Order of Operations — Fiche d'exercices de Grade 6 Math

Grade 6 Difficulté moyenne 10 problèmes

The order of operations is the set of rules that makes everyone evaluate an expression the same way. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), then Addition and Subtraction (from left to right).

Parentheses come first because they mark a part of the expression that must be treated as a single value. In (7+5)×2(7 + 5) \times 2, you add inside the parentheses before multiplying, so the value is 2424, not 1717.

Exponents are evaluated right after parentheses and before multiplying or dividing: in 5+325 + 3^2, square the 33 first to get 5+9=145 + 9 = 14. Multiplication and division share the same rank, and so do addition and subtraction, so within each pair you simply work from left to right.

Nested expressions place one set of grouping symbols inside another, such as 2[(3+1)×5]2[(3 + 1) \times 5]. Work from the innermost group outward, one layer at a time, and rewrite the expression after each step so you can track your work.

Compétences travaillées

  • Applying PEMDAS to multi-step expressions
  • Evaluating exponents before multiplying or dividing
  • Working left to right for operations of equal rank
  • Simplifying parentheses and nested brackets
  • Rewriting expressions step by step to avoid errors
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Fiche d'exercices : Order of Operations

Consignes : Résous chaque problème avec soin. Montre clairement tout ton travail. Écris ta réponse finale dans l'espace prévu ou sur une feuille séparée comme indiqué.

  1. 1.12+8÷4×312 + 8 \div 4 \times 3

Order of Operations — Fiche d'exercices (suite)

  1. 2.(15−6)×2+7(15 - 6) \times 2 + 7
  2. 3.52−3×4+65^2 - 3 \times 4 + 6

Order of Operations — Fiche d'exercices (suite)

  1. 4.24÷(8−2)+3×524 \div (8 - 2) + 3 \times 5
  2. 5.7+2×(9−4)27 + 2 \times (9 - 4)^2

Order of Operations — Fiche d'exercices (suite)

  1. 6.36÷6×2+8−536 \div 6 \times 2 + 8 - 5

Order of Operations — Fiche d'exercices (suite)

  1. 7.A bakery makes 4 batches of cookies. Each batch has 12 cookies. The bakery sells 3 boxes of cookies, and each box contains 8 cookies. Write an expression to represent the number of cookies left, then evaluate it using the order of operations.

Order of Operations — Fiche d'exercices (suite)

  1. 8.Sarah has $50. She buys 3 notebooks that cost $4 each and 2 pens that cost $2 each. Write an expression to represent how much money Sarah has left, then evaluate it.
  2. 9.18+2×(10−6)÷418 + 2 \times (10 - 6) \div 4

Order of Operations — Fiche d'exercices (suite)

  1. 10.43÷8+6×(3+1)−54^3 \div 8 + 6 \times (3 + 1) - 5

Corrigé

  1. 1.
    12+8÷4×3=12+2×3=12+6=1812 + 8 \div 4 \times 3 = 12 + 2 \times 3 = 12 + 6 = 18
    Réponse finale : 18
  2. 2.
    (15−6)×2+7=9×2+7=18+7=25(15 - 6) \times 2 + 7 = 9 \times 2 + 7 = 18 + 7 = 25
    Réponse finale : 25
  3. 3.
    52−3×4+6=25−12+6=13+6=195^2 - 3 \times 4 + 6 = 25 - 12 + 6 = 13 + 6 = 19
    Réponse finale : 19
  4. 4.
    24÷(8−2)+3×5=24÷6+15=4+15=1924 \div (8 - 2) + 3 \times 5 = 24 \div 6 + 15 = 4 + 15 = 19
    Réponse finale : 19
  5. 5.
    7+2×(9−4)2=7+2×52=7+2×25=7+50=577 + 2 \times (9 - 4)^2 = 7 + 2 \times 5^2 = 7 + 2 \times 25 = 7 + 50 = 57
    Réponse finale : 57
  6. 6.
    36÷6×2+8−5=6×2+8−5=12+8−5=20−5=1536 \div 6 \times 2 + 8 - 5 = 6 \times 2 + 8 - 5 = 12 + 8 - 5 = 20 - 5 = 15
    Réponse finale : 15
  7. 7.
    Expression: 4×12−3×8=48−24=244 \times 12 - 3 \times 8 = 48 - 24 = 24
    Réponse finale : 24 cookies left

Corrigé (suite)

  1. 8.
    Expression: 50−(3×4+2×2)=50−(12+4)=50−16=3450 - (3 \times 4 + 2 \times 2) = 50 - (12 + 4) = 50 - 16 = 34
    Réponse finale : $34 left
  2. 9.
    18+2×(10−6)÷4=18+2×4÷4=18+8÷4=18+2=2018 + 2 \times (10 - 6) \div 4 = 18 + 2 \times 4 \div 4 = 18 + 8 \div 4 = 18 + 2 = 20
    Réponse finale : 20
  3. 10.
    43÷8+6×(3+1)−5=64÷8+6×4−5=8+24−5=32−5=274^3 \div 8 + 6 \times (3 + 1) - 5 = 64 \div 8 + 6 \times 4 - 5 = 8 + 24 - 5 = 32 - 5 = 27
    Réponse finale : 27
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Erreurs fréquentes à éviter

  • Adding before multiplying, as in 3+4×53 + 4 \times 5
  • Computing 323^2 as 66 instead of 99
  • Ignoring parentheses and working strictly left to right
  • Multiplying before dividing when the division comes first on the left
  • Evaluating outer brackets before inner parentheses

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