Priority of operations with positive integers | Maths

Starter quiz

Complete the statement. The additive inverse of a number is a number that, __________

when added to the original number, gives the sum of 0 ✓

when added to the original number, gives the sum of 1

when multiplied by the reciprocal the product is 1

when multiplied by the reciprocal the product is (-1)
Match each number with its additive inverse.

4

⇔

(-4) ✓

(-40)

⇔

40 ✓

0.4

⇔

(-0.4) ✓

(-400)

⇔

400 ✓
Select all the fractions that are equivalent to ${2} \over {3}$ .

${1} \over {3}$

${1} \over {2}$

${4} \over {6}$ ✓

${20} \over {30}$ ✓

${3} \over {2}$
Match each calculation with an equivalent commutative calculation.

$A + B$

⇔

$B + A$ ✓

$A\times B$

⇔

$B\times A$ ✓

$A + B + C$

⇔

$B + C + A$ ✓
Work out the missing number: $9.8 \times 0.5 + 9.8 \times$ ______ $= 9.8$

'0.5' ✓
Work out the missing number: $34 \times 0.8 + 34 \times$ ______ $= 68$

'1.2' ✓

This image is a help guide to the priority of operations. Which set of operations must you always apply first when they are in a calculation?

Addition and subtraction

Multiplication and division

Roots and exponents

Brackets ✓
How would you complete a calculation when an operation is repeated?

Do them both at the same time ✓

Go left to right

Ignore them and do those operations last
Without using a calculator, work out: $4\times5 + 6\times7$ = ______

'62' ✓
Without using a calculator, work out: $200\;-(12\;–\;8)\times5\times3^2$ = ______

'20' ✓
The answer to this calculation is 54. Match the triangle, star, square and arrow to the correct operation or numerical value.

$\star$

⇔

+ ✓

$\triangle$

⇔

$\times$ ✓

$\square$

⇔

$-$ ✓

$\uparrow$

⇔

2 ✓
Without using a calculator, work out: $90 + \sqrt{40\times10}-12\times5$ = ______

'50' ✓

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

Students do not see the implicit brackets. Eg. Sqrt(49 + 36) is not sqrt(49) + sqrt(36)

Look for extended lines or operations which indicate an implicit brackets.

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.