# Equivalent Fractions

## Practise finding and simplifying equivalent fractions numerically and in fraction diagrams.

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This is level 4; Express the fractions in their simplest forms. You can earn a trophy if you get at least 9 correct and you do this activity online.

 $$\frac{6}{9}$$ =

 $$\frac{12}{18}$$ =

 $$\frac{24}{30}$$ =

 $$\frac{16}{40}$$ =

 $$\frac{20}{25}$$ =

 $$\frac{25}{30}$$ =

 $$\frac{15}{24}$$ =

 $$\frac{48}{56}$$ =

 $$\frac{20}{36}$$ =

 $$\frac{45}{105}$$ =

 $$\frac{26}{117}$$ =

 $$\frac{152}{171}$$ =

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This is Equivalent Fractions. You can also try:
Level 1 Level 2 Level 3 Level 5

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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## Description of Levels

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Level 1 - Colour in the fraction walls

Level 2 - Colour in the pizzas

Level 3 - Fill in the missing numerators

Level 4 - Express the fractions in their simplest forms

Level 5 - Find the denominator of the equivalent fraction

More Fractions including lesson Starters, visual aids, investigations and self-marking exercises.

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## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Equivalent Fractions

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Here is something from Transum Subscriber Ann that is really useful:

"When I think of cancelling fractions, I always think of times tables and perhaps the divisibility rules.  This is my preferred method, but sometimes I struggle, particularly with the last question.  Could we use a different method for these trickier fractions?

Look at the question 152/171

What's 171-152 ?  19 (a prime number)

Both numbers must be divisible by 19.

152÷19 = 8

171÷19 = 9

The fraction must be 8/9

Why does this work?

152 and 171 have a common factor.  This tells us that they're in the same times table.  Let's use a number line to demonstrate this times table as a sequence.  We know that 152 and 171 are numbers in our times table sequence.  We don't know if they are consecutive terms or not.  The difference between them is 19 (a prime number), this tells us that our numbers are consecutive terms.

Let's try that again.  Let's take the question 35/42

42-35 = 7 (a prime number)

Both numbers must be divisible by 7.

35÷7 = 5

42÷7= 6

The fraction must be 5/6

Does this always work?

Let's look at the fourth question 10/25

What's 25-10 ? It's 15 (NOT a prime number, that's important to notice)

Are 25 and 10 divisible by 15? No

What are the factors of 15? These are 1, 3, 5 and 15

It turns out that both numbers have a common factor of 5

Let's think about using a number line to demonstrate the sequence.  We know that 10 and 25 are numbers in our times table sequence.  We don't know if they are consecutive terms or not.  The difference between them is 15.

Is that one jump of 15 between the numbers?  so the 15 times table?

Or three jumps of 5 between them?   so the 5 times table?

Or five jumps of three between them?  so the 3 times table?

Can we make a general observation?

Yes.

Find the difference d between the two numbers.

If d is prime then that's your common factor.

If the difference d isn't prime, then your common factor will be one of the factors of d (possibly d itself, such as 16/20)

Disclaimer

This method is a method of "last resort" when the common factor doesn't jump out at you, like 22/99. It also assumes that there was a common factor.

Suppose we don't know if there is a common factor. For example the fraction 4/9

We find that d=5 (a prime number).  This means that there is only one possible common factor, namely 5.  We now test to see whether it is.

We consider whether 4 is exactly divisible by 5. It isn't, so we know that our fraction is already in its lowest terms."

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