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.