10/9 + 5/6 as a fraction

Learn how to find what is 10/9 plus 5/6 in fraction form just in a few minutes. We have covered the easiest method to write 10/9 + 5/6 as a fraction and decimal.

Summary: 10/9 plus 5/6 = 35/18
Since both fractions have unequal denominators, 10/9 plus 5/6 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 10/9 and fraction 5/6 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 9 and 6. 18 is the LCM of 9 and 6. Multiplying the LCM 18 with the numerators and denominators of both fractions (10/9 x 18/18) + (5/6 x 18/18), and simplify further in order to have the common denominator. So the equivalent fraction for 10/9 is 20/18 and for 5/6 is 15/18. By simplifying this fraction addition 20/18 + 15/18, it becomes 35/18.

CALCULATION: 10/9 + 5/6 as a fraction
10/9 + 5/6 = (?)
10/9 + 5/6 = [(10 x 6) + (5 x 9)]/(9 x 6)
= (60 + 45)/54
= 105/54
= (3 x 35)/(3 x 18)
= 35/18
10/9 + 5/6 = 35/18
10/9 plus 5/6 as a fraction is 35/18.

where
10/9 is a improper fraction as an addend,
5/6 is a proper fraction as an addend,
35/18 is the sum of 10/9 and 5/6.

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10/9 plus 5/6 as a decimal
10/9 + 5/6 = 35/18
35/18 = 1.9444
(10/9) + (5/6) as a decimal is 1.9444

where
1.9444 is the sum of 10/9 and 5/6.

The below workout with step by step calculation shows how to find the equivalent fraction between 10/9 and 5/6 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 10/9 plus 5/6 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(10/9) + (5/6) using LCM Method:
What is 10/9 plus 5/6 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/9
Fraction B: 5/6

What to be found?
(10/9) + (5/6) = ?
Find what's the sum of 10/9 and 5/6.

step 2 Compare the denominators of fractions 10/9 and 5/6 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 10/9 and 5/6 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 5/6:
The LCM of 9 and 6 is 18.

step 4 Write the fractions 10/9 and 5/6 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 10/9 + 5/6
= [(10 x 18)/(9 x 18)] + [(5 x 18)/(6 x 18)]

step 5 Simplify the expression to have common denominator:
= 20/18 + 15/18

step 6 Take the common values out and rewrite the above expression like the below:
= 1/18 x (20/1 + 15/1)
= 1/18 x (20 + 15)

step 7Simplify the above expression further:
= 1/18 x 35
= 35/18
10/9 + 5/6 = 35/18

Hence,
10/9 plus 5/6 as a fraction is 35/18.

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10/9 + 5/6 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/9
Fraction B: 5/6

What to be found?
(10/9)+(5/6) = ?
Find what's the sum of 10/9 and 5/6.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (10 x 6), find the product of numerator of Fraction B and denominator of Fraction A (5 x 9), and find the product of both denominators of Fraction A and Fraction B (9 x 6) and rewrite the equation as like the below:
= (10 x 6) + (5 x 9)/(9 x 6)

step 3 Simplify and rewrite the fraction:
= (60 + 45)/54
= 105/54
= 35/18
10/9 + 5/6 = 35/18

Hence,
10/9 plus 5/6 in fraction is 35/18