13/7 + 7/13 as a fraction

Learn how to find what is 13/7 plus 7/13 in fraction form just in a few minutes. We have covered the easiest method to write 13/7 + 7/13 as a fraction and decimal.

Summary: 13/7 plus 7/13 = 218/91
Since both fractions have unequal denominators, 13/7 plus 7/13 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/7 and fraction 7/13 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 7 and 13. 91 is the LCM of 7 and 13. Multiplying the LCM 91 with the numerators and denominators of both fractions (13/7 x 91/91) + (7/13 x 91/91), and simplify further in order to have the common denominator. So the equivalent fraction for 13/7 is 169/91 and for 7/13 is 49/91. By simplifying this fraction addition 169/91 + 49/91, it becomes 218/91.

CALCULATION: 13/7 + 7/13 as a fraction
13/7 + 7/13 = (?)
13/7 + 7/13 = [(13 x 13) + (7 x 7)]/(7 x 13)
= (169 + 49)/91
= 218/91
13/7 + 7/13 = 218/91
13/7 plus 7/13 as a fraction is 218/91.

where
13/7 is a improper fraction as an addend,
7/13 is a proper fraction as an addend,
218/91 is the sum of 13/7 and 7/13.

---

13/7 plus 7/13 as a decimal
13/7 + 7/13 = 218/91
218/91 = 2.3956
(13/7) + (7/13) as a decimal is 2.3956

where
2.3956 is the sum of 13/7 and 7/13.

The below workout with step by step calculation shows how to find the equivalent fraction between 13/7 and 7/13 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 13/7 plus 7/13 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(13/7) + (7/13) using LCM Method:
What is 13/7 plus 7/13 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/7
Fraction B: 7/13

What to be found?
(13/7) + (7/13) = ?
Find what's the sum of 13/7 and 7/13.

step 2 Compare the denominators of fractions 13/7 and 7/13 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 13/7 and 7/13 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 13/7 and 7/13:
The LCM of 7 and 13 is 91.

step 4 Write the fractions 13/7 and 7/13 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/7 + 7/13
= [(13 x 91)/(7 x 91)] + [(7 x 91)/(13 x 91)]

step 5 Simplify the expression to have common denominator:
= 169/91 + 49/91

step 6 Take the common values out and rewrite the above expression like the below:
= 1/91 x (169/1 + 49/1)
= 1/91 x (169 + 49)

step 7Simplify the above expression further:
= 1/91 x 218
= 218/91
13/7 + 7/13 = 218/91

Hence,
13/7 plus 7/13 as a fraction is 218/91.

---

13/7 + 7/13 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/7
Fraction B: 7/13

What to be found?
(13/7)+(7/13) = ?
Find what's the sum of 13/7 and 7/13.

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 (7 x 7), and find the product of both denominators of Fraction A and Fraction B (7 x 13) and rewrite the equation as like the below:
= (13 x 13) + (7 x 7)/(7 x 13)

step 3 Simplify and rewrite the fraction:
= (169 + 49)/91
13/7 + 7/13 = 218/91

Hence,
13/7 plus 7/13 in fraction is 218/91