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FRACTIONS

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Fractions are of the form: 1/2, 2/3, 4/5, 6/9 etc.

Here in 1/2 = 1 is Numerator and 2 is Denominator. In fractions Numerator is always < Denominator.

In fraction 1/2 it indicates 1 part out of 2 parts.

Fraction 1/2 is nothing else but 1 ÷ 2.

• 2/4 + 1/4 = (2+1)/4 = 3/4
• 1/7 + 2/7 + 3/7 = (1+2+3)/7 = 6/7

Subtraction of Fractions:

• 3/4 - 1/4 = (3-1)/4 = 2/4
• 28/31 - 16/31 = (28-16)/31 = 12/31

How do you arrange fractions in increasing order or decreasing order:

1/8, 1/2, 1/4

Step 1: Maximum denominator is 8 so convert all denominator to 8

• Therefore 1/2 x 4/4 = 4/8
• 1/4 x 2/2 = 2/8

Note here we have done one more thing by muliplying with same number with numerator and denominator we

are getting equivalent fraction i.e. 1/2 is same as 4/8 and 1/4 is same as 2/8

Now compare 1/8 , 4/8, 2/8

Step 2: here denominator is same in all fractions i.e. 8 so compare the numerator which is 1, 4, and 2

Therefore increasing order of fraction is 1/8 - 2/8 - 4/8 the original form is 1/8 - 1/4 - 1/2

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In Fractions one should know what is

one - half - 1/2

one -fourth - 1/4

three -fourth - 3/4

similarly we can say for

two - third - 2/3

two -sixth - 2/6

life goes on and on and on................

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Another thing one should know about fractions is multiplying fractions with numbers

For example what is

one - half of 8 i.e 1/2 x 8 = 8/2 = 4

one - fourth of 8 i.e. 1/4 x 8 = 8/4 = 2

three - fourth of 20 which is 3/4 x 20 = 60/4 = 15

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Creating equivalent fractions by multiplication:

Suppose the fraction is 1/2 then multiplying this fraction by 2 we get:

2(1/2) = 2x1/2x2 (here 2 is multiplied both in numerator and denominator)

= 2/4

This is equivalent fraction of 1/2 = 2/4

Now equivalent fraction can also be obtained by division as follows:

Suppose you have fraction 12/16

Then divide this fraction by 4 we get:

(12/4)/(16/4) = 3/4 which is equivalent fraction of 12/16.

The point to remember in both multiplication and division is that if you multiply or

divide both numerator and denominator by same number than you get equivalent fraction of the

original fraction.

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There is one more thing about equivalent fractions. Finding appropriate numerator of an fraction.

5/7 = ?/49

These kind of sums can be solved by cross multiplication

Answer:  ? = (5 x 49)/7 = 5 x 7 = 35

Therefore equivalent fraction is 5/7 = 35/49

Similarly

?/6 = 2/12 so

Answer is cross multiplication: ? = (6 x 2)/12 = 1

Therefore equivalent fraction is 1/6 = 2/12

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