10/3 + 7/13 as a fraction

Learn how to find what is 10/3 plus 7/13 in fraction form just in a few minutes. We have covered the easiest method to write 10/3 + 7/13 as a fraction and decimal.

Summary: 10/3 plus 7/13 = 151/39
Since both fractions have unequal denominators, 10/3 plus 7/13 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 10/3 and fraction 7/13 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 (10/3 x 39/39) + (7/13 x 39/39), and simplify further in order to have the common denominator. So the equivalent fraction for 10/3 is 130/39 and for 7/13 is 21/39. By simplifying this fraction addition 130/39 + 21/39, it becomes 151/39.

CALCULATION: 10/3 + 7/13 as a fraction
10/3 + 7/13 = (?)
10/3 + 7/13 = [(10 x 13) + (7 x 3)]/(3 x 13)
= (130 + 21)/39
= 151/39
10/3 + 7/13 = 151/39
10/3 plus 7/13 as a fraction is 151/39.

where
10/3 is a improper fraction as an addend,
7/13 is a proper fraction as an addend,
151/39 is the sum of 10/3 and 7/13.

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10/3 plus 7/13 as a decimal
10/3 + 7/13 = 151/39
151/39 = 3.8718
(10/3) + (7/13) as a decimal is 3.8718

where
3.8718 is the sum of 10/3 and 7/13.

The below workout with step by step calculation shows how to find the equivalent fraction between 10/3 and 7/13 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 10/3 plus 7/13 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(10/3) + (7/13) using LCM Method:
What is 10/3 plus 7/13 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/3
Fraction B: 7/13

What to be found?
(10/3) + (7/13) = ?
Find what's the sum of 10/3 and 7/13.

step 2 Compare the denominators of fractions 10/3 and 7/13 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 10/3 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 10/3 and 7/13:
The LCM of 3 and 13 is 39.

step 4 Write the fractions 10/3 and 7/13 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 10/3 + 7/13
= [(10 x 39)/(3 x 39)] + [(7 x 39)/(13 x 39)]

step 5 Simplify the expression to have common denominator:
= 130/39 + 21/39

step 6 Take the common values out and rewrite the above expression like the below:
= 1/39 x (130/1 + 21/1)
= 1/39 x (130 + 21)

step 7Simplify the above expression further:
= 1/39 x 151
= 151/39
10/3 + 7/13 = 151/39

Hence,
10/3 plus 7/13 as a fraction is 151/39.

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10/3 + 7/13 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/3
Fraction B: 7/13

What to be found?
(10/3)+(7/13) = ?
Find what's the sum of 10/3 and 7/13.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (10 x 13), find the product of numerator of Fraction B and denominator of Fraction A (7 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:
= (10 x 13) + (7 x 3)/(3 x 13)

step 3 Simplify and rewrite the fraction:
= (130 + 21)/39
10/3 + 7/13 = 151/39

Hence,
10/3 plus 7/13 in fraction is 151/39