9/4 + 16/9 as a fraction

Learn how to find what is 9/4 plus 16/9 in fraction form just in a few minutes. We have covered the easiest method to write 9/4 + 16/9 as a fraction and decimal.

Summary: 9/4 plus 16/9 = 145/36
Since both fractions have unequal denominators, 9/4 plus 16/9 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 9/4 and fraction 16/9 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 4 and 9. 36 is the LCM of 4 and 9. Multiplying the LCM 36 with the numerators and denominators of both fractions (9/4 x 36/36) + (16/9 x 36/36), and simplify further in order to have the common denominator. So the equivalent fraction for 9/4 is 81/36 and for 16/9 is 64/36. By simplifying this fraction addition 81/36 + 64/36, it becomes 145/36.

CALCULATION: 9/4 + 16/9 as a fraction
9/4 + 16/9 = (?)
9/4 + 16/9 = [(9 x 9) + (16 x 4)]/(4 x 9)
= (81 + 64)/36
= 145/36
9/4 + 16/9 = 145/36
9/4 plus 16/9 as a fraction is 145/36.

where
9/4 is a improper fraction as an addend,
16/9 is a improper fraction as an addend,
145/36 is the sum of 9/4 and 16/9.

---

9/4 plus 16/9 as a decimal
9/4 + 16/9 = 145/36
145/36 = 4.0278
(9/4) + (16/9) as a decimal is 4.0278

where
4.0278 is the sum of 9/4 and 16/9.

The below workout with step by step calculation shows how to find the equivalent fraction between 9/4 and 16/9 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 9/4 plus 16/9 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(9/4) + (16/9) using LCM Method:
What is 9/4 plus 16/9 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 9/4
Fraction B: 16/9

What to be found?
(9/4) + (16/9) = ?
Find what's the sum of 9/4 and 16/9.

step 2 Compare the denominators of fractions 9/4 and 16/9 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 9/4 and 16/9 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 9/4 and 16/9:
The LCM of 4 and 9 is 36.

step 4 Write the fractions 9/4 and 16/9 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 9/4 + 16/9
= [(9 x 36)/(4 x 36)] + [(16 x 36)/(9 x 36)]

step 5 Simplify the expression to have common denominator:
= 81/36 + 64/36

step 6 Take the common values out and rewrite the above expression like the below:
= 1/36 x (81/1 + 64/1)
= 1/36 x (81 + 64)

step 7Simplify the above expression further:
= 1/36 x 145
= 145/36
9/4 + 16/9 = 145/36

Hence,
9/4 plus 16/9 as a fraction is 145/36.

---

9/4 + 16/9 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 9/4
Fraction B: 16/9

What to be found?
(9/4)+(16/9) = ?
Find what's the sum of 9/4 and 16/9.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (9 x 9), find the product of numerator of Fraction B and denominator of Fraction A (16 x 4), and find the product of both denominators of Fraction A and Fraction B (4 x 9) and rewrite the equation as like the below:
= (9 x 9) + (16 x 4)/(4 x 9)

step 3 Simplify and rewrite the fraction:
= (81 + 64)/36
9/4 + 16/9 = 145/36

Hence,
9/4 plus 16/9 in fraction is 145/36