SUBTRACTING FRACTIONS MADE EASY - LUCID EXPLANATION OF FRACTION PROBLEMS

Please study

Fractions before Subtracting Fractions

if you have not already done so.

There we studied about half, quarter, three fourth with examples and exercises.

Learn/Teach
Fractions through Fun Games.
For details, see near
the bottom of this page.

Also study Fractions Made Easy.





There we studied about concept of fraction in general with examples and exercises. We also introduced Like and Unlike Fractions which are used here.

The knowledge of

Equivalent Fractions,

Conversion of Improper to Mixed and Mixed to Improper Fractions

and

Least Common Multiple (L.C.M.)

is also used here.

Here, we explain subtraction of fractions with like and unlike denominators in a lucid way. We include solved examples and problems for practice with answers.

Subtracting of Like Fractions

Difference of like fractions
= (Difference of their numerators)⁄(Common denominator)

Examples :
(i) 5⁄7 - 4⁄7 = (5 - 4)⁄7 = 1⁄7

(ii) 9⁄11 - 2⁄11 - 4⁄11 - 1⁄11 = (9 - 2 - 4 - 1)⁄11 = 2⁄11

Subtracting of Unlike Fractions

Method of Subtracting Unlike Fractions

Step 1 :
Find the L.C.M. of denominators of given fractions.

Step 2 :
Convert the given fractions into equivalent like fractions with their L.C.M. as common denominator.

Step 3 :
Subtract the like fractions so obtained.

Step 4 :
Reduce the fraction obtained in step 3 to its
lowest terms and convert it into
mixed fraction  if required.

Solved Example 1 of Subtracting Fractions

Find the difference 13⁄18 - 7⁄12

Solution :
Let us find the L.C.M. of the denominators.

        6|    18    12  
        ----------------
               3     2    
       

Solved Example 2 of Subtracting Fractions

Simplify 8⁄9 - 5⁄12 - 13⁄27 + 5⁄6

Solution :
Let us find the L.C.M.. of the denominators.

        3|    9     12     27     6
       -------------------------------
        3|    3      4      9     2
       -------------------------------
        2|    1      4      3     2
       -------------------------------
              1      2      3     1
       

Solved Example 3 of Subtracting Fractions

Find the value of
6  ⁴⁄₅ - 3  ⁴⁄₁₅ + 4  ³⁄₁₀ .

Solution :
6  ⁴⁄₅ - 3  ⁴⁄₁₅ + 4  ³⁄₁₀ .
. = (6 x 5 + 4)⁄5 - (3 x 15 + 4)⁄15 + (4 x 10 + 3)⁄10
= 34⁄5 - 49⁄15 + 43⁄10

Let us find the L.C.M.. of the denominators.

        5|    5     15     10
        -----------------------
              1      3      2
        

Word Problems on Subtracting Fractions

For Application of various topics of Fractions including Subtracting Fractions to Word Problems go to

Fraction Word problems.

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Exercise on Subtracting Fractions

Find the values of

1. 9⁄13 - 4⁄13
2. 16⁄17 - 9⁄17 - 3⁄17 - 1⁄17
3. 13⁄63 - 7⁄42
4. 4⁄21 - 9⁄14 - 11⁄35 + 49⁄30
5. 5  ³⁄₄ - 4  ⁵⁄₁₆ + 6  ⁷⁄₁₂

Answers to Exercise on Subtracting Fractions

1. 5⁄13
2. 3⁄17
3. 5⁄126
4. 91⁄105
5. 8  ¹⁄₄₈