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

Starter quiz

Using the priority of operations, which operations come before multiplication and division?
- Brackets ✓
- Roots ✓
- Exponents ✓
- Addition
- Subtraction or the addition of the additive inverse
Match the calculations on the left with the correct answer on the right.
- $3 + 4\times5$
  
  ⇔
  
  23 ✓
- $4 + 3\times5$
  
  ⇔
  
  19 ✓
- $3 + 6\div 2$
  
  ⇔
  
  6 ✓
- $2 + 4\times5 + 5\times 1$
  
  ⇔
  
  27 ✓
The priority of operations applies to:
- positive and negative integers only
- positive and negative integers, fractions and decimals ✓
- positive numbers only
Look at the calculation using the priority of operations. Write what number is represented by the star.
- '24' ✓
Using your knowledge on the addition of fractions, work out the answer to $\frac{11}{12}+ \left(-\frac{1}{3}\right)+ \frac{1}{4}$ .
- $\frac{13}{13}$
- $\frac{5}{6}$ ✓
- 1
- $\frac{6}{5}$
Using your knowledge on the addition of fractions and additive inverses, work out the answer to $\frac{9}{10}+ \left(-\frac{1}{5}\right)+ \frac{7}{20}+ \left(-\frac{3}{10}\right)$ .
- $\frac{4}{5}$
- $\frac{3}{4}$ ✓
- $\frac{12}{15}$
- $\frac{11}{12}$

Work out $\frac{9}{10}+ \frac{3}{5}\times \frac{1}{2}$ .
- $\frac{4}{3}$
- $\frac{3}{4}$
- $\frac{5}{6}$
- $\frac{6}{5}$ ✓
Match the calculations on the left with the correct answer on the right.
- $\left(\frac{2}{5}\right)^2$
  
  ⇔
  
  $\frac{4}{25}$ ✓
- $\left(\frac{3}{5}\right)^2$
  
  ⇔
  
  $\frac{9}{25}$ ✓
- $\left(\frac{4}{3}\right)^2$
  
  ⇔
  
  $\frac{16}{9}$ ✓
- $\left(\frac{5}{6}\right)^2$
  
  ⇔
  
  $\frac{25}{36}$ ✓
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.
- When dividing, division can be written as multiplication by the reciprocal. ✓
Which of the following equals $\frac{16}{25}$ ?
- $\frac{4^2}{5^2}$ ✓
- $\left(\frac{4}{5}\right)^2$ ✓
- $\sqrt{{256}\over{625}}$ ✓
- $\frac{4}{5}\div \frac{5}{4}$ ✓
- $\frac{4}{5}\times 2$
Work out $1 + \sqrt[3]{15 {{5} \over {8}}}\times \frac{1}{2}$ .
- $\frac{9}{4}$ ✓
- $\frac{4}{9}$
- 1.5
- 1
- $\frac{13}{8}$
Without using a calculator, work out $3 + \frac{2}{3} - \sqrt{\frac{25}{36}}$ .
- $1 {{5} \over {6}}$
- $2 {{5} \over {6}}$ ✓
- $3 {{5} \over {36}}$
- $3 {{25} \over {36}}$

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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.

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