4/9 + 5/12 as a fraction

Learn how to find what is 4/9 plus 5/12 in fraction form just in a few minutes. We have covered the easiest method to write 4/9 + 5/12 as a fraction and decimal.

Summary: 4/9 plus 5/12 = 31/36
Since both fractions have unequal denominators, 4/9 plus 5/12 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 4/9 and fraction 5/12 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 9 and 12. 36 is the LCM of 9 and 12. Multiplying the LCM 36 with the numerators and denominators of both fractions (4/9 x 36/36) + (5/12 x 36/36), and simplify further in order to have the common denominator. So the equivalent fraction for 4/9 is 16/36 and for 5/12 is 15/36. By simplifying this fraction addition 16/36 + 15/36, it becomes 31/36.

Pie Chart Representation: 4/9 + 5/12 = 31/36

CALCULATION: 4/9 + 5/12 as a fraction
4/9 + 5/12 = (?)
4/9 + 5/12 = [(4 x 12) + (5 x 9)]/(9 x 12)
= (48 + 45)/108
= 93/108
= (3 x 31)/(3 x 36)
= 31/36
4/9 + 5/12 = 31/36
4/9 plus 5/12 as a fraction is 31/36.

where
4/9 is a proper fraction as an addend,
5/12 is a proper fraction as an addend,
31/36 is the sum of 4/9 and 5/12.

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4/9 plus 5/12 as a decimal
4/9 + 5/12 = 31/36
31/36 = 0.8611
(4/9) + (5/12) as a decimal is 0.8611

where
0.8611 is the sum of 4/9 and 5/12.

The below workout with step by step calculation shows how to find the equivalent fraction between 4/9 and 5/12 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 4/9 plus 5/12 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(4/9) + (5/12) using LCM Method:
What is 4/9 plus 5/12 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 4/9
Fraction B: 5/12

What to be found?
(4/9) + (5/12) = ?
Find what's the sum of 4/9 and 5/12.

step 2 Compare the denominators of fractions 4/9 and 5/12 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 4/9 and 5/12 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 5/12:
The LCM of 9 and 12 is 36.

step 4 Write the fractions 4/9 and 5/12 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 4/9 + 5/12
= [(4 x 36)/(9 x 36)] + [(5 x 36)/(12 x 36)]

step 5 Simplify the expression to have common denominator:
= 16/36 + 15/36

step 6 Take the common values out and rewrite the above expression like the below:
= 1/36 x (16/1 + 15/1)
= 1/36 x (16 + 15)

step 7Simplify the above expression further:
= 1/36 x 31
= 31/36
4/9 + 5/12 = 31/36

Hence,
4/9 plus 5/12 as a fraction is 31/36.

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4/9 + 5/12 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 4/9
Fraction B: 5/12

What to be found?
(4/9)+(5/12) = ?
Find what's the sum of 4/9 and 5/12.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (4 x 12), 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 12) and rewrite the equation as like the below:
= (4 x 12) + (5 x 9)/(9 x 12)

step 3 Simplify and rewrite the fraction:
= (48 + 45)/108
= 93/108
= 31/36
4/9 + 5/12 = 31/36

Hence,
4/9 plus 5/12 in fraction is 31/36