1/3 + 2/21 as a fraction

Learn how to find what is 1/3 plus 2/21 in fraction form just in a few minutes. We have covered the easiest method to write 1/3 + 2/21 as a fraction and decimal.

Summary: 1/3 plus 2/21 = 3/7
Since both fractions have unequal denominators, 1/3 plus 2/21 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 1/3 and fraction 2/21 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 3 and 21. 21 is the LCM of 3 and 21. Multiplying the LCM 21 with the numerators and denominators of both fractions (1/3 x 21/21) + (2/21 x 21/21), and simplify further in order to have the common denominator. So the equivalent fraction for 1/3 is 7/21 and for 2/21 is 2/21. By simplifying this fraction addition 7/21 + 2/21, it becomes 9/21.

Pie Chart Representation: 1/3 + 2/21 = 3/7

CALCULATION: 1/3 + 2/21 as a fraction
1/3 + 2/21 = (?)
1/3 + 2/21 = [(1 x 21) + (2 x 3)]/(3 x 21)
= (21 + 6)/63
= 27/63
= (9 x 3)/(9 x 7)
= 3/7
1/3 + 2/21 = 3/7
1/3 plus 2/21 as a fraction is 3/7.

where
1/3 is a proper fraction as an addend,
2/21 is a proper fraction as an addend,
3/7 is the sum of 1/3 and 2/21.

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1/3 plus 2/21 as a decimal
1/3 + 2/21 = 3/7
3/7 = 0.4286
(1/3) + (2/21) as a decimal is 0.4286

where
0.4286 is the sum of 1/3 and 2/21.

The below workout with step by step calculation shows how to find the equivalent fraction between 1/3 and 2/21 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 1/3 plus 2/21 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(1/3) + (2/21) using LCM Method:
What is 1/3 plus 2/21 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 1/3
Fraction B: 2/21

What to be found?
(1/3) + (2/21) = ?
Find what's the sum of 1/3 and 2/21.

step 2 Compare the denominators of fractions 1/3 and 2/21 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 1/3 and 2/21 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 1/3 and 2/21:
The LCM of 3 and 21 is 21.

step 4 Write the fractions 1/3 and 2/21 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 1/3 + 2/21
= [(1 x 21)/(3 x 21)] + [(2 x 21)/(21 x 21)]

step 5 Simplify the expression to have common denominator:
= 7/21 + 2/21

step 6 Take the common values out and rewrite the above expression like the below:
= 1/21 x (7/1 + 2/1)
= 1/21 x (7 + 2)

step 7Simplify the above expression further:
= 1/21 x 9
= 9/21
= 3/7
1/3 + 2/21 = 3/7

Hence,
1/3 plus 2/21 as a fraction is 3/7.

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1/3 + 2/21 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 1/3
Fraction B: 2/21

What to be found?
(1/3)+(2/21) = ?
Find what's the sum of 1/3 and 2/21.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (1 x 21), find the product of numerator of Fraction B and denominator of Fraction A (2 x 3), and find the product of both denominators of Fraction A and Fraction B (3 x 21) and rewrite the equation as like the below:
= (1 x 21) + (2 x 3)/(3 x 21)

step 3 Simplify and rewrite the fraction:
= (21 + 6)/63
= 27/63
= 3/7
1/3 + 2/21 = 3/7

Hence,
1/3 plus 2/21 in fraction is 3/7