5(2)+402−(2−1)⏟Brackets(6−4)⏟Braclet3=5(2)+\dfrac{40}{2}-\underbrace{\bco{(2-1)}}_\text{Brackets}{{{\underbrace{\bco{({6}-4)}}_\text{Braclet}}}^3}

=5(2)+402−(1)(2)3=5(2)+\dfrac{40}{2}-\bco{(1)}\bco{(2)}^3

=5(2)+402−(1)(2)3⏟Exponent=5(2)+\dfrac{40}{2}-(1)\underbrace{\bct{(2)^3}}_\text{Exponent}

=5(2)+402−(1)(8)=5(2)+\dfrac{40}{2}-(1)\bm(\colorTwo{8})

=5(2)⏟Multiplication+402⏟Division−(1)(8)⏟Multiplication=\underbrace{\bcth{5(2)}}_\text{Multiplication}+\underbrace{\bcth{\dfrac{40}{2}}}_\text{Division}-\underbrace{\bcth{(1)(8)}}_\text{Multiplication}

=10+20−8=\bcth{10}+\bcth{20}-\bcth{8}

=10+20−8⏟Do the Addition & Subtraction from left to right=\underbrace{\bcfi{10+20-8}}_\text{Do the Addition \& Subtraction from left to right}

=22=\boxed{22}

Practice: Order of Operations

Without using a calculator, evaluate 23+7(14−6)2^3+7\left(14-6\right).

Practice: Order of Operations

Without using a calculator, evaluate 5×44−3(4+2×3)225\times44-\dfrac{3\left(4+2\times 3\right)^2}{2}.

Practice: Order of Operations

Simplify 32+2(14−22×3)413−253^2+\dfrac{2(14-2^2\times 3)^4}{13-\sqrt{25}}.