13/4 + 13/16 as a fraction

Learn how to find what is 13/4 plus 13/16 in fraction form just in a few minutes. We have covered the easiest method to write 13/4 + 13/16 as a fraction and decimal.

Summary: 13/4 plus 13/16 = 65/16
Since both fractions have unequal denominators, 13/4 plus 13/16 is an unlike fractions addition. For adding unlike fractions, you have to first find the equivalent fractions for fraction 13/4 and fraction 13/16 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 4 and 16. 16 is the LCM of 4 and 16. Multiplying the LCM 16 with the numerators and denominators of both fractions (13/4 x 16/16) + (13/16 x 16/16), and simplify further in order to have the common denominator. So the equivalent fraction for 13/4 is 52/16 and for 13/16 is 13/16. By simplifying this fraction addition 52/16 + 13/16, it becomes 65/16.

CALCULATION: 13/4 + 13/16 as a fraction
13/4 + 13/16 = (?)
13/4 + 13/16 = [(13 x 16) + (13 x 4)]/(4 x 16)
= (208 + 52)/64
= 260/64
= (4 x 65)/(4 x 16)
= 65/16
13/4 + 13/16 = 65/16
13/4 plus 13/16 as a fraction is 65/16.

where
13/4 is a improper fraction as an addend,
13/16 is a proper fraction as an addend,
65/16 is the sum of 13/4 and 13/16.

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13/4 plus 13/16 as a decimal
13/4 + 13/16 = 65/16
65/16 = 4.0625
(13/4) + (13/16) as a decimal is 4.0625

where
4.0625 is the sum of 13/4 and 13/16.

The below workout with step by step calculation shows how to find the equivalent fraction between 13/4 and 13/16 by adding two fractions with different, unequal or unlike denominators. The sum in fraction form for 13/4 plus 13/16 can be obtained by using anyone of the two methods below.
1. LCM method
2. Cross multiplication method.

(13/4) + (13/16) using LCM Method:
What is 13/4 plus 13/16 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/4
Fraction B: 13/16

What to be found?
(13/4) + (13/16) = ?
Find what's the sum of 13/4 and 13/16.

step 2 Compare the denominators of fractions 13/4 and 13/16 to identify whether it is a like or unlike fraction addition. Since the denominators of given fractions 13/4 and 13/16 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 13/16:
The LCM of 4 and 16 is 16.

step 4 Write the fractions 13/4 and 13/16 in the addition expression form and multiply LCM with all the numerators and denominators of both fractions.
= 13/4 + 13/16
= [(13 x 16)/(4 x 16)] + [(13 x 16)/(16 x 16)]

step 5 Simplify the expression to have common denominator:
= 52/16 + 13/16

step 6 Take the common values out and rewrite the above expression like the below:
= 1/16 x (52/1 + 13/1)
= 1/16 x (52 + 13)

step 7Simplify the above expression further:
= 1/16 x 65
= 65/16
13/4 + 13/16 = 65/16

Hence,
13/4 plus 13/16 as a fraction is 65/16.

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13/4 + 13/16 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 13/4
Fraction B: 13/16

What to be found?
(13/4)+(13/16) = ?
Find what's the sum of 13/4 and 13/16.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (13 x 16), find the product of numerator of Fraction B and denominator of Fraction A (13 x 4), and find the product of both denominators of Fraction A and Fraction B (4 x 16) and rewrite the equation as like the below:
= (13 x 16) + (13 x 4)/(4 x 16)

step 3 Simplify and rewrite the fraction:
= (208 + 52)/64
= 260/64
= 65/16
13/4 + 13/16 = 65/16

Hence,
13/4 plus 13/16 in fraction is 65/16