13/5 + 5/13 as a fraction

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

Summary: 13/5 plus 5/13 = 194/65
Since both fractions have unequal denominators, 13/5 plus 5/13 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/5 and fraction 5/13 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 5 and 13. 65 is the LCM of 5 and 13. Multiplying the LCM 65 with the numerators and denominators of both fractions (13/5 x 65/65) + (5/13 x 65/65), and simplify further in order to have the common denominator. So the equivalent fraction for 13/5 is 169/65 and for 5/13 is 25/65. By simplifying this fraction addition 169/65 + 25/65, it becomes 194/65.

CALCULATION: 13/5 + 5/13 as a fraction
13/5 + 5/13 = (?)
13/5 + 5/13 = [(13 x 13) + (5 x 5)]/(5 x 13)
= (169 + 25)/65
= 194/65
13/5 + 5/13 = 194/65
13/5 plus 5/13 as a fraction is 194/65.

where
13/5 is a improper fraction as an addend,
5/13 is a proper fraction as an addend,
194/65 is the sum of 13/5 and 5/13.

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13/5 plus 5/13 as a decimal
13/5 + 5/13 = 194/65
194/65 = 2.9846
(13/5) + (5/13) as a decimal is 2.9846

where
2.9846 is the sum of 13/5 and 5/13.

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

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

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

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

step 2 Compare the denominators of fractions 13/5 and 5/13 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 13/5 and 5/13 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 13/5 and 5/13:
The LCM of 5 and 13 is 65.

step 4 Write the fractions 13/5 and 5/13 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/5 + 5/13
= [(13 x 65)/(5 x 65)] + [(5 x 65)/(13 x 65)]

step 5 Simplify the expression to have common denominator:
= 169/65 + 25/65

step 6 Take the common values out and rewrite the above expression like the below:
= 1/65 x (169/1 + 25/1)
= 1/65 x (169 + 25)

step 7Simplify the above expression further:
= 1/65 x 194
= 194/65
13/5 + 5/13 = 194/65

Hence,
13/5 plus 5/13 as a fraction is 194/65.

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

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

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

step 3 Simplify and rewrite the fraction:
= (169 + 25)/65
13/5 + 5/13 = 194/65

Hence,
13/5 plus 5/13 in fraction is 194/65