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Simplifying Fractions

Fractions | Other Types of Fractions | Cancelling a Fraction |
Adding and Subtracting | Multiplication and Division

Fractions

1/8	1/8	1/8	1/8
1/8	1/8	1/8	1/8

This rectangle has been divided into eight equal parts.
Each part is one eighth of the rectangle (1/8).

Shading fractions of diagrams

Shade three quarters of the rectangle

1 //////////////////////////////	1 //////////////////////////////	1 //////////////////////////////	1
4 //////////////////////////////	4 //////////////////////////////	4 //////////////////////////////	4

Note each quarter is made up of two eighths. So ¾ is the same as 6/8.

These are called equivalent fractions. We say ¾ = 6/8.
If we multiply the top and the bottom of a fraction by the same number we get an equivalent fraction.

	½ = 3/6 (x 3 top and bottom )

	2/3 = 8/12 ( x 4 top and bottom ) Back to top

Other Types of Fractions

1) Improper or top heavy fractions: The top number is bigger than the bottom. For example, 3/2 is a top heavy fraction.

2) Mixed numbers: A mixture of whole numbers and fractions. For example, 1½.

This can be changed to a top heavy fraction:

1½ =	2x1+1	=	3
	2		2

We multiply the whole number by the bottom number of the fraction and add the top of the fraction:
2 x 1 + 1 = 3 , over the bottom , gives 3/2.

For example:

5	2	=	3 x 5 + 2	=	17
	3		3		3

Changing a top heavy to a mixed:

17 = 17 ÷ 3 = 5 remainder 2

This is written as 5 and 2/3 (5	2	)
	3

Cancelling a Fraction

This is converting a fraction to its simplest form (lowest terms).
We do this by dividing the top and bottom by the same number.

For example:

	5/10 = ½ (÷ top and bottom by 5)
	6/8 = ¾ (÷ 2)
	12/20 = 3/5 (÷ 4)

Note: ½ , ¾ and 3/5 cannot be simplified further.

Writing as a fraction

For example: I have 20 sweets and I eat 15, what fraction have I eaten?
Fraction eaten is 15 out of 20, this is written as a fraction 15/20.
We must always simplify: 15/20 = ¾ (÷ 5)

Finding ‘a fraction of’:
For example: What is ¾ of 8 ?
Rule: Divide by the bottom and times by the top.

	8 ÷ 4 x 3 = 6
So,	¾ of 8 = 6

For example: 2/5 of 15 = 15 ÷ 5 x 2 = 6

Adding and Subtracting

For example:

3/5 +1/5 = 4/5		4/5 – 1/5 = 3/5
2/7 + 3/7 = 5/7		7/8 – 3/8 = 4/8 =1/2

When the bottom numbers are the same: We add or subtract the top numbers.

When the bottom numbers are different. For example: ½ + 1/3 = ?
We must make them the same by multiplying: 2 x 3 = 6. By making the bottom numbers 6, we must multiply the top numbers by the same amount:

In other words, ½ = 3/6 and 1/3 = 2/6 and these can now be added to get 5/6.

½ + 1/3 =	3	+	2	=	5
	6		6		6

For example:

4/5 – 2/3 = ?
(5 x 3 =15)
4/5 = 12/15					2/3 = 10/15
So,					12/15 – 10/15 = 2/15

Mixed numbers

We can add or subtract the whole numbers and then the fractions.

For example:

3	1	+ 2	1	+ 5	7
	4		3		12

5	7	– 2	1	= 3	3	= 3	1
	12		3		12		4

Multiplication and Division

¾ x 2/3 =	3 x 2	= 6/12 = ½
	4 x 3

We multiply the top numbers and multiply the bottom. Then simplify the answer, if possible.

If the numbers are large:	15/16 x 24/35 = ?
We can cancel diagonally:
	15 and 35 cancel by 5 giving 3/16 x 24/7 16 and 24 cancel by 8 giving 3/2 and 3/7

So, 15/16 x 24/35 = 3/2 x 3/7 = 9/14

Mixed numbers

3	1	x 2	1	= ?
	4		3

Change to top heavy:

13/4 x 7/3 = 91/12 = 7