Order of Operations — Grade 6 Math 練習ワークシート

Grade 6 ふつう 10問

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 $(7 + 5) \times 2$ , you add inside the parentheses before multiplying, so the value is $24$ , not $17$ .

Exponents are evaluated right after parentheses and before multiplying or dividing: in $5 + 3^2$ , square the $3$ first to get $5 + 9 = 14$ . 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 $2[(3 + 1) \times 5]$ . Work from the innermost group outward, one layer at a time, and rewrite the expression after each step so you can track your work.

練習するスキル

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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練習ワークシート：Order of Operations

指示： 各問題を丁寧に解きましょう。途中式もはっきりと書きましょう。最終的な答えは、指定された場所または指示に従って別の用紙に書いてください。

1. $12 + 8 \div 4 \times 3$

Order of Operations — 練習ワークシート（続き）

2. $(15 - 6) \times 2 + 7$
3. $5^2 - 3 \times 4 + 6$

Order of Operations — 練習ワークシート（続き）

4. $24 \div (8 - 2) + 3 \times 5$
5. $7 + 2 \times (9 - 4)^2$

Order of Operations — 練習ワークシート（続き）

6. $36 \div 6 \times 2 + 8 - 5$

Order of Operations — 練習ワークシート（続き）

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 — 練習ワークシート（続き）

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.
9. $18 + 2 \times (10 - 6) \div 4$

Order of Operations — 練習ワークシート（続き）

10. $4^3 \div 8 + 6 \times (3 + 1) - 5$

解答集

1.

$12 + 8 \div 4 \times 3 = 12 + 2 \times 3 = 12 + 6 = 18$

最終回答： 18
2.

$(15 - 6) \times 2 + 7 = 9 \times 2 + 7 = 18 + 7 = 25$

最終回答： 25
3.

$5^2 - 3 \times 4 + 6 = 25 - 12 + 6 = 13 + 6 = 19$

最終回答： 19
4.

$24 \div (8 - 2) + 3 \times 5 = 24 \div 6 + 15 = 4 + 15 = 19$

最終回答： 19
5.

$7 + 2 \times (9 - 4)^2 = 7 + 2 \times 5^2 = 7 + 2 \times 25 = 7 + 50 = 57$

最終回答： 57
6.

$36 \div 6 \times 2 + 8 - 5 = 6 \times 2 + 8 - 5 = 12 + 8 - 5 = 20 - 5 = 15$

最終回答： 15
7.

Expression: $4 \times 12 - 3 \times 8 = 48 - 24 = 24$

最終回答： 24 cookies left

解答集（続き）

8.

Expression: $50 - (3 \times 4 + 2 \times 2) = 50 - (12 + 4) = 50 - 16 = 34$

最終回答： $34 left
9.

$18 + 2 \times (10 - 6) \div 4 = 18 + 2 \times 4 \div 4 = 18 + 8 \div 4 = 18 + 2 = 20$

最終回答： 20
10.

$4^3 \div 8 + 6 \times (3 + 1) - 5 = 64 \div 8 + 6 \times 4 - 5 = 8 + 24 - 5 = 32 - 5 = 27$

最終回答： 27

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避けるべきよくある間違い

Adding before multiplying, as in $3 + 4 \times 5$
Computing $3^2$ as $6$ instead of $9$
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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