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Priority of operations with positive and negative integers, decimals and fractions

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

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Lesson 9 of 10

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Year 7

Priority of operations with positive and negative integers, decimals and fractions

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

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Lesson slides

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Lesson details

Key learning points

Division and multiplication have the same priority.
With addition and subtraction the convention is to move from left to right.
Brackets make the priority much clearer and avoid ambiguity.
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.

Common misconception

Priority of operations does not apply to fractions

Priority of operations applies to all numbers. They can check with a scientific calculator as the priority of operations is programmed in.

For each check and/or explanation example, do a class vote of which operation should be applied first, ensuring the priority of operations is illustrated in exercise books and/or the board. This allows them to see all the operations before voting.

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Licence

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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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
Using the priority of operations, which operations come before multiplication and division?

Correct answer: Brackets

Correct answer: Roots

Correct answer: Exponents

Addition

Subtraction or the addition of the additive inverse

Q2.
Match the calculations on the left with the correct answer on the right.

Correct Answer:$$3 + 4\times5$$,23

Correct Answer:$$4 + 3\times5$$,19

Correct Answer:$$3 + 6\div 2$$,6

Correct Answer:$$2 + 4\times5 + 5\times 1$$,27

Q3.
The priority of operations applies to:

positive and negative integers only

Correct answer: positive and negative integers, fractions and decimals

positive numbers only

Q4.
Look at the calculation using the priority of operations. Write what number is represented by the star.

Correct Answer: 24, twenty four

Q5.
Using your knowledge on the addition of fractions, work out the answer to $$\frac{11}{12}+ \left(-\frac{1}{3}\right)+ \frac{1}{4}$$.

$$\frac{13}{13}$$

Correct answer: $$\frac{5}{6}$$

$$\frac{6}{5}$$

Q6.
Using your knowledge on the addition of fractions and additive inverses, work out the answer to $$\frac{9}{10}+ \left(-\frac{1}{5}\right)+ \frac{7}{20}+ \left(-\frac{3}{10}\right)$$.

$$\frac{4}{5}$$

Correct answer: $$\frac{3}{4}$$

$$\frac{12}{15}$$

$$\frac{11}{12}$$

Assessment exit quiz

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6 Questions

Q1.
Work out $$\frac{9}{10}+ \frac{3}{5}\times \frac{1}{2} $$.

$$\frac{4}{3}$$

$$\frac{3}{4}$$

$$\frac{5}{6}$$

Correct answer: $$\frac{6}{5}$$

Q2.
Match the calculations on the left with the correct answer on the right.

Correct Answer:$$\left(\frac{2}{5}\right)^2$$,$$\frac{4}{25}$$

Correct Answer:$$\left(\frac{3}{5}\right)^2$$,$$\frac{9}{25}$$

Correct Answer:$$\left(\frac{4}{3}\right)^2$$,$$\frac{16}{9}$$

Correct Answer:$$\left(\frac{5}{6}\right)^2$$,$$\frac{25}{36}$$

Q3.
Select the correct explanation for why the following is correct.

Using the priority of operations, multiplication comes first before division.

Changing fractions to their reciprocals makes things easier.

Addition comes after multiplication.

Correct answer: When dividing, division can be written as multiplication by the reciprocal.

Q4.
Which of the following equals $$\frac{16}{25}$$?

Correct answer: $$\frac{4^2}{5^2}$$

Correct answer: $$\left(\frac{4}{5}\right)^2$$

Correct answer: $$\sqrt{{256}\over{625}}$$

Correct answer: $$\frac{4}{5}\div \frac{5}{4}$$

$$\frac{4}{5}\times 2$$

Q5.
Work out $$1 + \sqrt[3]{15 {{5} \over {8}}}\times \frac{1}{2}$$.

Correct answer: $$\frac{9}{4}$$

$$\frac{4}{9}$$

1.5

$$\frac{13}{8}$$

Q6.
Without using a calculator, work out $$3 + \frac{2}{3} - \sqrt{\frac{25}{36}}$$.

$$1 {{5} \over {6}}$$

Correct answer: $$2 {{5} \over {6}}$$

$$3 {{5} \over {36}}$$

$$3 {{25} \over {36}}$$

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Priority of operations with positive and negative integers, decimals and fractions

Priority of operations with positive and negative integers, decimals and fractions

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Using the priority of operations, which operations come before multiplication and division?

Q2.Match the calculations on the left with the correct answer on the right.

Q3.The priority of operations applies to:

Q4.Look at the calculation using the priority of operations. Write what number is represented by the star.

Q5.Using your knowledge on the addition of fractions, work out the answer to $$\frac{11}{12}+ \left(-\frac{1}{3}\right)+ \frac{1}{4}$$.

Q6.Using your knowledge on the addition of fractions and additive inverses, work out the answer to $$\frac{9}{10}+ \left(-\frac{1}{5}\right)+ \frac{7}{20}+ \left(-\frac{3}{10}\right)$$.

Assessment exit quiz

6 Questions

Q1.Work out $$\frac{9}{10}+ \frac{3}{5}\times \frac{1}{2} $$.

Q2.Match the calculations on the left with the correct answer on the right.

Q3.Select the correct explanation for why the following is correct.

Q4.Which of the following equals $$\frac{16}{25}$$?

Q5.Work out $$1 + \sqrt[3]{15 {{5} \over {8}}}\times \frac{1}{2}$$.

Q6.Without using a calculator, work out $$3 + \frac{2}{3} - \sqrt{\frac{25}{36}}$$.

Lesson appears in

UnitMaths / Arithmetic procedures with fractions

Maths

Q1.
Using the priority of operations, which operations come before multiplication and division?

Q2.
Match the calculations on the left with the correct answer on the right.

Q3.
The priority of operations applies to:

Q4.
Look at the calculation using the priority of operations. Write what number is represented by the star.

Q5.
Using your knowledge on the addition of fractions, work out the answer to $$\frac{11}{12}+ \left(-\frac{1}{3}\right)+ \frac{1}{4}$$.

Q6.
Using your knowledge on the addition of fractions and additive inverses, work out the answer to $$\frac{9}{10}+ \left(-\frac{1}{5}\right)+ \frac{7}{20}+ \left(-\frac{3}{10}\right)$$.

Q1.
Work out $$\frac{9}{10}+ \frac{3}{5}\times \frac{1}{2} $$.

Q2.
Match the calculations on the left with the correct answer on the right.

Q3.
Select the correct explanation for why the following is correct.

Q4.
Which of the following equals $$\frac{16}{25}$$?

Q5.
Work out $$1 + \sqrt[3]{15 {{5} \over {8}}}\times \frac{1}{2}$$.

Q6.
Without using a calculator, work out $$3 + \frac{2}{3} - \sqrt{\frac{25}{36}}$$.