Question

Malik earns an average of 4 1/ 2 points on his daily quizzes. Near the end of the quarter, his average decreases by 3/ 4 point. Write and evaluate a subtraction expression to find his current quiz grade average.

Answer 1

To find Malik's current quiz grade average after it decreases, we start with his original average and subtract the decrease.

1. Malik's original average: \( 4 \frac{1}{2} \) points.
2. Convert \( 4 \frac{1}{2} \) to an improper fraction:
\[
4 \frac{1}{2} = \frac{9}{2}
\]

3. Decrease in average: \( \frac{3}{4} \) points.

4. We need to express the subtraction:
\[
\text{Current Average} = 4 \frac{1}{2} - \frac{3}{4}
\]
or
\[
\text{Current Average} = \frac{9}{2} - \frac{3}{4}
\]

5. To subtract these fractions, we need a common denominator. The least common multiple of 2 and 4 is 4. Convert \( \frac{9}{2} \) to a fraction with a denominator of 4:
\[
\frac{9}{2} = \frac{9 \times 2}{2 \times 2} = \frac{18}{4}
\]

6. Now, we can subtract:
\[
\frac{18}{4} - \frac{3}{4} = \frac{18 - 3}{4} = \frac{15}{4}
\]

7. Finally, convert \( \frac{15}{4} \) back to a mixed number:
\[
\frac{15}{4} = 3 \frac{3}{4}
\]

So, Malik's current quiz grade average is \( \mathbf{3 \frac{3}{4}} \) points.