Question

What is the value of this expression?

9 3/4−2 1/5+1/2

Enter your answer as a mixed number in simplest form by filling in the boxes.

Answer 1

To evaluate the expression \( 9 \frac{3}{4} - 2 \frac{1}{5} + \frac{1}{2} \), we first convert all mixed numbers to improper fractions.

1. Convert \( 9 \frac{3}{4} \) to an improper fraction:
\[
9 \frac{3}{4} = 9 \times 4 + 3 = 36 + 3 = \frac{39}{4}
\]

2. Convert \( 2 \frac{1}{5} \) to an improper fraction:
\[
2 \frac{1}{5} = 2 \times 5 + 1 = 10 + 1 = \frac{11}{5}
\]

Now we rewrite the expression with the improper fractions:
\[
\frac{39}{4} - \frac{11}{5} + \frac{1}{2}
\]

Next, we need a common denominator to perform the operations. The denominators are 4, 5, and 2. The least common multiple (LCM) of these numbers is 20.

3. Convert each fraction to have a denominator of 20:
- For \( \frac{39}{4} \):
\[
\frac{39}{4} = \frac{39 \times 5}{4 \times 5} = \frac{195}{20}
\]
- For \( \frac{11}{5} \):
\[
\frac{11}{5} = \frac{11 \times 4}{5 \times 4} = \frac{44}{20}
\]
- For \( \frac{1}{2} \):
\[
\frac{1}{2} = \frac{1 \times 10}{2 \times 10} = \frac{10}{20}
\]

Now we substitute these back into the expression:
\[
\frac{195}{20} - \frac{44}{20} + \frac{10}{20}
\]

4. Combine the fractions:
\[
\frac{195 - 44 + 10}{20} = \frac{195 - 44 = 151 + 10 = 161}{20}
\]
\[
= \frac{161}{20}
\]

5. Now convert \( \frac{161}{20} \) to a mixed number:
- Divide 161 by 20:
- \( 161 \div 20 = 8 \) remainder \( 1 \).
- Therefore, \( \frac{161}{20} = 8 \frac{1}{20} \).

Thus, the final answer in its simplest mixed number form is:
\[
\boxed{8 \frac{1}{20}}
\]