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Year 7

Priority of operations with positive and negative integers and decimals

I can calculate using priority of operations, including brackets, powers and exponents with positive and negative integers and decimals.

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Year 7

Priority of operations with positive and negative integers and decimals

I can calculate using priority of operations, including brackets, powers and exponents with positive and negative integers and decimals.

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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. Division and multiplication have the same priority
  2. With addition and subtraction, subtractions can all be re-written as additions of the additive inverse
  3. Brackets make the priority much clearer and avoid ambiguity
  4. Sometimes brackets can be implicit

Keywords

  • Additive inverse - The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

  • Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

Common misconception

The use of negatives are confused with subtractions.

Writing the negative numbers in brackets and using the additive inverse will help minimise errors.


To help you plan your year 7 maths lesson on: Priority of operations with positive and negative integers and decimals, download all teaching resources for free and adapt to suit your pupils' needs...

A class task will be to give all the pupils the numbers 12, 10, 1.4, 2.8, 6.2 and 3. They can use any operation and use the additive inverse of these numbers to make a randomly chosen 3 digit number. They can use the same number more than once.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which operation is last in the priority of operations?
Brackets
Roots and exponents
Multiplication and division
Correct answer: Addition and subtraction
Q2.
The __________ of a number is a number that, when added to the original number, gives the sum of 0
opposite
negative
Correct answer: additive inverse
reciprocal
Q3.
Without using a calculator, work out: $$11\times5 - 2\times3 =$$
Correct Answer: 49
Q4.
Without using a calculator, work out: $$3000\;–\;(54\;–\;4)\times2\times5^2 =$$
Correct Answer: 500
Q5.
Select the calculation with an answer of 1
$$(4+5)\times(6+7)$$
$$4\times(5+6)\times7$$
$$4+5\times(6+7)$$
Correct answer: $$(4-5)\times6+7$$
Q6.
Work out the value of $$12 + 3 \times 10 - 8 + 1$$
Correct answer: 35
143
33
141

Exit quiz

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6 Questions

Q1.
Using the priority of operations, work out: $$20-(-5)\times10 =$$
Correct Answer: 70
Q2.
Using the priority of operations, work out: $$100+(-50)\times2=$$
Correct Answer: 0, zero
Q3.
Using the priority of operations, work out the answer to $$(-8)+30\div2 =$$
Correct Answer: 7
Q4.
Starting with the calculation with the lowest answer, put these calculations in order of size from lowest answer to highest answer.
1 - $$10-3\times3$$
2 - $${200+(-60)} \over {10-(-10)}$$
3 - $$10-(-4)\times2$$
4 - $$(-12)\div(-3) + 4^2$$
Q5.
Without using a calculator, evaluate $$10+(-9)\div (-3)-(- 4) $$
Correct Answer: 17
Q6.
Without using a calculator, evaluate $$9.4 -3.2+ \frac {12^2} {\sqrt{75+25}}$$
Correct Answer: 20.6