18/5 + 13/4 as a fraction

Learn how to find what is 18/5 plus 13/4 in fraction form just in a few minutes. We have covered the easiest method to write 18/5 + 13/4 as a fraction and decimal.

Summary: 18/5 plus 13/4 = 137/20
Since both fractions have unequal denominators, 18/5 plus 13/4 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 18/5 and fraction 13/4 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 5 and 4. 20 is the LCM of 5 and 4. Multiplying the LCM 20 with the numerators and denominators of both fractions (18/5 x 20/20) + (13/4 x 20/20), and simplify further in order to have the common denominator. So the equivalent fraction for 18/5 is 72/20 and for 13/4 is 65/20. By simplifying this fraction addition 72/20 + 65/20, it becomes 137/20.

CALCULATION: 18/5 + 13/4 as a fraction
18/5 + 13/4 = (?)
18/5 + 13/4 = [(18 x 4) + (13 x 5)]/(5 x 4)
= (72 + 65)/20
= 137/20
18/5 + 13/4 = 137/20
18/5 plus 13/4 as a fraction is 137/20.

where
18/5 is a improper fraction as an addend,
13/4 is a improper fraction as an addend,
137/20 is the sum of 18/5 and 13/4.

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18/5 plus 13/4 as a decimal
18/5 + 13/4 = 137/20
137/20 = 6.85
(18/5) + (13/4) as a decimal is 6.85

where
6.85 is the sum of 18/5 and 13/4.

The below workout with step by step calculation shows how to find the equivalent fraction between 18/5 and 13/4 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 18/5 plus 13/4 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(18/5) + (13/4) using LCM Method:
What is 18/5 plus 13/4 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 18/5
Fraction B: 13/4

What to be found?
(18/5) + (13/4) = ?
Find what's the sum of 18/5 and 13/4.

step 2 Compare the denominators of fractions 18/5 and 13/4 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 18/5 and 13/4 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 18/5 and 13/4:
The LCM of 5 and 4 is 20.

step 4 Write the fractions 18/5 and 13/4 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 18/5 + 13/4
= [(18 x 20)/(5 x 20)] + [(13 x 20)/(4 x 20)]

step 5 Simplify the expression to have common denominator:
= 72/20 + 65/20

step 6 Take the common values out and rewrite the above expression like the below:
= 1/20 x (72/1 + 65/1)
= 1/20 x (72 + 65)

step 7Simplify the above expression further:
= 1/20 x 137
= 137/20
18/5 + 13/4 = 137/20

Hence,
18/5 plus 13/4 as a fraction is 137/20.

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18/5 + 13/4 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 18/5
Fraction B: 13/4

What to be found?
(18/5)+(13/4) = ?
Find what's the sum of 18/5 and 13/4.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (18 x 4), find the product of numerator of Fraction B and denominator of Fraction A (13 x 5), and find the product of both denominators of Fraction A and Fraction B (5 x 4) and rewrite the equation as like the below:
= (18 x 4) + (13 x 5)/(5 x 4)

step 3 Simplify and rewrite the fraction:
= (72 + 65)/20
18/5 + 13/4 = 137/20

Hence,
18/5 plus 13/4 in fraction is 137/20