How to do Add/Subtract Rationals with Unlike Denominators
Solve.
3/5+4/7
Solve
2/3+1/4
Solve
7/10 - 2/3
Solve
7/12 - 3/8
To add or subtract rationals with unlike denominators, you need to find a common denominator for the fractions involved.
1. 3/5 + 4/7:
Find a common denominator for 5 and 7, which is 35.
Convert the fractions to have the common denominator:
(3/5)(7/7) + (4/7)(5/5) = 21/35 + 20/35
Now that the denominators are the same, you can add the numerators:
21/35 + 20/35 = (21 + 20)/35 = 41/35
2. 2/3 + 1/4:
Find a common denominator for 3 and 4, which is 12.
Convert the fractions to have the common denominator:
(2/3)(4/4) + (1/4)(3/3) = 8/12 + 3/12
Now that the denominators are the same, you can add the numerators:
8/12 + 3/12 = (8 + 3)/12 = 11/12
3. 7/10 - 2/3:
Find a common denominator for 10 and 3, which is 30.
Convert the fractions to have the common denominator:
(7/10)(3/3) - (2/3)(10/10) = 21/30 - 20/30
Now that the denominators are the same, you can subtract the numerators:
21/30 - 20/30 = (21 - 20)/30 = 1/30
4. 7/12 - 3/8:
Find a common denominator for 12 and 8, which is 24.
Convert the fractions to have the common denominator:
(7/12)(2/2) - (3/8)(3/3) = 14/24 - 9/24
Now that the denominators are the same, you can subtract the numerators:
14/24 - 9/24 = (14 - 9)/24 = 5/24