10/9 + 1/4 as a fraction

Learn how to find what is 10/9 plus 1/4 in fraction form just in a few minutes. We have covered the easiest method to write 10/9 + 1/4 as a fraction and decimal.

Summary: 10/9 plus 1/4 = 49/36
Since both fractions have unequal denominators, 10/9 plus 1/4 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 10/9 and fraction 1/4 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 9 and 4. 36 is the LCM of 9 and 4. Multiplying the LCM 36 with the numerators and denominators of both fractions (10/9 x 36/36) + (1/4 x 36/36), and simplify further in order to have the common denominator. So the equivalent fraction for 10/9 is 40/36 and for 1/4 is 9/36. By simplifying this fraction addition 40/36 + 9/36, it becomes 49/36.

CALCULATION: 10/9 + 1/4 as a fraction
10/9 + 1/4 = (?)
10/9 + 1/4 = [(10 x 4) + (1 x 9)]/(9 x 4)
= (40 + 9)/36
= 49/36
10/9 + 1/4 = 49/36
10/9 plus 1/4 as a fraction is 49/36.

where
10/9 is a improper fraction as an addend,
1/4 is a proper fraction as an addend,
49/36 is the sum of 10/9 and 1/4.

---

10/9 plus 1/4 as a decimal
10/9 + 1/4 = 49/36
49/36 = 1.3611
(10/9) + (1/4) as a decimal is 1.3611

where
1.3611 is the sum of 10/9 and 1/4.

The below workout with step by step calculation shows how to find the equivalent fraction between 10/9 and 1/4 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 10/9 plus 1/4 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(10/9) + (1/4) using LCM Method:
What is 10/9 plus 1/4 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/9
Fraction B: 1/4

What to be found?
(10/9) + (1/4) = ?
Find what's the sum of 10/9 and 1/4.

step 2 Compare the denominators of fractions 10/9 and 1/4 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 10/9 and 1/4 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 1/4:
The LCM of 9 and 4 is 36.

step 4 Write the fractions 10/9 and 1/4 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 10/9 + 1/4
= [(10 x 36)/(9 x 36)] + [(1 x 36)/(4 x 36)]

step 5 Simplify the expression to have common denominator:
= 40/36 + 9/36

step 6 Take the common values out and rewrite the above expression like the below:
= 1/36 x (40/1 + 9/1)
= 1/36 x (40 + 9)

step 7Simplify the above expression further:
= 1/36 x 49
= 49/36
10/9 + 1/4 = 49/36

Hence,
10/9 plus 1/4 as a fraction is 49/36.

---

10/9 + 1/4 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/9
Fraction B: 1/4

What to be found?
(10/9)+(1/4) = ?
Find what's the sum of 10/9 and 1/4.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (10 x 4), find the product of numerator of Fraction B and denominator of Fraction A (1 x 9), and find the product of both denominators of Fraction A and Fraction B (9 x 4) and rewrite the equation as like the below:
= (10 x 4) + (1 x 9)/(9 x 4)

step 3 Simplify and rewrite the fraction:
= (40 + 9)/36
10/9 + 1/4 = 49/36

Hence,
10/9 plus 1/4 in fraction is 49/36