18/7 + 3/8 as a fraction

Learn how to find what is 18/7 plus 3/8 in fraction form just in a few minutes. We have covered the easiest method to write 18/7 + 3/8 as a fraction and decimal.

Summary: 18/7 plus 3/8 = 165/56
Since both fractions have unequal denominators, 18/7 plus 3/8 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 18/7 and fraction 3/8 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 7 and 8. 56 is the LCM of 7 and 8. Multiplying the LCM 56 with the numerators and denominators of both fractions (18/7 x 56/56) + (3/8 x 56/56), and simplify further in order to have the common denominator. So the equivalent fraction for 18/7 is 144/56 and for 3/8 is 21/56. By simplifying this fraction addition 144/56 + 21/56, it becomes 165/56.

CALCULATION: 18/7 + 3/8 as a fraction
18/7 + 3/8 = (?)
18/7 + 3/8 = [(18 x 8) + (3 x 7)]/(7 x 8)
= (144 + 21)/56
= 165/56
18/7 + 3/8 = 165/56
18/7 plus 3/8 as a fraction is 165/56.

where
18/7 is a improper fraction as an addend,
3/8 is a proper fraction as an addend,
165/56 is the sum of 18/7 and 3/8.

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18/7 plus 3/8 as a decimal
18/7 + 3/8 = 165/56
165/56 = 2.9464
(18/7) + (3/8) as a decimal is 2.9464

where
2.9464 is the sum of 18/7 and 3/8.

The below workout with step by step calculation shows how to find the equivalent fraction between 18/7 and 3/8 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 18/7 plus 3/8 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(18/7) + (3/8) using LCM Method:
What is 18/7 plus 3/8 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 18/7
Fraction B: 3/8

What to be found?
(18/7) + (3/8) = ?
Find what's the sum of 18/7 and 3/8.

step 2 Compare the denominators of fractions 18/7 and 3/8 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 18/7 and 3/8 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 18/7 and 3/8:
The LCM of 7 and 8 is 56.

step 4 Write the fractions 18/7 and 3/8 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 18/7 + 3/8
= [(18 x 56)/(7 x 56)] + [(3 x 56)/(8 x 56)]

step 5 Simplify the expression to have common denominator:
= 144/56 + 21/56

step 6 Take the common values out and rewrite the above expression like the below:
= 1/56 x (144/1 + 21/1)
= 1/56 x (144 + 21)

step 7Simplify the above expression further:
= 1/56 x 165
= 165/56
18/7 + 3/8 = 165/56

Hence,
18/7 plus 3/8 as a fraction is 165/56.

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18/7 + 3/8 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 18/7
Fraction B: 3/8

What to be found?
(18/7)+(3/8) = ?
Find what's the sum of 18/7 and 3/8.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (18 x 8), find the product of numerator of Fraction B and denominator of Fraction A (3 x 7), and find the product of both denominators of Fraction A and Fraction B (7 x 8) and rewrite the equation as like the below:
= (18 x 8) + (3 x 7)/(7 x 8)

step 3 Simplify and rewrite the fraction:
= (144 + 21)/56
18/7 + 3/8 = 165/56

Hence,
18/7 plus 3/8 in fraction is 165/56