13/3 + 10/7 as a fraction

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

Summary: 13/3 plus 10/7 = 121/21
Since both fractions have unequal denominators, 13/3 plus 10/7 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/3 and fraction 10/7 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 3 and 7. 21 is the LCM of 3 and 7. Multiplying the LCM 21 with the numerators and denominators of both fractions (13/3 x 21/21) + (10/7 x 21/21), and simplify further in order to have the common denominator. So the equivalent fraction for 13/3 is 91/21 and for 10/7 is 30/21. By simplifying this fraction addition 91/21 + 30/21, it becomes 121/21.

CALCULATION: 13/3 + 10/7 as a fraction
13/3 + 10/7 = (?)
13/3 + 10/7 = [(13 x 7) + (10 x 3)]/(3 x 7)
= (91 + 30)/21
= 121/21
13/3 + 10/7 = 121/21
13/3 plus 10/7 as a fraction is 121/21.

where
13/3 is a improper fraction as an addend,
10/7 is a improper fraction as an addend,
121/21 is the sum of 13/3 and 10/7.

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13/3 plus 10/7 as a decimal
13/3 + 10/7 = 121/21
121/21 = 5.7619
(13/3) + (10/7) as a decimal is 5.7619

where
5.7619 is the sum of 13/3 and 10/7.

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

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

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

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

step 2 Compare the denominators of fractions 13/3 and 10/7 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 13/3 and 10/7 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 13/3 and 10/7:
The LCM of 3 and 7 is 21.

step 4 Write the fractions 13/3 and 10/7 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/3 + 10/7
= [(13 x 21)/(3 x 21)] + [(10 x 21)/(7 x 21)]

step 5 Simplify the expression to have common denominator:
= 91/21 + 30/21

step 6 Take the common values out and rewrite the above expression like the below:
= 1/21 x (91/1 + 30/1)
= 1/21 x (91 + 30)

step 7Simplify the above expression further:
= 1/21 x 121
= 121/21
13/3 + 10/7 = 121/21

Hence,
13/3 plus 10/7 as a fraction is 121/21.

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

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

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (13 x 7), find the product of numerator of Fraction B and denominator of Fraction A (10 x 3), and find the product of both denominators of Fraction A and Fraction B (3 x 7) and rewrite the equation as like the below:
= (13 x 7) + (10 x 3)/(3 x 7)

step 3 Simplify and rewrite the fraction:
= (91 + 30)/21
13/3 + 10/7 = 121/21

Hence,
13/3 plus 10/7 in fraction is 121/21