10/9 + 1/3 as a fraction

Learn how to find what is 10/9 plus 1/3 in fraction form just in a few minutes. We have covered the easiest method to write 10/9 + 1/3 as a fraction and decimal.

Summary: 10/9 plus 1/3 = 13/9
Since both fractions have unequal denominators, 10/9 plus 1/3 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 10/9 and fraction 1/3 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 9 and 3. 9 is the LCM of 9 and 3. Multiplying the LCM 9 with the numerators and denominators of both fractions (10/9 x 9/9) + (1/3 x 9/9), and simplify further in order to have the common denominator. So the equivalent fraction for 10/9 is 10/9 and for 1/3 is 3/9. By simplifying this fraction addition 10/9 + 3/9, it becomes 13/9.

CALCULATION: 10/9 + 1/3 as a fraction
10/9 + 1/3 = (?)
10/9 + 1/3 = [(10 x 3) + (1 x 9)]/(9 x 3)
= (30 + 9)/27
= 39/27
= (3 x 13)/(3 x 9)
= 13/9
10/9 + 1/3 = 13/9
10/9 plus 1/3 as a fraction is 13/9.

where
10/9 is a improper fraction as an addend,
1/3 is a proper fraction as an addend,
13/9 is the sum of 10/9 and 1/3.

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10/9 plus 1/3 as a decimal
10/9 + 1/3 = 13/9
13/9 = 1.4444
(10/9) + (1/3) as a decimal is 1.4444

where
1.4444 is the sum of 10/9 and 1/3.

The below workout with step by step calculation shows how to find the equivalent fraction between 10/9 and 1/3 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 10/9 plus 1/3 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(10/9) + (1/3) using LCM Method:
What is 10/9 plus 1/3 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/9
Fraction B: 1/3

What to be found?
(10/9) + (1/3) = ?
Find what's the sum of 10/9 and 1/3.

step 2 Compare the denominators of fractions 10/9 and 1/3 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 10/9 and 1/3 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 10/9 and 1/3:
The LCM of 9 and 3 is 9.

step 4 Write the fractions 10/9 and 1/3 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 10/9 + 1/3
= [(10 x 9)/(9 x 9)] + [(1 x 9)/(3 x 9)]

step 5 Simplify the expression to have common denominator:
= 10/9 + 3/9

step 6 Take the common values out and rewrite the above expression like the below:
= 1/9 x (10/1 + 3/1)
= 1/9 x (10 + 3)

step 7Simplify the above expression further:
= 1/9 x 13
= 13/9
10/9 + 1/3 = 13/9

Hence,
10/9 plus 1/3 as a fraction is 13/9.

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10/9 + 1/3 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/9
Fraction B: 1/3

What to be found?
(10/9)+(1/3) = ?
Find what's the sum of 10/9 and 1/3.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (10 x 3), find the product of numerator of Fraction B and denominator of Fraction A (1 x 9), and find the product of both denominators of Fraction A and Fraction B (9 x 3) and rewrite the equation as like the below:
= (10 x 3) + (1 x 9)/(9 x 3)

step 3 Simplify and rewrite the fraction:
= (30 + 9)/27
= 39/27
= 13/9
10/9 + 1/3 = 13/9

Hence,
10/9 plus 1/3 in fraction is 13/9