4/9 + 2/5 as a fraction

Learn how to find what is 4/9 plus 2/5 in fraction form just in a few minutes. We have covered the easiest method to write 4/9 + 2/5 as a fraction and decimal.

Summary: 4/9 plus 2/5 = 38/45
Since both fractions have unequal denominators, 4/9 plus 2/5 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 4/9 and fraction 2/5 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 9 and 5. 45 is the LCM of 9 and 5. Multiplying the LCM 45 with the numerators and denominators of both fractions (4/9 x 45/45) + (2/5 x 45/45), and simplify further in order to have the common denominator. So the equivalent fraction for 4/9 is 20/45 and for 2/5 is 18/45. By simplifying this fraction addition 20/45 + 18/45, it becomes 38/45.

Pie Chart Representation: 4/9 + 2/5 = 38/45

CALCULATION: 4/9 + 2/5 as a fraction
4/9 + 2/5 = (?)
4/9 + 2/5 = [(4 x 5) + (2 x 9)]/(9 x 5)
= (20 + 18)/45
= 38/45
4/9 + 2/5 = 38/45
4/9 plus 2/5 as a fraction is 38/45.

where
4/9 is a proper fraction as an addend,
2/5 is a proper fraction as an addend,
38/45 is the sum of 4/9 and 2/5.

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4/9 plus 2/5 as a decimal
4/9 + 2/5 = 38/45
38/45 = 0.8444
(4/9) + (2/5) as a decimal is 0.8444

where
0.8444 is the sum of 4/9 and 2/5.

The below workout with step by step calculation shows how to find the equivalent fraction between 4/9 and 2/5 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 4/9 plus 2/5 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(4/9) + (2/5) using LCM Method:
What is 4/9 plus 2/5 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 4/9
Fraction B: 2/5

What to be found?
(4/9) + (2/5) = ?
Find what's the sum of 4/9 and 2/5.

step 2 Compare the denominators of fractions 4/9 and 2/5 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 4/9 and 2/5 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 4/9 and 2/5:
The LCM of 9 and 5 is 45.

step 4 Write the fractions 4/9 and 2/5 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 4/9 + 2/5
= [(4 x 45)/(9 x 45)] + [(2 x 45)/(5 x 45)]

step 5 Simplify the expression to have common denominator:
= 20/45 + 18/45

step 6 Take the common values out and rewrite the above expression like the below:
= 1/45 x (20/1 + 18/1)
= 1/45 x (20 + 18)

step 7Simplify the above expression further:
= 1/45 x 38
= 38/45
4/9 + 2/5 = 38/45

Hence,
4/9 plus 2/5 as a fraction is 38/45.

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4/9 + 2/5 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 4/9
Fraction B: 2/5

What to be found?
(4/9)+(2/5) = ?
Find what's the sum of 4/9 and 2/5.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (4 x 5), 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 5) and rewrite the equation as like the below:
= (4 x 5) + (2 x 9)/(9 x 5)

step 3 Simplify and rewrite the fraction:
= (20 + 18)/45
4/9 + 2/5 = 38/45

Hence,
4/9 plus 2/5 in fraction is 38/45