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GEMA Order of Operations

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GEMA Order of Operations

A workshop’s sorting machine has jammed. Solve each number code using GEMA: Grouping (brackets), Exponents (powers), Multiplication and division from left to right, then Addition and subtraction from left to right. Show one step per line and use one equals sign on each line.

Warm-up: Spot the First Move

For each expression, name the operation you must do first. Then solve it.

1.The first code is 3 + 2 × 4. Which operation comes first, and what is the value of the expression?

2.A panel displays (5 + 3) × 2. Choose the correct first step.

Multiply 3 by 2
Add 5 and 3 inside the brackets
Add 3 and 2

3.Solve the power code: 2³ + 4. Write the value of 2³, then finish the expression.

Crack the Codes

Work carefully through each expression. Multiplication and division have equal priority, as do addition and subtraction; when they appear together, work from left to right.

4.Find the gearbox code: 12 ÷ 3 + 2 × 5.

5.Solve the maintenance check: (8 − 3) × 2². Show the bracket step and the exponent step.

6.A trainee says the answer to 20 − 4 × 3 + 1 is 49 because they worked strictly from left to right. Explain the mistake and give the correct value.

7.The final lock shows 6 + 2 × (4 + 1). Which operation must be done first?

6 + 2
4 + 1
2 × 4

8.Complete the longer lock code: 3 × (2 + 4)² − 5. Show each GEMA step.

9.True or false? In 18 ÷ 3 × 2, you must multiply before dividing. Give the correct value.

TrueFalse

10.Invent a short expression using brackets, one exponent, multiplication, and addition. Make its value 20. Write the expression and show how GEMA gives 20.

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2 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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