MATHEMATICSEquivalent Fractions

Lesson Objectives

•The aim of this powerpoint is to help you…

• to find equivalent fractions

• to simplify or cancel fractions down

• to compare and order fractions

Equivalence

• Things that are equivalent are worth the same as each other.

• The diagrams below are all the same size and half of each diagram has been shaded in.

• These diagrams should demonstrate that the following fractions are all equivalent…

≡

2 out of 4 parts shaded 3 out of 6 parts shaded 6 out of 12 parts shaded

≡ ≡

Finding Equivalent Fractions• To find equivalent fractions without the use of diagrams, you simply multiply BOTH the top and the bottom numbers of the original fraction by the SAME amount.

• E.g. Find three fractions equivalent to

23

23

×5 10×5 15

≡23

×100 200×100 300

≡×2 4×2 6≡

Cancelling Fractions Down• To simplify or cancel fractions down without the use of diagrams, you simply divide BOTH the top and the bottom numbers of the original fraction by the SAME amount.

• E.g. Give in its simplest form

2436

÷2 6÷2 9 ÷3 2

÷3 3÷2 12

÷2 18

HINT: Sometimes the biggest

number you can divide by is the

difference between the two numbers in

the fraction!

You may have spotted that 24 and 36 are both in the 12 times table so you could have simply divided BOTH numbers by 12!

2436

÷12 2÷12 3

Quick Practice Q1

What values are missing in each fraction to make sure they are all worth ?

2 10 16

5 10 55

Work out your answers before clicking on to the next slide.

= == =

Answer to Q1

2 10 16

5 10 55

Compare known numbers in both fractions…

= == =4

The bottom 5 x 2 gives the bottom 10 so multiply the top 2 by 2 to get…The top 2 x 5 gives the top 10 so multiply the bottom 5 by 5 as well to get…The top 2 x 8 gives the top 16 so multiply the bottom 5 by 8 as well to get…The bottom 5 x 11 gives the bottom 55 so multiply the top 2 by 11 to get…

25 40

22

Quick Practice Q2

Cancel each of the following fractions down to their simplest form.

A 25 C 70

40 100

B 14 D 28

18 42

Work out your answers before clicking on to the next slide.

=

==

=

Answer to Q2

A 25

40

B 14

18

C 70

100

D 28

42

=

=

=

=

Both numbers end in 5 or 0 so divide them BOTH by 5

The difference between the two values is 14 and BOTH numbers can be divided by 14!

Both numbers end in 0 so divide them BOTH by 10

Both numbers are even so divide them BOTH by 2

5 8

7 9

710

2 3

Comparing Fractions

• To compare fractions you may need to find equivalent fractions with the same bottom number.

• The easiest way is to multiply the top and bottom of each fraction by the bottom of the other fraction(s)

• Remember to quote the ORIGINAL fractions (not their equivalents) in your answer.

Example

• Which is bigger or ?

• Work out your answer before clicking…

• 5/8 (x15) 75/120

• 9/15 (x8) 72/120

• Therefore the answer is: is bigger

75 > 72 so

5/8 > 9/15

Quick Practice

• What sign needs to be put between each pair of fractions… < or > or = ?

A C

B D

Work out the answers before moving on to the next slide.

Answers

A

B

C

D

1/3 (x8) 8/24

3/8 (x3) 9/24

8 is smaller than 9, i.e. 8 < 9<

<

>

=

7/10 (x3) 21/30

2/3 (x10) 20/30

21 is bigger than 20, i.e. 21 > 20

5/6 (x15) 75/90

13/15 (x6) 78/90

75 is smaller than 78, i.e. 75 < 78

28/35 (x5) 140/175

4/5 (x35) 140/175

These are EQUAL!

What next?

• Print out the notes called Frac3a and Frac3b. Read them and make sure you answer any questions

• Work through all of the MyMaths lesson called Equivalent Fractions found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=fractions/equivalentFractions&taskID=1042

• Work through pages 1 to 5 of the MyMaths lesson called Comparing Fractions found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=fractions/comparingFractions&taskID=1075

• If you need more practice, try the worksheet called EquivFrac-S1.xlsx.

• Now move on to the Frac-4 powerpoint