CLASS-4
FRACTION - ADDITION OF MIX FRACTION
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.
πΉππππππ ππ
πΈπππππππ = -------------
π«ππππππ
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.
πΉππππππ ππ
πΈπππππππ = -------------
π«ππππππ
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
STEP.4) Add the equivalent fractions
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 Γ· 15 8
--------- = ----------- = ------- = 8
15 15 Γ· 15 1
The required sum is 8. (Ans.)