5/7 - 13/5 as a fraction

Learn how to find what is 5/7 minus 13/5 in fraction form just in a few minutes. We have covered the easiest method to write 5/7 - 13/5 as a fraction and decimal.

Summary: 5/7 minus 13/5 = -66/35
Since both fractions have unequal denominators, 5/7 minus 13/5 is an unlike fractions subtraction. For subtracting unlike fractions, you have to first find the equivalent fractions for fraction 5/7 and fraction 13/5 in order to have the same denominators for both fractions. Therefore, you have to find the LCM of denominators 7 and 5. 35 is the LCM of 7 and 5. Multiplying the LCM 35 with the numerators and denominators of both fractions (5/7 x 35/35) - (13/5 x 35/35), and simplify further in order to have the common denominator. So the equivalent fraction for 5/7 is 25/35 and for 13/5 is 91/35. By simplifying this fraction subtraction 25/35 - 91/35, it becomes -66/35.

CALCULATION: 5/7 - 13/5 as a fraction
5/7 - 13/5 = (?)
5/7 - 13/5 = [(5 x 5) - (13 x 7)]/(7 x 5)
= (25 - 91)/35
= -66/35
5/7 - 13/5 = -66/35
5/7 minus 13/5 as a fraction is -66/35.

where
5/7 is a proper fraction as a minuend,
13/5 is a improper fraction as a subtrahend,
-66/35 is the difference between 5/7 and 13/5.

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5/7 minus 13/5 as a decimal
5/7 - 13/5 = -66/35
-66/35 = -1.8857
(5/7) - (13/5) as a decimal is -1.8857

where
-1.8857 is the difference between 5/7 and 13/5.

The below workout with step by step calculation shows how to find what is the difference between two fractions by subtracting a fraction 13/5 from 5/7. For different, unequal or unlike denominators, use any one of the following methods to find the equivalent fraction for 5/7 minus 13/5.
1. LCM method
2. Cross multiplication method.

(5/7) - (13/5) using LCM Method:
What is 5/7 minus 13/5 as a fraction?

step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 5/7
Fraction B: 13/5

What to be found?
(5/7) - (13/5) = ?
Find what's the difference between 5/7 and 13/5.

step 2 Compare the denominators of fractions 5/7 and 13/5 to identify whether it is a like or unlike fraction subtraction. Since the denominators of given fractions 5/7 and 13/5 are not equal, it is said to be unlike fractions subtraction.

step 3For unlike fractions subtraction, find the LCM (least common multiple) of both denominators of fractions 5/7 and 13/5:
The LCM of 7 and 5 is 35.

step 4 Write the fractions 5/7 and 13/5 in the subtraction expression form and multiply LCM with all the numerators and denominators of both fractions.
= 5/7 - 13/5
= [(5 x 35)/(7 x 35)] - [(13 x 35)/(5 x 35)]

step 5 Simplify the expression to have common denominator:
= 25/35 - 91/35

step 6 Take the common values out and rewrite the above expression like the below:
= 1/35 x (25/1 - 91/1)
= 1/35 x (25 - 91)

step 7Simplify the above expression further:
= 1/35 x -66
= -66/35
5/7 - 13/5 = -66/35

Hence,
5/7 minus 13/5 as a fraction is -66/35.

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5/7 - 13/5 using Cross Multiplication Method:
step 1 Observe the input parameters and what to be found:
Input:
Fraction A: 5/7
Fraction B: 13/5

What to be found?
(5/7)-(13/5) = ?
Find what's the difference between 5/7 and 13/5.

step 2 Find the product of numerator of Fraction A and denominator of Fraction B (5 x 5), find the product of numerator of Fraction B and denominator of Fraction A (13 x 7), and find the product of both denominators of Fraction A and Fraction B (7 x 5) and rewrite the equation as like the below:
= (5 x 5) - (13 x 7)/(7 x 5)

step 3 Simplify and rewrite the fraction:
= (25 - 91)/35
5/7 - 13/5 = -66/35

Hence,
5/7 minus 13/5 in fraction is -66/35