10/3 + 14/19 as a fraction

Learn how to find what is 10/3 plus 14/19 in fraction form just in a few minutes. We have covered the easiest method to write 10/3 + 14/19 as a fraction and decimal.

Summary: 10/3 plus 14/19 = 232/57
Since both fractions have unequal denominators, 10/3 plus 14/19 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 10/3 and fraction 14/19 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 3 and 19. 57 is the LCM of 3 and 19. Multiplying the LCM 57 with the numerators and denominators of both fractions (10/3 x 57/57) + (14/19 x 57/57), and simplify further in order to have the common denominator. So the equivalent fraction for 10/3 is 190/57 and for 14/19 is 42/57. By simplifying this fraction addition 190/57 + 42/57, it becomes 232/57.

CALCULATION: 10/3 + 14/19 as a fraction
10/3 + 14/19 = (?)
10/3 + 14/19 = [(10 x 19) + (14 x 3)]/(3 x 19)
= (190 + 42)/57
= 232/57
10/3 + 14/19 = 232/57
10/3 plus 14/19 as a fraction is 232/57.

where
10/3 is a improper fraction as an addend,
14/19 is a proper fraction as an addend,
232/57 is the sum of 10/3 and 14/19.

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10/3 plus 14/19 as a decimal
10/3 + 14/19 = 232/57
232/57 = 4.0702
(10/3) + (14/19) as a decimal is 4.0702

where
4.0702 is the sum of 10/3 and 14/19.

The below workout with step by step calculation shows how to find the equivalent fraction between 10/3 and 14/19 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 10/3 plus 14/19 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(10/3) + (14/19) using LCM Method:
What is 10/3 plus 14/19 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/3
Fraction B: 14/19

What to be found?
(10/3) + (14/19) = ?
Find what's the sum of 10/3 and 14/19.

step 2 Compare the denominators of fractions 10/3 and 14/19 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 10/3 and 14/19 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 14/19:
The LCM of 3 and 19 is 57.

step 4 Write the fractions 10/3 and 14/19 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 10/3 + 14/19
= [(10 x 57)/(3 x 57)] + [(14 x 57)/(19 x 57)]

step 5 Simplify the expression to have common denominator:
= 190/57 + 42/57

step 6 Take the common values out and rewrite the above expression like the below:
= 1/57 x (190/1 + 42/1)
= 1/57 x (190 + 42)

step 7Simplify the above expression further:
= 1/57 x 232
= 232/57
10/3 + 14/19 = 232/57

Hence,
10/3 plus 14/19 as a fraction is 232/57.

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10/3 + 14/19 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 10/3
Fraction B: 14/19

What to be found?
(10/3)+(14/19) = ?
Find what's the sum of 10/3 and 14/19.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (10 x 19), find the product of numerator of Fraction B and denominator of Fraction A (14 x 3), and find the product of both denominators of Fraction A and Fraction B (3 x 19) and rewrite the equation as like the below:
= (10 x 19) + (14 x 3)/(3 x 19)

step 3 Simplify and rewrite the fraction:
= (190 + 42)/57
10/3 + 14/19 = 232/57

Hence,
10/3 plus 14/19 in fraction is 232/57