6/7 + 2/3 as a fraction

Learn how to find what is 6/7 plus 2/3 in fraction form just in a few minutes. We have covered the easiest method to write 6/7 + 2/3 as a fraction and decimal.

Summary: 6/7 plus 2/3 = 32/21
Since both fractions have unequal denominators, 6/7 plus 2/3 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 6/7 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 (6/7 x 21/21) + (2/3 x 21/21), and simplify further in order to have the common denominator. So the equivalent fraction for 6/7 is 18/21 and for 2/3 is 14/21. By simplifying this fraction addition 18/21 + 14/21, it becomes 32/21.

CALCULATION: 6/7 + 2/3 as a fraction
6/7 + 2/3 = (?)
6/7 + 2/3 = [(6 x 3) + (2 x 7)]/(7 x 3)
= (18 + 14)/21
= 32/21
6/7 + 2/3 = 32/21
6/7 plus 2/3 as a fraction is 32/21.

where
6/7 is a proper fraction as an addend,
2/3 is a proper fraction as an addend,
32/21 is the sum of 6/7 and 2/3.

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6/7 plus 2/3 as a decimal
6/7 + 2/3 = 32/21
32/21 = 1.5238
(6/7) + (2/3) as a decimal is 1.5238

where
1.5238 is the sum of 6/7 and 2/3.

The below workout with step by step calculation shows how to find the equivalent fraction between 6/7 and 2/3 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 6/7 plus 2/3 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(6/7) + (2/3) using LCM Method:
What is 6/7 plus 2/3 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 6/7
Fraction B: 2/3

What to be found?
(6/7) + (2/3) = ?
Find what's the sum of 6/7 and 2/3.

step 2 Compare the denominators of fractions 6/7 and 2/3 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 6/7 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 6/7 and 2/3:
The LCM of 7 and 3 is 21.

step 4 Write the fractions 6/7 and 2/3 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 6/7 + 2/3
= [(6 x 21)/(7 x 21)] + [(2 x 21)/(3 x 21)]

step 5 Simplify the expression to have common denominator:
= 18/21 + 14/21

step 6 Take the common values out and rewrite the above expression like the below:
= 1/21 x (18/1 + 14/1)
= 1/21 x (18 + 14)

step 7Simplify the above expression further:
= 1/21 x 32
= 32/21
6/7 + 2/3 = 32/21

Hence,
6/7 plus 2/3 as a fraction is 32/21.

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6/7 + 2/3 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 6/7
Fraction B: 2/3

What to be found?
(6/7)+(2/3) = ?
Find what's the sum of 6/7 and 2/3.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (6 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:
= (6 x 3) + (2 x 7)/(7 x 3)

step 3 Simplify and rewrite the fraction:
= (18 + 14)/21
6/7 + 2/3 = 32/21

Hence,
6/7 plus 2/3 in fraction is 32/21