**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. **

**Addition of Subtraction:**

**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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