Explain that addition and subtraction of fractions are inverse operations | Maths

Starter quiz

$The bar model shows seven equal parts of the whole. What fraction can be used to label this?$

The bar model shows seven equal parts of the whole. What fraction can be used to label this?

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{7}$ ✓

$\frac{1}{8}$
Each marble in a bag is $\frac{1}{8}$ of the whole bag. How many marbles are there in the bag?

1

8 ✓

9

10
A full box of eggs contains 12 eggs. First there were 9 eggs in the box, then 6 were used to make pancakes. Which equation matches this problem?

$\frac{9}{12}$ − $\frac{6}{12}$ = $\frac{15}{12}$

$\frac{9}{12}$ − $\frac{6}{12}$ = $\frac{3}{12}$ ✓

$\frac{9}{12}$ − $\frac{6}{12}$ = $\frac{3}{0}$

$\frac{9}{12}$ − $\frac{6}{12}$ = $\frac{3}{24}$
$A full box of eggs contains 12 eggs. First there were 6 eggs in the box, then 2 were used to make pancakes. Which fraction represents the number of eggs left?$

A full box of eggs contains 12 eggs. First there were 6 eggs in the box, then 2 were used to make pancakes. Which fraction represents the number of eggs left?

$\frac{4}{8}$

$\frac{4}{12}$ ✓

$\frac{2}{12}$

$\frac{6}{12}$
Which expressions have a total less than $\frac{4}{10}$ ?

$\frac{9}{10}$ − $\frac{5}{10}$

$\frac{2}{10}$ + $\frac{3}{10}$

$\frac{1}{10}$ + $\frac{2}{10}$ ✓

$\frac{7}{10}$ − $\frac{5}{10}$ ✓
What are the possible values of the missing numerator?

1 ✓

2 ✓

3 ✓

4

5

Exit quiz

Which equation is the inverse of 5 + 3 = 8?

3 + 5 = 8

8 − 5 = 3

8 − 3 = 5 ✓

3 − 5 = 8
Which equation does the number line show?

$\frac{7}{10}$ + $\frac{2}{10}$ = $\frac{9}{10}$

$\frac{7}{10}$ − $\frac{2}{10}$ = $\frac{5}{10}$

$\frac{2}{10}$ + $\frac{5}{10}$ = $\frac{7}{10}$ ✓
True or false. Addition and subtraction are inverse operations when using fractions as units.

True ✓
False
What is the inverse of this calculation shown on the number line?

$\frac{7}{10}$ − $\frac{2}{10}$ = $\frac{5}{10}$

$\frac{7}{10}$ − $\frac{5}{10}$ = $\frac{2}{10}$ ✓

$\frac{7}{10}$ − $\frac{2}{10}$ = $\frac{2}{10}$
Which equation is the inverse of $\frac{3}{10}$ + $\frac{6}{10}$ = $\frac{9}{10}$ ?

$\frac{9}{10}$ − $\frac{6}{10}$ = $\frac{3}{10}$ ✓

$\frac{3}{10}$ − $\frac{6}{10}$ = $\frac{9}{10}$

$\frac{9}{10}$ − $\frac{3}{10}$ = $\frac{6}{10}$
Which of the additive equations is incorrect?

$\frac{12}{15}$ − $\frac{9}{15}$ = $\frac{3}{15}$

$\frac{9}{15}$ − $\frac{3}{15}$ = $\frac{12}{15}$ ✓

$\frac{9}{15}$ + $\frac{3}{15}$ = $\frac{12}{15}$

$\frac{3}{15}$ + $\frac{9}{15}$ = $\frac{12}{15}$

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

You know that if 3 + 4 = 7 then 7 - 4 = 3
Facts about whole numbers can be applied to the numerators of fractions with the same denominator.
If 3 tenths plus 4 tenths is equal to 7 tenths then 7 tenths subtract 4 tenths is equal to 3 tenths.

Common misconception

Children might add or subtract the denominator as well.

Reinforce to children that the denominator denotes the unit fraction being used in calculation so does not need changing. Count aloud with physical objects to start with before moving onto counting in unit fractions.

Keywords

Additive - Additive equations involve addition or subtraction.
Inverse - Inverse means the opposite in effect or reverse of. For example, subtraction is the inverse operation of addition.
Numerator - A numerator is the top number in a fraction. It shows how many parts we have.
Denominator - A denominator is the bottom number in a fraction. It shows how many parts a whole has been divided into.