5/7 + 5/13 as a fraction

Learn how to find what is 5/7 plus 5/13 in fraction form just in a few minutes. We have covered the easiest method to write 5/7 + 5/13 as a fraction and decimal.

Summary: 5/7 plus 5/13 = 100/91
Since both fractions have unequal denominators, 5/7 plus 5/13 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 5/7 and fraction 5/13 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 (5/7 x 91/91) + (5/13 x 91/91), and simplify further in order to have the common denominator. So the equivalent fraction for 5/7 is 65/91 and for 5/13 is 35/91. By simplifying this fraction addition 65/91 + 35/91, it becomes 100/91.

CALCULATION: 5/7 + 5/13 as a fraction
5/7 + 5/13 = (?)
5/7 + 5/13 = [(5 x 13) + (5 x 7)]/(7 x 13)
= (65 + 35)/91
= 100/91
5/7 + 5/13 = 100/91
5/7 plus 5/13 as a fraction is 100/91.

where
5/7 is a proper fraction as an addend,
5/13 is a proper fraction as an addend,
100/91 is the sum of 5/7 and 5/13.

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5/7 plus 5/13 as a decimal
5/7 + 5/13 = 100/91
100/91 = 1.0989
(5/7) + (5/13) as a decimal is 1.0989

where
1.0989 is the sum of 5/7 and 5/13.

The below workout with step by step calculation shows how to find the equivalent fraction between 5/7 and 5/13 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 5/7 plus 5/13 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(5/7) + (5/13) using LCM Method:
What is 5/7 plus 5/13 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 5/7
Fraction B: 5/13

What to be found?
(5/7) + (5/13) = ?
Find what's the sum of 5/7 and 5/13.

step 2 Compare the denominators of fractions 5/7 and 5/13 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 5/7 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 5/7 and 5/13:
The LCM of 7 and 13 is 91.

step 4 Write the fractions 5/7 and 5/13 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 5/7 + 5/13
= [(5 x 91)/(7 x 91)] + [(5 x 91)/(13 x 91)]

step 5 Simplify the expression to have common denominator:
= 65/91 + 35/91

step 6 Take the common values out and rewrite the above expression like the below:
= 1/91 x (65/1 + 35/1)
= 1/91 x (65 + 35)

step 7Simplify the above expression further:
= 1/91 x 100
= 100/91
5/7 + 5/13 = 100/91

Hence,
5/7 plus 5/13 as a fraction is 100/91.

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5/7 + 5/13 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 5/7
Fraction B: 5/13

What to be found?
(5/7)+(5/13) = ?
Find what's the sum of 5/7 and 5/13.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (5 x 13), find the product of numerator of Fraction B and denominator of Fraction A (5 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:
= (5 x 13) + (5 x 7)/(7 x 13)

step 3 Simplify and rewrite the fraction:
= (65 + 35)/91
5/7 + 5/13 = 100/91

Hence,
5/7 plus 5/13 in fraction is 100/91