Addition and Subtraction of Mixed Fractions.

ADDITION AND SUBTRACTION OF MIXED FRACTIONS:

Steps to solve Mixed fractions:

We  can solve the Mixed fractions in two methods:

Steps for Method-1:

a) Solve (Add or Subtract) the whole number part.

b) Solve the Fractional part.

c) The required Solution is writing the obtained Whole part and Fractional part together.  

 

Steps for Method-2:

a) Converting the mixed number into Improper fractions.

b) Solve the Improper fractions.

c) Convert again the obtained New Improper fractions into Mixed fractions gives the required solution.

 

Add the following:

1)  3 3/4  and  2 1/8

Solution:

Given: Whole number = 3, 2 ; Fractional part = 3/4 , 1/8.

Method-1:

a) Add the whole numbers: 3 + 2 = 5.

b) Add the fractional numbers:

 3/4 + 1/8 ; Unlike fractions.

Convert Unlike fractions into Like fractions:

L.C.M of 4,8 = 8

Equivalent fractions: 3 /4 = 6/8 ; 1/8 = 1/8.

Therefore, 3 /4 + 1/8 = 6/8 + 1/8 = 7/8.

c) Thus required solution of 3 3 /4 + 2 1/8  = 5 7/8.

                   ( OR )

Method-2:

a) Converting Mixed fractions into Improper fractions:

3 3/ 4 = 15/4  ;  2 1/8 = 17/8.

b) Solve : 15/4 + 17/8 ; Unlike fractions.

Convert Unlike into Like fractions.

L.C.M of 4, 8 = 8.

Therefore, Equivalent fractions: 15/4 = 30/8  ; 17/8 = 17/8.

Add:  30/8 + 17/8 =  47/8.

c) Convert obtained Improper fraction into Mixed fraction:

Divide 47/8 ; we get Quotient = 5, Remainder = 7, denominator = 8.

Thus, required solution is :  Q R/denominator = 5  7/8.

 

Subtract the Mixed fractions:

2) 5 2/3 – 2 1/2

Solution:

Given: Whole numbers = 5, 2 ; Fractional part = 2/3 , 1 /2.

Method-1:

a) Subtract the whole numbers: 5 – 2 = 3.

b) Subtract Fractional part: 2/3 – 1 /2; Unlike fractions.

L.C.M of  3, 2 = 6.

Equivalent fractions: 2/3 = 4/6 ; 1/ 2 = 3/6.

Therefore, 4/6 – 3/6 = 1/6.

c) Therefore, required solution: 5 2/3 – 2 1 /2 = 3 1/6.   

 

                             (OR)

Method- 2 :

a) Convert Mixed fractions into Improper fractions:

5 2/3 = 17/3 ; 2 1/ 2 = 5/2.

b) Solve the unlike fractions: L.C.M of 3, 2 = 6.

Equivalent fractions: 17/3 = 34/6 ;  5/2 = 15/6.

Subtract the fractions: 34/6 – 15/6 = 19/6.

c) Convert Improper fraction into Mixed fraction:

Divide: 19/6; Quotient Q = 3; Remainder R = 1; Denominator = 6.

Thus, required solution = 3 1/6.

 

3) Solve: 2 2/3 – 1 ¼  + 3 1/6

Solution:

Given: Whole numbers = 2,  1 , 3 ; Fractional part = 2/3, 1 /4 , 1/6.

a) Solve the whole numbers:

  2 – 1 + 3 = 4.

b) Solve the Fractional part:

 2/3 – 1/ 4 + 1/6 =

L.C.M( 3, 4, 6) = 12.

Equivalent fractions:  2/3 = 8/12 ; 1/ 4 = 3/12 ; 1/6 = 2/12.  

Therefore, 8/12 – 3/12 + 2/12 = 7/12.

c) Thus, required solution is:  4 7/12.