Priority of operations with positive and negative integers and decimals | Maths

Starter quiz

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

Using the priority of operations, work out: $20-(-5)\times10 =$ ______
- '70' ✓
Using the priority of operations, work out: $100+(-50)\times2=$ ______
- '0' ✓
Using the priority of operations, work out the answer to $(-8)+30\div2 =$ ______
- '7' ✓
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
  
  ⇔
  
  $(-12)\div(-3) + 4^2$
Without using a calculator, evaluate $10+(-9)\div (-3)-(- 4)$
- '17' ✓
Without using a calculator, evaluate $9.4 -3.2+ \frac {12^2} {\sqrt{75+25}}$
- '20.6' ✓

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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 make the priority much clearer and avoid ambiguity
Sometimes brackets can be implicit

The use of negatives are confused with subtractions.

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

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.