Question

Evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.
minus, start fraction, 7, divided by, 10, end fraction, plus, start fraction, 7, divided by, 50, end fraction
− -7/50
​
+ 7/50

Answer 1

To evaluate the expression \(-\frac{7}{10} + \frac{7}{50}\), we first need to find a common denominator.

The denominators are \(10\) and \(50\). The least common multiple (LCM) of \(10\) and \(50\) is \(50\).

Next, we convert \(-\frac{7}{10}\) to a fraction with a denominator of \(50\):

\[
-\frac{7}{10} = -\frac{7 \times 5}{10 \times 5} = -\frac{35}{50}
\]

Now, we can rewrite the expression:

\[
-\frac{35}{50} + \frac{7}{50}
\]

Since both fractions now have the same denominator, we can combine them:

\[
-\frac{35}{50} + \frac{7}{50} = \frac{-35 + 7}{50} = \frac{-28}{50}
\]

Next, we simplify \(\frac{-28}{50}\). The greatest common divisor (GCD) of \(28\) and \(50\) is \(2\). Dividing both the numerator and the denominator by \(2\):

\[
\frac{-28 \div 2}{50 \div 2} = \frac{-14}{25}
\]

Thus, the expression evaluates to:

\[
\boxed{-\frac{14}{25}}
\]