Question

Add or Subtract Fraction.
$-\frac{39}{56}-\frac{22}{35}$

Short answer

The value of the given fraction is $-\frac{53}{40}$.

Step-by-step solution

Step 1. Given information

The given expression is $-\frac{39}{56}-\frac{22}{35}$.

Step 2. Determine the whether the given fraction has the same denominator.

The given fraction does not have the same denominator.

So, find the least common denominator of $56$and $35$.

$\begin{array}{rcl}56& =& 7·8\\ 35& =& 7·5\\ & \Rightarrow & LCD=7·8·5\\ & \Rightarrow & LCD=280\end{array}$

Step 3. Multiply the numerator and denominator of each fraction by a factor to get the denominator 280.

$\begin{array}{rcl}-\frac{39}{56}-\frac{22}{35}& =& -\frac{39·5}{56·5}-\frac{22·8}{35·8}\\ & =& -\frac{195}{280}-\frac{176}{280}\end{array}$

Step 4. Apply the Fraction Addition rule:ac+bc=a+bc, where c≠0.

$\begin{array}{rcl}-\frac{195}{280}-\frac{176}{280}& =& \frac{-195-176}{280}\\ & =& -\frac{(195+176)}{280}\\ & =& -\frac{371}{280}\\ & =& -\frac{53}{40}\end{array}$

Hence, the value is $-\frac{53}{40}$.