An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

A mixed number is an improper fraction written as its integer part plus the fractional part where the fractional part is a proper fraction.

LCM is an abbreviation for lowest common multiple.

Securing understanding of addition and subtraction with fractions

Maths

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

What is the name of a number that has both an integer part and a fractional part?

Which of the following is $$3 {{2} \over {3}}$$ as an improper fraction?

(3 - 1) + $$\left(\frac13-\frac56\right)$$

(3 - 1) - $$\left(\frac13-\frac56\right)$$

Which of the following show a correct first step to calculate $$3 {{1} \over {3}}$$ - $$1 {{5} \over {6}}$$?

Which of the following can be simplified before calculating?

What is the missing digit in this calculation $$1 {{1} \over {3}}$$ + $$2 {{\square} \over {6}}$$ = $$4 {{1} \over {6}}$$?

Calculate $$3 {{1} \over {3}}$$ - $$1 {{5} \over {6}}$$, give your answer in its simplest form.

When subtracting fractions you must have {{ }}.

Which of the following are not common denominators of $${1}\over{4}$$ and $${7}\over{20}$$?

Which symbol is missing here? $$\frac{2}{9} + \frac{1}{8}  \square \frac{2}{9} + \frac{1}{7}$$.

Calculate $${7}\over{12}$$ - $${1}\over{3}$$.

$${3}\over{8}$$ + $${7}\over{16}$$ - $${3}\over{4}$$ 

$${3}\over{8}$$ + $${7}\over{16}$$ + $$\left(-\frac34\right)$$

$${3}\over{8}$$ - $$\left(\frac{3}{4} + \frac{7}{16}\right)$$

Which of the following is not a correct alternative for $${3}\over{8}$$ - $${3}\over{4}$$ + $${7}\over{16}$$?

Calculate $${3}\over{8}$$ - $${3}\over{4}$$ + $${7}\over{16}$$.

This lesson will be removed by end of Summer Term 2025.

Securing understanding of addition and subtraction with fractions

Lesson outcome

This lesson will be removed by end of Summer Term 2025.