Question

Evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.
minus, start fraction, 10, divided by, 3, end fraction, plus, start fraction, 11, divided by, 24, end fraction
− 10/3
+ 11/24

Answer 1

To evaluate the expression \(-\frac{10}{3} + \frac{11}{24}\), we first need to find a common denominator for the fractions. The denominators are 3 and 24. The least common multiple (LCM) of 3 and 24 is 24.

Now, we can convert \(-\frac{10}{3}\) to a fraction with a denominator of 24:

\[
-\frac{10}{3} = -\frac{10 \times 8}{3 \times 8} = -\frac{80}{24}
\]

Now we can rewrite the expression:

\[
-\frac{80}{24} + \frac{11}{24}
\]

Now that both fractions have the same denominator, we can combine them:

\[
-\frac{80}{24} + \frac{11}{24} = \frac{-80 + 11}{24} = \frac{-69}{24}
\]

Next, we simplify \(\frac{-69}{24}\). We can check for any common factors between 69 and 24. The greatest common divisor (GCD) of 69 and 24 is 3.

Now we can simplify the fraction:

\[
\frac{-69 \div 3}{24 \div 3} = \frac{-23}{8}
\]

Thus, the simplified result of the expression \(-\frac{10}{3} + \frac{11}{24}\) is:

\[
\boxed{-\frac{23}{8}}
\]