Subtraction of Fractions

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Subtraction of fractions is same as the addition of fractions.

Subtracting like fractions : In this as the denominators(bottom numbers) are same just subtract the numerators( top numbers) .



Subtraction of like fractions
  12       8
 ----- - ----
   5        5

   12 - 8           4
  ---------- = ----
        5            5

In subtracting unlike fractions use the following steps.
1) Find the LCM (LCD) of the denominator.
2) Make the denominator same as that of LCM(LCD).
3) New fractions are like fractions.
4) Subtract the numerators keeping the common denominator.

For example :
Subtraction of unlike fractions
  12       5
 ----- - ----
   5        6
  LCM of 5 and 6 = 30
  12 x 6        5 x 5
 --------   - -------
   5 x 6        6 x 5

  72        25       72 - 25
 -----  - ---- =   --------
   30        30         30
        47
  =  ------
        30

Subtracting mixed fractions :

1) convert them to Improper fractions
2) then subtract them (using subtract the Fractions)
3) then convert back to Mixed Fractions

Examples :
1) The milkman had 2 2/3 liters of milk in the can. He sold 1 1/4 liter to a customer. How much milk is left in the can?
Solution :
2 2/3 - 1 1/4
• Change to improper fractions ------> 8/3 – 5/4
• Using LCM make the denominators same ----> 32/12 – 15/12 = 17/12
• Change the answer to mixed fraction --------> 15/12 .
There is 1 5/12 liter milk left in the can.
------------------------------------------------------------------------
2) You get one-fifth of a bottle of juice and your sister gets one-third of a bottle of juice. Who gets more? How much more?
Solution :
You get one-fifth of a bottle of juice = 1/5
your sister gets one-third of a bottle of juice = 1/3
1/5 and 1/3
(1 x3)< (1 x 5) [by cross multiplication] 3 < 5
∴ your sister gets more.
1/3 - 1/5
LCM of 3 and 5 is 15. So make the denominators same as that of LCM.
(1x5)/(3x5) - (1x3)/(5x3)
⇒ 5/15 - 3/15
⇒ (5-3)/15 = 2/15
So your sister will get 2/15 of a bottle juice more.

Fraction

Types of Fractions
Conversion of improper to mixed fraction
Equivalent Fractions
Fractions in Simplest form
Like and Unlike Fractions
Add fractions
Subtraction of fractions
Multiplying Fractions

Subtracting fractions to Fractions

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