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

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

Maths

Checking understanding of addition and subtraction with fractions

Securing understanding of addition and subtraction with fractions

Checking understanding of multiplication with fractions

Securing understanding of multiplication with fractions

Deepening understanding of multiplication with fractions

Checking and securing dividing a fraction by a whole number

Dividing a whole number by a fraction

Dividing a fraction by a fraction

Problem solving with arithmetic procedures involving fractions

In this unit, pupils generalised and developed their fluency of multiplying with fractions. In the future unit, this understanding is extended to ratio and connections between ratios and fractions are explored.

In the prior unit, pupils explored the structure of fractions and their relationship with decimals and integers. In this unit, pupils deepen their understanding of the arithmetic procedures involving fractions and integers.

This unit revisits and secures fraction operations and extends pupil understanding to division of whole numbers by fractions and division of fractions by fractions.

Arithmetic procedures with fractions

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

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

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

Changing fractions to their reciprocals makes things easier.

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

Select the correct explanation for why the following is correct.

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

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

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

Subtraction or the addition of the additive inverse

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

positive and negative integers, fractions and decimals

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

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

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

Starter Quiz

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