13/9 + 16/19 as a fraction

Learn how to find what is 13/9 plus 16/19 in fraction form just in a few minutes. We have covered the easiest method to write 13/9 + 16/19 as a fraction and decimal.

Summary: 13/9 plus 16/19 = 391/171
Since both fractions have unequal denominators, 13/9 plus 16/19 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/9 and fraction 16/19 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 9 and 19. 171 is the LCM of 9 and 19. Multiplying the LCM 171 with the numerators and denominators of both fractions (13/9 x 171/171) + (16/19 x 171/171), and simplify further in order to have the common denominator. So the equivalent fraction for 13/9 is 247/171 and for 16/19 is 144/171. By simplifying this fraction addition 247/171 + 144/171, it becomes 391/171.

CALCULATION: 13/9 + 16/19 as a fraction
13/9 + 16/19 = (?)
13/9 + 16/19 = [(13 x 19) + (16 x 9)]/(9 x 19)
= (247 + 144)/171
= 391/171
13/9 + 16/19 = 391/171
13/9 plus 16/19 as a fraction is 391/171.

where
13/9 is a improper fraction as an addend,
16/19 is a proper fraction as an addend,
391/171 is the sum of 13/9 and 16/19.

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13/9 plus 16/19 as a decimal
13/9 + 16/19 = 391/171
391/171 = 2.2865
(13/9) + (16/19) as a decimal is 2.2865

where
2.2865 is the sum of 13/9 and 16/19.

The below workout with step by step calculation shows how to find the equivalent fraction between 13/9 and 16/19 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 13/9 plus 16/19 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(13/9) + (16/19) using LCM Method:
What is 13/9 plus 16/19 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/9
Fraction B: 16/19

What to be found?
(13/9) + (16/19) = ?
Find what's the sum of 13/9 and 16/19.

step 2 Compare the denominators of fractions 13/9 and 16/19 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 13/9 and 16/19 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 13/9 and 16/19:
The LCM of 9 and 19 is 171.

step 4 Write the fractions 13/9 and 16/19 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/9 + 16/19
= [(13 x 171)/(9 x 171)] + [(16 x 171)/(19 x 171)]

step 5 Simplify the expression to have common denominator:
= 247/171 + 144/171

step 6 Take the common values out and rewrite the above expression like the below:
= 1/171 x (247/1 + 144/1)
= 1/171 x (247 + 144)

step 7Simplify the above expression further:
= 1/171 x 391
= 391/171
13/9 + 16/19 = 391/171

Hence,
13/9 plus 16/19 as a fraction is 391/171.

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13/9 + 16/19 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/9
Fraction B: 16/19

What to be found?
(13/9)+(16/19) = ?
Find what's the sum of 13/9 and 16/19.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (13 x 19), find the product of numerator of Fraction B and denominator of Fraction A (16 x 9), and find the product of both denominators of Fraction A and Fraction B (9 x 19) and rewrite the equation as like the below:
= (13 x 19) + (16 x 9)/(9 x 19)

step 3 Simplify and rewrite the fraction:
= (247 + 144)/171
13/9 + 16/19 = 391/171

Hence,
13/9 plus 16/19 in fraction is 391/171