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Simplifying fractions

I can simplify fractions by dividing both the numerator and denominator by common factors and know why this works.

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Lesson 8 of 18

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Year 7

Simplifying fractions

I can simplify fractions by dividing both the numerator and denominator by common factors and know why this works.

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Lesson details

Key learning points

When a fraction is multiplied by 1 it remains the same but may look different.
Simplifying fractions can be shown to be the inverse of multiplying to find equivalent fractions.
A fraction can be written more simply but remain equivalent by dividing the numerator and denominator by a common factor
A fraction can be written in simplest form by dividing the numerator.

Keywords

Factor - A factor is a term which exactly divides another term.
Highest common factor - The highest common factor is the common factor which can be divided by all other possible common factors.
Product of primes - Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.

Common misconception

Pupils may think they just 'get rid' of integers which appear in both numerator and denominator.

Reinforce that you are multiplying by 1, which doesn't change the value and therefore can be omitted from further calculations.

When looking at other ways of writing 1, challenge pupils to write down as many fractions equivalent to 1 as they can. This can be made more challenging by stipulating a condition which must be met. E.g. your fraction must include prime numbers.

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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).

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Prior knowledge starter quiz

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6 Questions

Q1.
What word should go in the blank spaces to complete the following statement? Terminating have a finite number of places.

Correct Answer: decimal

Q2.
Write $$0.825$$ as a simplified fraction.

$$7\over8$$

$$825\over1000$$

Correct answer: $$33\over40$$

$$31\over40$$

$$15\over16$$

Q3.
The fraction which is halfway between 0.2 and 0.9 is $$\square \over 20$$. What number should be written in the square?

Correct Answer: 11

Q4.
Which of the following are equivalent to $$5.555$$ ?

Correct answer: $$1111\over200$$

$$5555\over200$$

$$5 \frac{55}{200}$$

Correct answer: $$5 \frac{111}{200}$$

Q5.
Match each decimal to a fraction with the denominator in exponential form.

Correct Answer:$$0.00067$$,$$\frac{67}{10^5}$$

Correct Answer:$$6.7$$,$$\frac{67}{10^1}$$

Correct Answer:$$0.067$$,$$\frac{67}{10^3}$$

Correct Answer:$$0.67$$,$$\frac{67}{10^2}$$

Q6.
Sofia writes $$12.34 = \frac {1234}{10^ \square}$$. What number should she write in the box to make her statement true?

Correct Answer: 2, two

Assessment exit quiz

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6 Questions

Q1.
Complete the statement. A is a term which exactly divides another term.

Correct Answer: factor

Q2.
Select all the fractions that simplify to $$2 \over 3$$.

Correct answer: $$8\over 12$$

$$9\over 12$$

$$15\over 18$$

Correct answer: $$12\over 18$$

$$9\over 15$$

Q3.
Which of the following factors of 24 and 90 is the best choice to efficiently simplify $$24\over90$$?

Correct answer: 6

Q4.
Write 180 as a product of prime factors.

Correct answer: $$2^2 \times 3^2 \times 5$$

$$2 \times 3^2 \times 5$$

$$2 \times 3^2 \times 5^2$$

$$2 \times 3 \times 5$$

$$2^2 \times 3^2 \times 5^2$$

Q5.
Which of these fractions is equivalent to $$360 \over 700$$

$$\frac{2^2 \times 3^2 \times 5}{2^2 \times 5^2 \times7}$$

$$\frac{2^3 \times 3^2 \times 5}{2^2 \times 5 \times7}$$

$$\frac{2^3 \times 3^2 \times 5^2}{2^2 \times 5^2 \times7^2}$$

Correct answer: $$\frac{2^3 \times 3^2 \times 5}{2^2 \times 5^2 \times7}$$

$$\frac{2^3 \times 3 \times 5}{2^2 \times 5 \times7}$$

Q6.
Match each fraction to its simplified equivalent fraction. Use the fact that $$120 = 2^3 \times 3 \times 5$$; $$84 = 2^2 \times 3 \times 7$$ and $$210 = 2 \times 3 \times 5 \times 7$$

Correct Answer:$$84\over210$$,$$2\over5$$

Correct Answer:$$84\over120$$,$$7\over10$$

Correct Answer:$$120\over210$$,$$4\over7$$

Correct Answer:$$120\over84$$,$$1 \frac{3}{7}$$

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UnitMaths / Comparing and ordering fractions and decimals (positive and negative)

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Simplifying fractions

Simplifying fractions

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Equipment

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.What word should go in the blank spaces to complete the following statement? Terminating __________ have a finite number of __________ places.

Q2.Write $$0.825$$ as a simplified fraction.

Q3.The fraction which is halfway between 0.2 and 0.9 is $$\square \over 20$$. What number should be written in the square?

Q4.Which of the following are equivalent to $$5.555$$ ?

Q5.Match each decimal to a fraction with the denominator in exponential form.

Q6.Sofia writes $$12.34 = \frac {1234}{10^ \square}$$. What number should she write in the box to make her statement true?

Assessment exit quiz

6 Questions

Q1.Complete the statement. A is a term which exactly divides another term.

Q2.Select all the fractions that simplify to $$2 \over 3$$.

Q3.Which of the following factors of 24 and 90 is the best choice to efficiently simplify $$24\over90$$?

Q4.Write 180 as a product of prime factors.

Q5.Which of these fractions is equivalent to $$360 \over 700$$

Q6.Match each fraction to its simplified equivalent fraction. Use the fact that $$120 = 2^3 \times 3 \times 5$$; $$84 = 2^2 \times 3 \times 7$$ and $$210 = 2 \times 3 \times 5 \times 7$$

Lesson appears in

UnitMaths / Comparing and ordering fractions and decimals (positive and negative)

Maths

Q1.
What word should go in the blank spaces to complete the following statement? Terminating have a finite number of places.

Q2.
Write $$0.825$$ as a simplified fraction.

Q3.
The fraction which is halfway between 0.2 and 0.9 is $$\square \over 20$$. What number should be written in the square?

Q4.
Which of the following are equivalent to $$5.555$$ ?

Q5.
Match each decimal to a fraction with the denominator in exponential form.

Q6.
Sofia writes $$12.34 = \frac {1234}{10^ \square}$$. What number should she write in the box to make her statement true?

Q1.
Complete the statement. A is a term which exactly divides another term.

Q2.
Select all the fractions that simplify to $$2 \over 3$$.

Q3.
Which of the following factors of 24 and 90 is the best choice to efficiently simplify $$24\over90$$?

Q4.
Write 180 as a product of prime factors.

Q5.
Which of these fractions is equivalent to $$360 \over 700$$

Q6.
Match each fraction to its simplified equivalent fraction. Use the fact that $$120 = 2^3 \times 3 \times 5$$; $$84 = 2^2 \times 3 \times 7$$ and $$210 = 2 \times 3 \times 5 \times 7$$