10/9 + 3/13 as a fraction

Learn how to find what is 10/9 plus 3/13 in fraction form just in a few minutes. We have covered the easiest method to write 10/9 + 3/13 as a fraction and decimal.

Summary: 10/9 plus 3/13 = 157/117
Since both fractions have unequal denominators, 10/9 plus 3/13 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 10/9 and fraction 3/13 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 9 and 13. 117 is the LCM of 9 and 13. Multiplying the LCM 117 with the numerators and denominators of both fractions (10/9 x 117/117) + (3/13 x 117/117), and simplify further in order to have the common denominator. So the equivalent fraction for 10/9 is 130/117 and for 3/13 is 27/117. By simplifying this fraction addition 130/117 + 27/117, it becomes 157/117.

CALCULATION: 10/9 + 3/13 as a fraction
10/9 + 3/13 = (?)
10/9 + 3/13 = [(10 x 13) + (3 x 9)]/(9 x 13)
= (130 + 27)/117
= 157/117
10/9 + 3/13 = 157/117
10/9 plus 3/13 as a fraction is 157/117.

where
10/9 is a improper fraction as an addend,
3/13 is a proper fraction as an addend,
157/117 is the sum of 10/9 and 3/13.

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10/9 plus 3/13 as a decimal
10/9 + 3/13 = 157/117
157/117 = 1.3419
(10/9) + (3/13) as a decimal is 1.3419

where
1.3419 is the sum of 10/9 and 3/13.

The below workout with step by step calculation shows how to find the equivalent fraction between 10/9 and 3/13 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 10/9 plus 3/13 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(10/9) + (3/13) using LCM Method:
What is 10/9 plus 3/13 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/9
Fraction B: 3/13

What to be found?
(10/9) + (3/13) = ?
Find what's the sum of 10/9 and 3/13.

step 2 Compare the denominators of fractions 10/9 and 3/13 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 10/9 and 3/13 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 10/9 and 3/13:
The LCM of 9 and 13 is 117.

step 4 Write the fractions 10/9 and 3/13 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 10/9 + 3/13
= [(10 x 117)/(9 x 117)] + [(3 x 117)/(13 x 117)]

step 5 Simplify the expression to have common denominator:
= 130/117 + 27/117

step 6 Take the common values out and rewrite the above expression like the below:
= 1/117 x (130/1 + 27/1)
= 1/117 x (130 + 27)

step 7Simplify the above expression further:
= 1/117 x 157
= 157/117
10/9 + 3/13 = 157/117

Hence,
10/9 plus 3/13 as a fraction is 157/117.

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10/9 + 3/13 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/9
Fraction B: 3/13

What to be found?
(10/9)+(3/13) = ?
Find what's the sum of 10/9 and 3/13.

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 (3 x 9), and find the product of both denominators of Fraction A and Fraction B (9 x 13) and rewrite the equation as like the below:
= (10 x 13) + (3 x 9)/(9 x 13)

step 3 Simplify and rewrite the fraction:
= (130 + 27)/117
10/9 + 3/13 = 157/117

Hence,
10/9 plus 3/13 in fraction is 157/117