5/3 + 5/13 as a fraction

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

Summary: 5/3 plus 5/13 = 80/39
Since both fractions have unequal denominators, 5/3 plus 5/13 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 5/3 and fraction 5/13 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 3 and 13. 39 is the LCM of 3 and 13. Multiplying the LCM 39 with the numerators and denominators of both fractions (5/3 x 39/39) + (5/13 x 39/39), and simplify further in order to have the common denominator. So the equivalent fraction for 5/3 is 65/39 and for 5/13 is 15/39. By simplifying this fraction addition 65/39 + 15/39, it becomes 80/39.

CALCULATION: 5/3 + 5/13 as a fraction
5/3 + 5/13 = (?)
5/3 + 5/13 = [(5 x 13) + (5 x 3)]/(3 x 13)
= (65 + 15)/39
= 80/39
5/3 + 5/13 = 80/39
5/3 plus 5/13 as a fraction is 80/39.

where
5/3 is a improper fraction as an addend,
5/13 is a proper fraction as an addend,
80/39 is the sum of 5/3 and 5/13.

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5/3 plus 5/13 as a decimal
5/3 + 5/13 = 80/39
80/39 = 2.0513
(5/3) + (5/13) as a decimal is 2.0513

where
2.0513 is the sum of 5/3 and 5/13.

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

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

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

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

step 2 Compare the denominators of fractions 5/3 and 5/13 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 5/3 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 5/3 and 5/13:
The LCM of 3 and 13 is 39.

step 4 Write the fractions 5/3 and 5/13 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 5/3 + 5/13
= [(5 x 39)/(3 x 39)] + [(5 x 39)/(13 x 39)]

step 5 Simplify the expression to have common denominator:
= 65/39 + 15/39

step 6 Take the common values out and rewrite the above expression like the below:
= 1/39 x (65/1 + 15/1)
= 1/39 x (65 + 15)

step 7Simplify the above expression further:
= 1/39 x 80
= 80/39
5/3 + 5/13 = 80/39

Hence,
5/3 plus 5/13 as a fraction is 80/39.

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

What to be found?
(5/3)+(5/13) = ?
Find what's the sum of 5/3 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 3), and find the product of both denominators of Fraction A and Fraction B (3 x 13) and rewrite the equation as like the below:
= (5 x 13) + (5 x 3)/(3 x 13)

step 3 Simplify and rewrite the fraction:
= (65 + 15)/39
5/3 + 5/13 = 80/39

Hence,
5/3 plus 5/13 in fraction is 80/39