13/4 + 2/3 as a fraction

Learn how to find what is 13/4 plus 2/3 in fraction form just in a few minutes. We have covered the easiest method to write 13/4 + 2/3 as a fraction and decimal.

Summary: 13/4 plus 2/3 = 47/12
Since both fractions have unequal denominators, 13/4 plus 2/3 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/4 and fraction 2/3 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 4 and 3. 12 is the LCM of 4 and 3. Multiplying the LCM 12 with the numerators and denominators of both fractions (13/4 x 12/12) + (2/3 x 12/12), and simplify further in order to have the common denominator. So the equivalent fraction for 13/4 is 39/12 and for 2/3 is 8/12. By simplifying this fraction addition 39/12 + 8/12, it becomes 47/12.

CALCULATION: 13/4 + 2/3 as a fraction
13/4 + 2/3 = (?)
13/4 + 2/3 = [(13 x 3) + (2 x 4)]/(4 x 3)
= (39 + 8)/12
= 47/12
13/4 + 2/3 = 47/12
13/4 plus 2/3 as a fraction is 47/12.

where
13/4 is a improper fraction as an addend,
2/3 is a proper fraction as an addend,
47/12 is the sum of 13/4 and 2/3.

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13/4 plus 2/3 as a decimal
13/4 + 2/3 = 47/12
47/12 = 3.9167
(13/4) + (2/3) as a decimal is 3.9167

where
3.9167 is the sum of 13/4 and 2/3.

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

(13/4) + (2/3) using LCM Method:
What is 13/4 plus 2/3 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/4
Fraction B: 2/3

What to be found?
(13/4) + (2/3) = ?
Find what's the sum of 13/4 and 2/3.

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

step 4 Write the fractions 13/4 and 2/3 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/4 + 2/3
= [(13 x 12)/(4 x 12)] + [(2 x 12)/(3 x 12)]

step 5 Simplify the expression to have common denominator:
= 39/12 + 8/12

step 6 Take the common values out and rewrite the above expression like the below:
= 1/12 x (39/1 + 8/1)
= 1/12 x (39 + 8)

step 7Simplify the above expression further:
= 1/12 x 47
= 47/12
13/4 + 2/3 = 47/12

Hence,
13/4 plus 2/3 as a fraction is 47/12.

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13/4 + 2/3 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/4
Fraction B: 2/3

What to be found?
(13/4)+(2/3) = ?
Find what's the sum of 13/4 and 2/3.

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

step 3 Simplify and rewrite the fraction:
= (39 + 8)/12
13/4 + 2/3 = 47/12

Hence,
13/4 plus 2/3 in fraction is 47/12