1/9 + 2/21 as a fraction

Learn how to find what is 1/9 plus 2/21 in fraction form just in a few minutes. We have covered the easiest method to write 1/9 + 2/21 as a fraction and decimal.

Summary: 1/9 plus 2/21 = 13/63
Since both fractions have unequal denominators, 1/9 plus 2/21 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 1/9 and fraction 2/21 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 9 and 21. 63 is the LCM of 9 and 21. Multiplying the LCM 63 with the numerators and denominators of both fractions (1/9 x 63/63) + (2/21 x 63/63), and simplify further in order to have the common denominator. So the equivalent fraction for 1/9 is 7/63 and for 2/21 is 6/63. By simplifying this fraction addition 7/63 + 6/63, it becomes 13/63.

Pie Chart Representation: 1/9 + 2/21 = 13/63

CALCULATION: 1/9 + 2/21 as a fraction
1/9 + 2/21 = (?)
1/9 + 2/21 = [(1 x 21) + (2 x 9)]/(9 x 21)
= (21 + 18)/189
= 39/189
= (3 x 13)/(3 x 63)
= 13/63
1/9 + 2/21 = 13/63
1/9 plus 2/21 as a fraction is 13/63.

where
1/9 is a proper fraction as an addend,
2/21 is a proper fraction as an addend,
13/63 is the sum of 1/9 and 2/21.

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1/9 plus 2/21 as a decimal
1/9 + 2/21 = 13/63
13/63 = 0.2063
(1/9) + (2/21) as a decimal is 0.2063

where
0.2063 is the sum of 1/9 and 2/21.

The below workout with step by step calculation shows how to find the equivalent fraction between 1/9 and 2/21 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 1/9 plus 2/21 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(1/9) + (2/21) using LCM Method:
What is 1/9 plus 2/21 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 1/9
Fraction B: 2/21

What to be found?
(1/9) + (2/21) = ?
Find what's the sum of 1/9 and 2/21.

step 2 Compare the denominators of fractions 1/9 and 2/21 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 1/9 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 1/9 and 2/21:
The LCM of 9 and 21 is 63.

step 4 Write the fractions 1/9 and 2/21 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 1/9 + 2/21
= [(1 x 63)/(9 x 63)] + [(2 x 63)/(21 x 63)]

step 5 Simplify the expression to have common denominator:
= 7/63 + 6/63

step 6 Take the common values out and rewrite the above expression like the below:
= 1/63 x (7/1 + 6/1)
= 1/63 x (7 + 6)

step 7Simplify the above expression further:
= 1/63 x 13
= 13/63
1/9 + 2/21 = 13/63

Hence,
1/9 plus 2/21 as a fraction is 13/63.

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1/9 + 2/21 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 1/9
Fraction B: 2/21

What to be found?
(1/9)+(2/21) = ?
Find what's the sum of 1/9 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 9), and find the product of both denominators of Fraction A and Fraction B (9 x 21) and rewrite the equation as like the below:
= (1 x 21) + (2 x 9)/(9 x 21)

step 3 Simplify and rewrite the fraction:
= (21 + 18)/189
= 39/189
= 13/63
1/9 + 2/21 = 13/63

Hence,
1/9 plus 2/21 in fraction is 13/63