Question

Add or Subtract Fraction.

$-\frac{33}{49}-\frac{18}{35}$

Short answer

The value of the given fraction is $-\frac{291}{245}$.

Step-by-step solution

Step 1. Given information

The given expression is $-\frac{33}{49}-\frac{18}{35}$.

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 $49$and $35$.

$\begin{array}{rcl}49& =& 7·7\\ 35& =& 7·5\\ & \Rightarrow & LCD=7·7·5\\ & \Rightarrow & LCD=245\end{array}$

Step 3. Multiply the numerator and denominator of each fraction by a factor to get the denominator 245.

$\begin{array}{rcl}-\frac{33}{49}-\frac{18}{35}& =& -\frac{33·5}{49·5}-\frac{18·7}{35·7}\\ & =& -\frac{165}{245}-\frac{126}{245}\end{array}$

Step 4. Apply the Fraction Addition rule:ac+bc=a+bc, where src="data:image/svg+xml;base64,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" role="math" localid="1644386958492" src="https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-exercise-images/643bfd28-68b5-49c9-878b-f6ccc473b088.svg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220222%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220222T075437Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=e1764d5aabf2b1c407736829c7c6d1c1e6c2333f946cb4db7794f31385a463bf" src="https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-exercise-images/643bfd28-68b5-49c9-878b-f6ccc473b088.svg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220209%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220209T061119Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=31de56b9368904018874f60ebe44abba93429989b008cac6ddcea9eb7932d8c4" c≠0.

$\begin{array}{rcl}-\frac{33}{49}-\frac{18}{35}& =& \frac{-(165+126)}{245}\\ & =& -\frac{291}{245}\end{array}$

Hence, the value is $-\frac{291}{245}$.