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Pre-Algebra

Order of Operations

Lesson

When an expression has more than one operation, the answer depends on the order we do them in. To make sure everyone gets the same answer, math has a fixed order — often remembered as PEMDAS:

  • Parentheses (and other grouping symbols) first
  • Exponents next
  • Multiplication and Division — left to right, whichever comes first
  • Addition and Subtraction — left to right, whichever comes first

Important: multiplication and division are at the same level— you don’t do all multiplication before division. You go left to right and do whichever you see first. Same with addition and subtraction.

Worked example 1

3+4×53 + 4 \times 5

Multiplication before addition: 4×5=204 \times 5 = 20, then 3+203 + 20.

=23= 23

Worked example 2

(2+3)2−6÷2(2 + 3)^2 - 6 \div 2

Parentheses first: 2+3=52 + 3 = 5.

=52−6÷2= 5^2 - 6 \div 2

Exponent next: 52=255^2 = 25.

=25−6÷2= 25 - 6 \div 2

Division before subtraction: 6÷2=36 \div 2 = 3.

=25−3=22= 25 - 3 = 22

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

4+3×24 + 3 \times 2

Problem 2

9−2×39 - 2 \times 3

Problem 3

8+10÷28 + 10 \div 2

Problem 4

20÷4+120 \div 4 + 1

Practice

Standard problems matching the lesson.

Problem 5

3+4×23 + 4 \times 2

Problem 6

10−6÷210 - 6 \div 2

Problem 7

(2+5)×3(2 + 5) \times 3

Problem 8

2+322 + 3^2

Problem 9

8−2×38 - 2 \times 3

Problem 10

12÷4+512 \div 4 + 5

Problem 11

(4+6)÷2(4 + 6) \div 2

Problem 12

5+2×325 + 2 \times 3^2

Problem 13

20−(3+5)20 - (3 + 5)

Problem 14

(8−3)2+4(8 - 3)^2 + 4

Problem 15

(18÷3)×2(18 \div 3) \times 2

Problem 16

6+(10−4)÷36 + (10 - 4) \div 3

Problem 17

23+4×52^3 + 4 \times 5

Problem 18

(7−2)×(3+1)(7 - 2) \times (3 + 1)

Problem 19

3×12+73 \times 12 + 7

Problem 20

5+2×65 + 2 \times 6

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 21

2×(3+4)2−102 \times (3 + 4)^2 - 10

Problem 22

(4+2)2÷3−7(4 + 2)^2 \div 3 - 7

Problem 23

5×(8−3)+235 \times (8 - 3) + 2^3

Problem 24

50−2×(3+4)50 - 2 \times (3 + 4)

Problem 25

100÷(2×5)+32100 \div (2 \times 5) + 3^2

Problem 26

3×(2+1)2−4×53 \times (2 + 1)^2 - 4 \times 5

Problem 27

15×20−4×515 \times 20 - 4 \times 5

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