Additive equations involve addition or subtraction.

Inverse means the opposite in effect or reverse of. For example, subtraction is the inverse operation of addition.

A numerator is the top number in a fraction. It shows how many parts we have.

A denominator is the bottom number in a fraction. It shows how many parts a whole has been divided into.

Explain that addition and subtraction of fractions are inverse operations

Maths

In this unit pupils will use repeated addition of a unit fraction to form a non-unit fraction. They will compare non-unit fractions with the same denominator. They will add and subtract fractions with the same denominator. In the future unit pupils will identify equal parts when they do not look the same related to equivalence. They will construct a whole when given a part and the number of parts.

In the prior unit pupils explained that non-unit fractions are composed of more than one unit fraction using knowledge of unit fractions to find one whole. In this unit pupils will use repeated addition of a unit fraction to form a non-unit fraction. They will compare non-unit fractions with the same denominator. They will add and subtract fractions with the same denominator.

Composition of non-unit fractions: addition and subtraction

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

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

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

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

Which equation does the number line show?

True or false.
Addition and subtraction are inverse operations when using fractions as units.

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

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

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

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

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

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

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

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

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

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

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

Which of the additive equations is incorrect?

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

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

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

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

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

$$ \frac{9}{12} $$ − $$ \frac{6}{12} $$ = $$ \frac{3}{24} $$

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

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?

$$ \frac{9}{10} $$ − $$ \frac{5}{10} $$

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

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

What are the possible values of the missing numerator?

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

Explain that addition and subtraction of fractions are inverse operations

Lesson outcome

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