13/3 + 3/4 as a fraction

Learn how to find what is 13/3 plus 3/4 in fraction form just in a few minutes. We have covered the easiest method to write 13/3 + 3/4 as a fraction and decimal.

Summary: 13/3 plus 3/4 = 61/12
Since both fractions have unequal denominators, 13/3 plus 3/4 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/3 and fraction 3/4 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 3 and 4. 12 is the LCM of 3 and 4. Multiplying the LCM 12 with the numerators and denominators of both fractions (13/3 x 12/12) + (3/4 x 12/12), and simplify further in order to have the common denominator. So the equivalent fraction for 13/3 is 52/12 and for 3/4 is 9/12. By simplifying this fraction addition 52/12 + 9/12, it becomes 61/12.

CALCULATION: 13/3 + 3/4 as a fraction
13/3 + 3/4 = (?)
13/3 + 3/4 = [(13 x 4) + (3 x 3)]/(3 x 4)
= (52 + 9)/12
= 61/12
13/3 + 3/4 = 61/12
13/3 plus 3/4 as a fraction is 61/12.

where
13/3 is a improper fraction as an addend,
3/4 is a proper fraction as an addend,
61/12 is the sum of 13/3 and 3/4.

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13/3 plus 3/4 as a decimal
13/3 + 3/4 = 61/12
61/12 = 5.0833
(13/3) + (3/4) as a decimal is 5.0833

where
5.0833 is the sum of 13/3 and 3/4.

The below workout with step by step calculation shows how to find the equivalent fraction between 13/3 and 3/4 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 13/3 plus 3/4 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(13/3) + (3/4) using LCM Method:
What is 13/3 plus 3/4 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/3
Fraction B: 3/4

What to be found?
(13/3) + (3/4) = ?
Find what's the sum of 13/3 and 3/4.

step 2 Compare the denominators of fractions 13/3 and 3/4 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 13/3 and 3/4 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 13/3 and 3/4:
The LCM of 3 and 4 is 12.

step 4 Write the fractions 13/3 and 3/4 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/3 + 3/4
= [(13 x 12)/(3 x 12)] + [(3 x 12)/(4 x 12)]

step 5 Simplify the expression to have common denominator:
= 52/12 + 9/12

step 6 Take the common values out and rewrite the above expression like the below:
= 1/12 x (52/1 + 9/1)
= 1/12 x (52 + 9)

step 7Simplify the above expression further:
= 1/12 x 61
= 61/12
13/3 + 3/4 = 61/12

Hence,
13/3 plus 3/4 as a fraction is 61/12.

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13/3 + 3/4 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/3
Fraction B: 3/4

What to be found?
(13/3)+(3/4) = ?
Find what's the sum of 13/3 and 3/4.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (13 x 4), find the product of numerator of Fraction B and denominator of Fraction A (3 x 3), and find the product of both denominators of Fraction A and Fraction B (3 x 4) and rewrite the equation as like the below:
= (13 x 4) + (3 x 3)/(3 x 4)

step 3 Simplify and rewrite the fraction:
= (52 + 9)/12
13/3 + 3/4 = 61/12

Hence,
13/3 plus 3/4 in fraction is 61/12