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Explain that addition and subtraction of fractions are inverse operations

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Lesson details

Learning outcome

I can explain that addition and subtraction of fractions are inverse operations.

Key learning points

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

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.

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.

Teacher tip

When playing the game in the first lesson cycle, encourage children to use the language to explain their move as well. For example, "Three-tenths added to four-tenths is equal to seven-tenths."

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

Download starter quiz questions (PDF)

6 Questions

Q1.
The bar model shows seven equal parts of the whole. What fraction can be used to label this?

An image in a quiz
$$ \frac{1}{2} $$
$$ \frac{1}{4} $$
Correct answer: $$ \frac{1}{7} $$
$$ \frac{1}{8} $$

Q2.
Each marble in a bag is $$ \frac{1}{8} $$ of the whole bag. How many marbles are there in the bag?

1
Correct answer: 8
9
10

Q3.
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?

An image in a quiz
$$ \frac{9}{12} $$ − $$ \frac{6}{12} $$ = $$ \frac{15}{12} $$
Correct answer: $$ \frac{9}{12} $$ − $$ \frac{6}{12} $$ = $$ \frac{3}{12} $$
$$ \frac{9}{12} $$ − $$ \frac{6}{12} $$ = $$ \frac{3}{0} $$
$$ \frac{9}{12} $$ − $$ \frac{6}{12} $$ = $$ \frac{3}{24} $$

Q4.
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?

An image in a quiz
$$ \frac{4}{8} $$
Correct answer: $$ \frac{4}{12} $$
$$ \frac{2}{12} $$
$$ \frac{6}{12} $$

Q5.
Which expressions have a total less than $$ \frac{4}{10} $$?

$$ \frac{9}{10} $$ − $$ \frac{5}{10} $$
$$ \frac{2}{10} $$ + $$ \frac{3}{10} $$
Correct answer: $$ \frac{1}{10} $$ + $$ \frac{2}{10} $$
Correct answer: $$ \frac{7}{10} $$ − $$ \frac{5}{10} $$

Q6.
What are the possible values of the missing numerator?

An image in a quiz
Correct answer: 1
Correct answer: 2
Correct answer: 3
4
5

Assessment exit quiz

Download exit quiz questions (PDF)

6 Questions

Q1.
Which equation is the inverse of 5 + 3 = 8?

3 + 5 = 8
8 − 5 = 3
Correct answer: 8 − 3 = 5
3 − 5 = 8

Q2.
Which equation does the number line show?

An image in a quiz
$$ \frac{7}{10} $$ + $$ \frac{2}{10} $$ = $$ \frac{9}{10} $$
$$ \frac{7}{10} $$ − $$ \frac{2}{10} $$ = $$ \frac{5}{10} $$
Correct answer: $$ \frac{2}{10} $$ + $$ \frac{5}{10} $$ = $$ \frac{7}{10} $$

Q3.
True or false. Addition and subtraction are inverse operations when using fractions as units.

Correct answer: True
False

Q4.
What is the inverse of this calculation shown on the number line?

An image in a quiz
$$ \frac{7}{10} $$ − $$ \frac{2}{10} $$ = $$ \frac{5}{10} $$
Correct answer: $$ \frac{7}{10} $$ − $$ \frac{5}{10} $$ = $$ \frac{2}{10} $$
$$ \frac{7}{10} $$ − $$ \frac{2}{10} $$ = $$ \frac{2}{10} $$

Q5.
Which equation is the inverse of $$ \frac{3}{10} $$ + $$ \frac{6}{10} $$ = $$ \frac{9}{10} $$?

Correct answer: $$ \frac{9}{10} $$ − $$ \frac{6}{10} $$ = $$ \frac{3}{10} $$
$$ \frac{3}{10} $$ − $$ \frac{6}{10} $$ = $$ \frac{9}{10} $$
$$ \frac{9}{10} $$ − $$ \frac{3}{10} $$ = $$ \frac{6}{10} $$

Q6.
Which of the additive equations is incorrect?

An image in a quiz
$$ \frac{12}{15} $$ − $$ \frac{9}{15} $$ = $$ \frac{3}{15} $$
Correct answer: $$ \frac{9}{15} $$ − $$ \frac{3}{15} $$ = $$ \frac{12}{15} $$
$$ \frac{9}{15} $$ + $$ \frac{3}{15} $$ = $$ \frac{12}{15} $$
$$ \frac{3}{15} $$ + $$ \frac{9}{15} $$ = $$ \frac{12}{15} $$

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