Question

Find the Difference-
\[\dfrac{5}{8}+\dfrac{3}{4}-\dfrac{7}{12}\]

Answer 1

Hint: The fractions are added by doing LCM of denominators and placing the product in denominator. For the numerator part, multiply the uncommon factors of a fraction’s denominator and newly obtained denominator to the contents of the numerator and add all such numerators to get the final answer.

Complete step by step answer:
Let us consider the fraction as a variable namely, \[x\]
  \[ x=\dfrac{5}{8}+\dfrac{3}{4}-\dfrac{7}{2} \]
 \[ \Rightarrow x=\left( \dfrac{5}{8}+\dfrac{3}{4} \right)-\dfrac{7}{2} \]
Initially add the first two fractions to make the solution simple.
To do so consider the
  \[ LCM\left( 8,4 \right) \]
Since \[4\] is a factor of \[8\] The
  \[ LCM\left( 8,4 \right)=LCM\left( 2\times 2\times 2,2\times 2 \right) \]
 \[ \Rightarrow LCM\left( 8,4 \right)=2\times 2\times 2 \]
 \[ \Rightarrow LCM\left( 8,4 \right)=8 \]
We have \[8\times 1=8\] and \[2\times 4=8\].
So now we need to multiply \[5\] with \[1\] and \[3\] with \[2\]
  \[ \Rightarrow 5\times 1+3\times 2=5+6 \]
 \[ \Rightarrow 5\times 1+3\times 2=11 \]
The sum will be
\[\dfrac{11}{8}\]
That means
\[\dfrac{5}{8}+\dfrac{3}{4}=\dfrac{11}{8}\]
Now subtract the remaining part from the obtained sum.
\[x=\dfrac{11}{8}-\dfrac{7}{2}\]
Consider the \[LCM\left( 8,2 \right)\]
Since \[2\] is a factor of \[8\]
  \[ LCM\left( 8,2 \right)=LCM\left( 2\times 2\times 2,2 \right) \]
 \[ \Rightarrow LCM\left( 8,2 \right)=2\times 2\times 2 \]
 \[ \Rightarrow LCM\left( 8,2 \right)=8 \]
We have \[8\times 1=8\] and \[2\times 4=8\].
So now we need to multiply \[11\] with \[1\] and \[7\] with \[4\]
  \[ \Rightarrow 11\times 1-7\times 4=11-28 \]
 \[ \Rightarrow 11\times 1-7\times 4=-17 \]
The sum will be
\[\dfrac{-17}{8}\]
That means
 \[\dfrac{11}{8}-\dfrac{7}{2}=\dfrac{-17}{8}\]
Hence the value of
\[x=\dfrac{5}{8}+\dfrac{3}{4}-\dfrac{7}{2}=\dfrac{-17}{8}\]

Note: In order to do addition or subtraction of fractions we need to consider the Least Common Factor (LCM) of the denominators no matter how many are present. We can also take only two fractions at a time to make the process simple. The denominators may or may not have common factors. In case they do not have a common factor the Least Common Multiple (LCM) is taken as the product of two numbers.