8/7 + 2/3 as a fraction

Learn how to find what is 8/7 plus 2/3 in fraction form just in a few minutes. We have covered the easiest method to write 8/7 + 2/3 as a fraction and decimal.

Summary: 8/7 plus 2/3 = 38/21
Since both fractions have unequal denominators, 8/7 plus 2/3 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 8/7 and fraction 2/3 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 7 and 3. 21 is the LCM of 7 and 3. Multiplying the LCM 21 with the numerators and denominators of both fractions (8/7 x 21/21) + (2/3 x 21/21), and simplify further in order to have the common denominator. So the equivalent fraction for 8/7 is 24/21 and for 2/3 is 14/21. By simplifying this fraction addition 24/21 + 14/21, it becomes 38/21.

CALCULATION: 8/7 + 2/3 as a fraction
8/7 + 2/3 = (?)
8/7 + 2/3 = [(8 x 3) + (2 x 7)]/(7 x 3)
= (24 + 14)/21
= 38/21
8/7 + 2/3 = 38/21
8/7 plus 2/3 as a fraction is 38/21.

where
8/7 is a improper fraction as an addend,
2/3 is a proper fraction as an addend,
38/21 is the sum of 8/7 and 2/3.

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8/7 plus 2/3 as a decimal
8/7 + 2/3 = 38/21
38/21 = 1.8095
(8/7) + (2/3) as a decimal is 1.8095

where
1.8095 is the sum of 8/7 and 2/3.

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

(8/7) + (2/3) using LCM Method:
What is 8/7 plus 2/3 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 8/7
Fraction B: 2/3

What to be found?
(8/7) + (2/3) = ?
Find what's the sum of 8/7 and 2/3.

step 2 Compare the denominators of fractions 8/7 and 2/3 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 8/7 and 2/3 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 8/7 and 2/3:
The LCM of 7 and 3 is 21.

step 4 Write the fractions 8/7 and 2/3 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 8/7 + 2/3
= [(8 x 21)/(7 x 21)] + [(2 x 21)/(3 x 21)]

step 5 Simplify the expression to have common denominator:
= 24/21 + 14/21

step 6 Take the common values out and rewrite the above expression like the below:
= 1/21 x (24/1 + 14/1)
= 1/21 x (24 + 14)

step 7Simplify the above expression further:
= 1/21 x 38
= 38/21
8/7 + 2/3 = 38/21

Hence,
8/7 plus 2/3 as a fraction is 38/21.

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8/7 + 2/3 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 8/7
Fraction B: 2/3

What to be found?
(8/7)+(2/3) = ?
Find what's the sum of 8/7 and 2/3.

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

step 3 Simplify and rewrite the fraction:
= (24 + 14)/21
8/7 + 2/3 = 38/21

Hence,
8/7 plus 2/3 in fraction is 38/21