13/4 + 5/8 as a fraction

Learn how to find what is 13/4 plus 5/8 in fraction form just in a few minutes. We have covered the easiest method to write 13/4 + 5/8 as a fraction and decimal.

Summary: 13/4 plus 5/8 = 31/8
Since both fractions have unequal denominators, 13/4 plus 5/8 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/4 and fraction 5/8 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 4 and 8. 8 is the LCM of 4 and 8. Multiplying the LCM 8 with the numerators and denominators of both fractions (13/4 x 8/8) + (5/8 x 8/8), and simplify further in order to have the common denominator. So the equivalent fraction for 13/4 is 26/8 and for 5/8 is 5/8. By simplifying this fraction addition 26/8 + 5/8, it becomes 31/8.

CALCULATION: 13/4 + 5/8 as a fraction
13/4 + 5/8 = (?)
13/4 + 5/8 = [(13 x 8) + (5 x 4)]/(4 x 8)
= (104 + 20)/32
= 124/32
= (4 x 31)/(4 x 8)
= 31/8
13/4 + 5/8 = 31/8
13/4 plus 5/8 as a fraction is 31/8.

where
13/4 is a improper fraction as an addend,
5/8 is a proper fraction as an addend,
31/8 is the sum of 13/4 and 5/8.

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13/4 plus 5/8 as a decimal
13/4 + 5/8 = 31/8
31/8 = 3.875
(13/4) + (5/8) as a decimal is 3.875

where
3.875 is the sum of 13/4 and 5/8.

The below workout with step by step calculation shows how to find the equivalent fraction between 13/4 and 5/8 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 13/4 plus 5/8 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(13/4) + (5/8) using LCM Method:
What is 13/4 plus 5/8 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/4
Fraction B: 5/8

What to be found?
(13/4) + (5/8) = ?
Find what's the sum of 13/4 and 5/8.

step 2 Compare the denominators of fractions 13/4 and 5/8 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 13/4 and 5/8 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 13/4 and 5/8:
The LCM of 4 and 8 is 8.

step 4 Write the fractions 13/4 and 5/8 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/4 + 5/8
= [(13 x 8)/(4 x 8)] + [(5 x 8)/(8 x 8)]

step 5 Simplify the expression to have common denominator:
= 26/8 + 5/8

step 6 Take the common values out and rewrite the above expression like the below:
= 1/8 x (26/1 + 5/1)
= 1/8 x (26 + 5)

step 7Simplify the above expression further:
= 1/8 x 31
= 31/8
13/4 + 5/8 = 31/8

Hence,
13/4 plus 5/8 as a fraction is 31/8.

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13/4 + 5/8 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/4
Fraction B: 5/8

What to be found?
(13/4)+(5/8) = ?
Find what's the sum of 13/4 and 5/8.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (13 x 8), find the product of numerator of Fraction B and denominator of Fraction A (5 x 4), and find the product of both denominators of Fraction A and Fraction B (4 x 8) and rewrite the equation as like the below:
= (13 x 8) + (5 x 4)/(4 x 8)

step 3 Simplify and rewrite the fraction:
= (104 + 20)/32
= 124/32
= 31/8
13/4 + 5/8 = 31/8

Hence,
13/4 plus 5/8 in fraction is 31/8