18/5 + 5/9 as a fraction

Learn how to find what is 18/5 plus 5/9 in fraction form just in a few minutes. We have covered the easiest method to write 18/5 + 5/9 as a fraction and decimal.

Summary: 18/5 plus 5/9 = 187/45
Since both fractions have unequal denominators, 18/5 plus 5/9 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 18/5 and fraction 5/9 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 5 and 9. 45 is the LCM of 5 and 9. Multiplying the LCM 45 with the numerators and denominators of both fractions (18/5 x 45/45) + (5/9 x 45/45), and simplify further in order to have the common denominator. So the equivalent fraction for 18/5 is 162/45 and for 5/9 is 25/45. By simplifying this fraction addition 162/45 + 25/45, it becomes 187/45.

CALCULATION: 18/5 + 5/9 as a fraction
18/5 + 5/9 = (?)
18/5 + 5/9 = [(18 x 9) + (5 x 5)]/(5 x 9)
= (162 + 25)/45
= 187/45
18/5 + 5/9 = 187/45
18/5 plus 5/9 as a fraction is 187/45.

where
18/5 is a improper fraction as an addend,
5/9 is a proper fraction as an addend,
187/45 is the sum of 18/5 and 5/9.

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18/5 plus 5/9 as a decimal
18/5 + 5/9 = 187/45
187/45 = 4.1556
(18/5) + (5/9) as a decimal is 4.1556

where
4.1556 is the sum of 18/5 and 5/9.

The below workout with step by step calculation shows how to find the equivalent fraction between 18/5 and 5/9 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 18/5 plus 5/9 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(18/5) + (5/9) using LCM Method:
What is 18/5 plus 5/9 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 18/5
Fraction B: 5/9

What to be found?
(18/5) + (5/9) = ?
Find what's the sum of 18/5 and 5/9.

step 2 Compare the denominators of fractions 18/5 and 5/9 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 18/5 and 5/9 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 18/5 and 5/9:
The LCM of 5 and 9 is 45.

step 4 Write the fractions 18/5 and 5/9 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 18/5 + 5/9
= [(18 x 45)/(5 x 45)] + [(5 x 45)/(9 x 45)]

step 5 Simplify the expression to have common denominator:
= 162/45 + 25/45

step 6 Take the common values out and rewrite the above expression like the below:
= 1/45 x (162/1 + 25/1)
= 1/45 x (162 + 25)

step 7Simplify the above expression further:
= 1/45 x 187
= 187/45
18/5 + 5/9 = 187/45

Hence,
18/5 plus 5/9 as a fraction is 187/45.

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18/5 + 5/9 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 18/5
Fraction B: 5/9

What to be found?
(18/5)+(5/9) = ?
Find what's the sum of 18/5 and 5/9.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (18 x 9), find the product of numerator of Fraction B and denominator of Fraction A (5 x 5), and find the product of both denominators of Fraction A and Fraction B (5 x 9) and rewrite the equation as like the below:
= (18 x 9) + (5 x 5)/(5 x 9)

step 3 Simplify and rewrite the fraction:
= (162 + 25)/45
18/5 + 5/9 = 187/45

Hence,
18/5 plus 5/9 in fraction is 187/45