13/4 + 3/5 as a fraction

Learn how to find what is 13/4 plus 3/5 in fraction form just in a few minutes. We have covered the easiest method to write 13/4 + 3/5 as a fraction and decimal.

Summary: 13/4 plus 3/5 = 77/20
Since both fractions have unequal denominators, 13/4 plus 3/5 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/4 and fraction 3/5 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 4 and 5. 20 is the LCM of 4 and 5. Multiplying the LCM 20 with the numerators and denominators of both fractions (13/4 x 20/20) + (3/5 x 20/20), and simplify further in order to have the common denominator. So the equivalent fraction for 13/4 is 65/20 and for 3/5 is 12/20. By simplifying this fraction addition 65/20 + 12/20, it becomes 77/20.

CALCULATION: 13/4 + 3/5 as a fraction
13/4 + 3/5 = (?)
13/4 + 3/5 = [(13 x 5) + (3 x 4)]/(4 x 5)
= (65 + 12)/20
= 77/20
13/4 + 3/5 = 77/20
13/4 plus 3/5 as a fraction is 77/20.

where
13/4 is a improper fraction as an addend,
3/5 is a proper fraction as an addend,
77/20 is the sum of 13/4 and 3/5.

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13/4 plus 3/5 as a decimal
13/4 + 3/5 = 77/20
77/20 = 3.85
(13/4) + (3/5) as a decimal is 3.85

where
3.85 is the sum of 13/4 and 3/5.

The below workout with step by step calculation shows how to find the equivalent fraction between 13/4 and 3/5 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 13/4 plus 3/5 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(13/4) + (3/5) using LCM Method:
What is 13/4 plus 3/5 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/4
Fraction B: 3/5

What to be found?
(13/4) + (3/5) = ?
Find what's the sum of 13/4 and 3/5.

step 2 Compare the denominators of fractions 13/4 and 3/5 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 13/4 and 3/5 are not equal, it is said to be unlike fractions addition.

step 3For unlike fractions addition, find the LCM (least common multiple) of both denominators of fractions 13/4 and 3/5:
The LCM of 4 and 5 is 20.

step 4 Write the fractions 13/4 and 3/5 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/4 + 3/5
= [(13 x 20)/(4 x 20)] + [(3 x 20)/(5 x 20)]

step 5 Simplify the expression to have common denominator:
= 65/20 + 12/20

step 6 Take the common values out and rewrite the above expression like the below:
= 1/20 x (65/1 + 12/1)
= 1/20 x (65 + 12)

step 7Simplify the above expression further:
= 1/20 x 77
= 77/20
13/4 + 3/5 = 77/20

Hence,
13/4 plus 3/5 as a fraction is 77/20.

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13/4 + 3/5 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/4
Fraction B: 3/5

What to be found?
(13/4)+(3/5) = ?
Find what's the sum of 13/4 and 3/5.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (13 x 5), find the product of numerator of Fraction B and denominator of Fraction A (3 x 4), and find the product of both denominators of Fraction A and Fraction B (4 x 5) and rewrite the equation as like the below:
= (13 x 5) + (3 x 4)/(4 x 5)

step 3 Simplify and rewrite the fraction:
= (65 + 12)/20
13/4 + 3/5 = 77/20

Hence,
13/4 plus 3/5 in fraction is 77/20