Fractions guide

Hi... I am Fractionstein.

Did you know that fractionsare not as scary as you might think?

Learn along with meand you will be an expert

at fractions in no time at all!

What are fractions?

Fractions are parts of whole things.We use fractions every day!

The time isquarter past twelve.

Somebody has already eatenthree-quarters of this pizza!

Zack played really well in the first half of the match!

Mia is2 ½

years old.

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©

We write fractionsusing a numerator

and a denominator.34

The numerator tells us how many parts we have.

The denominator tells us how many parts something was (or is) divided into.

34 5

8There is one piece

of cake left.There are five green buttons.

There are eight buttons altogether.

16 The cake was cut

into six pieces.

There are three pieces left.

There werefour pieces.


©

There are lots of different types of fractions. Here are some of them...

What fractionof my flag is

coloured pink?

Halves

Quarters

Eighths

Thirds

Fifths

Tenthswww.teachingpacks.co.uk

©

12

13

14

15

18

110

What do you notice about the size of the

pieces in each

fraction?

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If the numerator and denominator are the same, we have 1 whole one!

100100 = 1

1212 = 1

44 = 13

3 = 1


Putting fractions on a number line can help us to

compare them.Here are some examples...

Which is bigger?

240 1

14

34

12

13

23

110

210

310

410

510

610

710

810

910

1010

010

15

25

35

45

13

34or 2

523or 3

43

10or 24

12or

Did you notice that some

fractions arethe same size?

If we have an amount of things, we may need to find a fraction of them.

Here are eight ants. I want to find one quarter of them.

To find of something, divide it by 2.



121314

To find of an amount,divide it into four equal groups.

So, one quarter of eight is 2.

14

Can you spot a pattern here?

To find of something, find and then multiply by 3.34

141

4 of 8 is 2, so is 6.34 www.teachingpacks.co.uk

Images: © ThinkStock

©

54

1Mixed numbers

(also calledmixed fractions)

have whole numbersand fractions.

Improper fractionsare ‘top heavy’ because the numerator is bigger than the denominator.

What are mixed numbersand improper fractions?

14

What do you notice about these two fractions?www.teachingpacks.co.uk

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Can we change mixed numbers into improper fractions... and back again?


©

To change an improper fraction to a mixed number, divide the numerator by the denominator.

To change a mixed number to an improper fraction, write the whole number as a fraction,

then add them together.

44

34

74+ =1 3

4 =

74 = 7 ÷ 4 = 3

41


Why are different fractions sometimes worth the same amount?

Look at these three flags. The same amount on each flagis coloured pink, even though they are split into different fractions!

14

28

416

We say that these are equivalent fractions, because they are worth the same, even though the

numerators and denominators are different.

is the simplest fraction here because its numeratorand denominator are the smallest.

14

Can you identify these

equivalent fractions?In each pair,

which fractionis the simplest?



How can we find even more equivalent fractions?

To make an equivalent fraction, just multiply (or divide) the numerator and denominator by the same number.

23

69

2436

1218

x 3

x 3

x 4

x 4

÷ 2

÷ 2

14

28

2080

520

x 2

x 2

x 10

x 10

÷ 4

÷ 4


How can we put different fractions in order of size?

If the denominators are all the same, it’s easy. Just look at the

numerators!18

58

78

But, if the denominators are different, we have to find a common denominator.

12

56

34

Step 1: Look at the denominators. Think of the lowest number that they will all divide into with no remainders.

Step 2: Change the fractions so that they are equivalent and so they all have this common denominator.

Step 3: Now, look at the new fractions to put the original ones in order!

The denominators here are 2, 6 and 4.

These numbers all divideinto 12 with no remainders.

12

34

56

, ,

, ,

34

912=5

61012=1

26

12= , ,


How can we simplify fractions?Simplifying fractions means finding an equivalent fraction where

the numerator and denominator are as small as they can be.

810

÷ 10

÷ 10

Simplifying a fraction can also be calledcancelling or reducing it to its lowest form.

80100

Just divide the numerator and denominator by the largest number that you can (without getting a remainder) and repeat if possible.

45

÷ 2

÷ 2


Did you know that we can

add and subtract

fractions?

If the denominators are the same, adding

and subtracting fractions is easy.

15

35

45

78

38

48

+ =

- =

If the denominators are different, we have to change the fractions

so that they have a common denominator.

?+ =45

34

3120+ =16

201520

?- =78

13

1324- =21

248

24


We can multiply

and divide fractions

too!

Multiplying Fractions• Multiply the numerators together,• Multiply the denominators together,• Simplify the answer if you can!

34

25

620x =

Dividing Fractions• Turn one of the fractions upside down,(put the numerator on the bottom and the denominator on the top!)• Multiply the fractions together,• Simplify the answer if you can!

310

which can be simplified to

48

73

2824x = 7

6which can be simplified to

48

37÷

What do you notice about this answer?


Fraction Decimal Percentage1 1 100%

3/4 0.75 75%2/3 0.6 66.6%1/2 0.5 50%1/3 0.3 33.3%1/4 0.25 25%1/5 0.2 20%1/8 0.125 12.5%

1/10 0.1 10%1/100 0.01 1%

It is helpful if you can remember these fractions, decimals and percentages!

Date post:	13-Feb-2017
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Fractions guide

Education