13/7 + 5/14 as a fraction

Learn how to find what is 13/7 plus 5/14 in fraction form just in a few minutes. We have covered the easiest method to write 13/7 + 5/14 as a fraction and decimal.

Summary: 13/7 plus 5/14 = 31/14
Since both fractions have unequal denominators, 13/7 plus 5/14 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/7 and fraction 5/14 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 7 and 14. 14 is the LCM of 7 and 14. Multiplying the LCM 14 with the numerators and denominators of both fractions (13/7 x 14/14) + (5/14 x 14/14), and simplify further in order to have the common denominator. So the equivalent fraction for 13/7 is 26/14 and for 5/14 is 5/14. By simplifying this fraction addition 26/14 + 5/14, it becomes 31/14.

CALCULATION: 13/7 + 5/14 as a fraction
13/7 + 5/14 = (?)
13/7 + 5/14 = [(13 x 14) + (5 x 7)]/(7 x 14)
= (182 + 35)/98
= 217/98
= (7 x 31)/(7 x 14)
= 31/14
13/7 + 5/14 = 31/14
13/7 plus 5/14 as a fraction is 31/14.

where
13/7 is a improper fraction as an addend,
5/14 is a proper fraction as an addend,
31/14 is the sum of 13/7 and 5/14.

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13/7 plus 5/14 as a decimal
13/7 + 5/14 = 31/14
31/14 = 2.2143
(13/7) + (5/14) as a decimal is 2.2143

where
2.2143 is the sum of 13/7 and 5/14.

The below workout with step by step calculation shows how to find the equivalent fraction between 13/7 and 5/14 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 13/7 plus 5/14 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(13/7) + (5/14) using LCM Method:
What is 13/7 plus 5/14 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/7
Fraction B: 5/14

What to be found?
(13/7) + (5/14) = ?
Find what's the sum of 13/7 and 5/14.

step 2 Compare the denominators of fractions 13/7 and 5/14 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 13/7 and 5/14 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 13/7 and 5/14:
The LCM of 7 and 14 is 14.

step 4 Write the fractions 13/7 and 5/14 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/7 + 5/14
= [(13 x 14)/(7 x 14)] + [(5 x 14)/(14 x 14)]

step 5 Simplify the expression to have common denominator:
= 26/14 + 5/14

step 6 Take the common values out and rewrite the above expression like the below:
= 1/14 x (26/1 + 5/1)
= 1/14 x (26 + 5)

step 7Simplify the above expression further:
= 1/14 x 31
= 31/14
13/7 + 5/14 = 31/14

Hence,
13/7 plus 5/14 as a fraction is 31/14.

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13/7 + 5/14 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/7
Fraction B: 5/14

What to be found?
(13/7)+(5/14) = ?
Find what's the sum of 13/7 and 5/14.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (13 x 14), find the product of numerator of Fraction B and denominator of Fraction A (5 x 7), and find the product of both denominators of Fraction A and Fraction B (7 x 14) and rewrite the equation as like the below:
= (13 x 14) + (5 x 7)/(7 x 14)

step 3 Simplify and rewrite the fraction:
= (182 + 35)/98
= 217/98
= 31/14
13/7 + 5/14 = 31/14

Hence,
13/7 plus 5/14 in fraction is 31/14