# CLASS-4FRACTION - ADDITION OF MIX FRACTION

3         7

Example.1) Find The addition of following mix Fraction 2----- + 3-----

8          8

3             7

Ans.)     2 ------ + 3 -------

8             8

STEP 1: Convert to improper fractions

19          31

= ------- + -------

8           8

STEP 2: Add only the numerators, not the denominators (When we add or subtract fractions with same denominator, we just add or subtract the numerators and keep the denominator same.),

19 + 31          50

= ----------- = -------

8               8

STEP 3: Reduce to lowest term if possible

25

=  ------

4

STEP 4: Convert the improper fraction to mixed number as the denominator is smaller than the numerator.

𝑹𝒆𝒎𝒂𝒊𝒏𝒅𝒆𝒓

𝑸𝒖𝒐𝒕𝒊𝒆𝒏𝒕 = -------------

𝑫𝒊𝒗𝒊𝒔𝒐𝒓

1

= 6 ------    (Ans.)

4

3            7

Example.2) Find The addition of following mix Fraction 3------ + 2------

5            8

3            7

Ans.)     3 ------ + 2 ------

5            8

STEP 1: Convert to improper fractions

18           23

= -------- + -------

5            8

STEP 2: Find LCM of denominator of given fraction

(18 X 8) + (23 X 5)

= ---------------------

40

144 + 115

= -------------

40

259

= --------

40

STEP 3: Reduce to lowest term if possible

259

=  -------

40

STEP 4: Convert the improper fraction to mixed number as the denominator is smaller than the numerator.

𝑹𝒆𝒎𝒂𝒊𝒏𝒅𝒆𝒓

𝑸𝒖𝒐𝒕𝒊𝒆𝒏𝒕 = -------------

𝑫𝒊𝒗𝒊𝒔𝒐𝒓

19

= 6 ------    (Ans.)

40

3          5

Example.3) Find The addition of following unlike Fraction ------ + ------

8         12

Ans.)            3           5

------- + -------

8          12

STEP.1) Find the L.C.M of the denominators 8 and 12. L.C.M of 8 and 12 is 24.

STEP.2) Change both the fractions to equivalent fractions with common denominators.

3             3 X 3            9

--------- = ----------- = --------

8             3 X 8           24

5               5 X 2            10

--------- =  ------------ = --------

12              12 X 2            24

9             10

--------- + ---------

24             24

STEP.3)  Add the equivalent fractions, (When we add or subtract fractions with same denominator, we just add or subtract the numerators and keep the denominator same.),

(9 + 10)

=  ------------

24

19

=  ----------

24

19/24 is a proper fraction i.e denominator is greater than numerator. So, this is the answer.   (Ans.)

2         11            3

Example.4) Add following mix-fraction 4----- + ------- + 2------

3         15            5

Ans.)

2         11            3

4----- + ------- + 2------

3         15            5

STEP.1) Convert the mixed numbers into improper fractions

14          11          13

------- + ------- + -------

3          15           5

STEP.2) Find the L.C.M of the denominators 3, 15 and 5 STEP.3) Change the improper fractions to Equivalent fractions with common denominators.

14          14 X 5           70

------- = ----------- = -------

3           3 X 5           15

11          11 X 1         11

------- = ---------- = -------

15          15 X 1         15

13          13 X 3         39

------- = ---------- = -------

5           5 X 3          15

70          11          39

-------- + ------- + -------

15          15          15

STEP.5) Add only the numerators, not the denominators (When we add or subtract fractions with same denominator, we just add or subtract the numerators and keep the denominator same.)

70 + 11 + 39

=  ----------------

15

120

=  ---------

15

STEP.6)  Reduce to lowest term if possible

120          120 ÷ 15         8

--------- = ----------- = ------- =  8

15            15 ÷ 15          1

The required sum is 8.         (Ans.)