Question

Evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.

− 3/10
​
+ 11/24

Answer 1

To evaluate the expression \( -\frac{3}{10} + \frac{11}{24} \), we first need to find a common denominator for the fractions.

The denominators are 10 and 24. The least common multiple (LCM) of 10 and 24 is 120.

Now, we can convert each fraction:

1. Convert \( -\frac{3}{10} \) to have a denominator of 120:
\[
-\frac{3}{10} = -\frac{3 \times 12}{10 \times 12} = -\frac{36}{120}
\]

2. Convert \( \frac{11}{24} \) to have a denominator of 120:
\[
\frac{11}{24} = \frac{11 \times 5}{24 \times 5} = \frac{55}{120}
\]

Now, we can add the two fractions:
\[
-\frac{36}{120} + \frac{55}{120} = \frac{55 - 36}{120} = \frac{19}{120}
\]

The fraction \( \frac{19}{120} \) is already in simplest form, as 19 is a prime number and does not divide 120.

Thus, the final answer is:
\[
\frac{19}{120}
\]