Explain how to compare non-related fractions finding equivalent fractions with common denominators | Maths

Starter quiz

20 is a common multiple of:
- 1 and 2 ✓
- 2 and 3
- 3 and 4
- 4 and 5 ✓
- 5 and 6
Tick the pairs of related fractions.
- ${1} \over {3}$ ${5} \over {16}$
- ${1} \over {6}$ ${3} \over {12}$ ✓
- ${3} \over {2}$ ${4} \over {15}$
- ${1} \over {5}$ ${1} \over {10}$ ✓
Two or more fractions where the denominators are not multiples of each other are known as:
- common denominators.
- related fractions.
- non-related fractions. ✓
- uncommon multiples.
Use the correct symbol to compare these two fractions: ${2} \over {7}$ ___ ${2} \over {3}$
- < ✓
- >
- =
$What fraction of the whole has been shaded?$

What fraction of the whole has been shaded?
- ${2} \over {5}$ ✓
- ${2} \over {9}$
- ${6} \over {9}$
- ${6} \over {15}$ ✓
- ${2} \over {3}$
Tick the correct solution for ${2} \over {5}$ + ${3} \over {8}$ =
- ${5} \over {13}$
- ${6} \over {13}$
- ${6} \over {40}$
- ${31} \over {40}$ ✓

Exit quiz

Use the correct symbol to compare: ${7} \over {15}$ ___ ${5} \over {15}$
- <
- > ✓
- =
Use the correct symbol to compare: $1 {{2} \over {5}}$ ___ ${7} \over {5}$
- <
- >
- = ✓
The whole is the same in each image. Which image has the greatest proportion of the whole shaded?
- A
- B
- C ✓
$Look closely at each image. Which fractional values can be compared?$

Look closely at each image. Which fractional values can be compared?
- A and B
- B and C
- A and D ✓
- B and D
- C and D
Use the correct symbol to compare: ${5} \over {7}$ ___ ${2} \over {3}$
- <
- > ✓
- =
Use the correct symbol to compare: $1 {{1} \over {5}}$ ___ $1 {{2} \over {11}}$
- <
- > ✓
- =

Worksheet

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Presentation

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Lesson Details

Key learning points

You can use knowledge of common multiples to convert fractions to an equivalent with a common denominator.
Common denominators for non-related fractions can be found using common multiples of the denominators.
If the denominators are the same, the greater the numerator, the larger the fraction.
If the denominators are the same, the smaller the numerator, the smaller the fraction.

Common misconception

Pupils try to compare fractions where the whole is not the same size.

Give an example where fractions represent different sized wholes. Discuss how fractions may not help us compare the area used/shaded if the wholes are different. Instead, highlight the show the relationship between the whole and its part(s).

Keywords

Portion - A portion is a part of a whole.
Common denominator - When two or more fractions share the same denominator, you can say they have a common denominator.
Related fractions - Related fractions are when the denominator of one fraction is a multiple of the denominator of the other fraction.