10/3 + 13/5 as a fraction

Learn how to find what is 10/3 plus 13/5 in fraction form just in a few minutes. We have covered the easiest method to write 10/3 + 13/5 as a fraction and decimal.

Summary: 10/3 plus 13/5 = 89/15
Since both fractions have unequal denominators, 10/3 plus 13/5 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 10/3 and fraction 13/5 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 3 and 5. 15 is the LCM of 3 and 5. Multiplying the LCM 15 with the numerators and denominators of both fractions (10/3 x 15/15) + (13/5 x 15/15), and simplify further in order to have the common denominator. So the equivalent fraction for 10/3 is 50/15 and for 13/5 is 39/15. By simplifying this fraction addition 50/15 + 39/15, it becomes 89/15.

CALCULATION: 10/3 + 13/5 as a fraction
10/3 + 13/5 = (?)
10/3 + 13/5 = [(10 x 5) + (13 x 3)]/(3 x 5)
= (50 + 39)/15
= 89/15
10/3 + 13/5 = 89/15
10/3 plus 13/5 as a fraction is 89/15.

where
10/3 is a improper fraction as an addend,
13/5 is a improper fraction as an addend,
89/15 is the sum of 10/3 and 13/5.

---

10/3 plus 13/5 as a decimal
10/3 + 13/5 = 89/15
89/15 = 5.9333
(10/3) + (13/5) as a decimal is 5.9333

where
5.9333 is the sum of 10/3 and 13/5.

The below workout with step by step calculation shows how to find the equivalent fraction between 10/3 and 13/5 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 10/3 plus 13/5 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(10/3) + (13/5) using LCM Method:
What is 10/3 plus 13/5 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/3
Fraction B: 13/5

What to be found?
(10/3) + (13/5) = ?
Find what's the sum of 10/3 and 13/5.

step 2 Compare the denominators of fractions 10/3 and 13/5 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 10/3 and 13/5 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 10/3 and 13/5:
The LCM of 3 and 5 is 15.

step 4 Write the fractions 10/3 and 13/5 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 10/3 + 13/5
= [(10 x 15)/(3 x 15)] + [(13 x 15)/(5 x 15)]

step 5 Simplify the expression to have common denominator:
= 50/15 + 39/15

step 6 Take the common values out and rewrite the above expression like the below:
= 1/15 x (50/1 + 39/1)
= 1/15 x (50 + 39)

step 7Simplify the above expression further:
= 1/15 x 89
= 89/15
10/3 + 13/5 = 89/15

Hence,
10/3 plus 13/5 as a fraction is 89/15.

---

10/3 + 13/5 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/3
Fraction B: 13/5

What to be found?
(10/3)+(13/5) = ?
Find what's the sum of 10/3 and 13/5.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (10 x 5), find the product of numerator of Fraction B and denominator of Fraction A (13 x 3), and find the product of both denominators of Fraction A and Fraction B (3 x 5) and rewrite the equation as like the below:
= (10 x 5) + (13 x 3)/(3 x 5)

step 3 Simplify and rewrite the fraction:
= (50 + 39)/15
10/3 + 13/5 = 89/15

Hence,
10/3 plus 13/5 in fraction is 89/15