To solve the expression \( 7 \frac{3}{4} \times -1 \frac{2}{3} \), we first convert the mixed numbers to improper fractions and then perform the multiplication.

1. Convert \( 7 \frac{3}{4} \) to an improper fraction:
   \[
   7 \frac{3}{4} = \frac{7 \times 4 + 3}{4} = \frac{28 + 3}{4} = \frac{31}{4}
   \]

2. Convert \( -1 \frac{2}{3} \) to an improper fraction:
   \[
   -1 \frac{2}{3} = -\frac{1 \times 3 + 2}{3} = -\frac{3 + 2}{3} = -\frac{5}{3}
   \]

3. Multiply the two fractions:
   \[
   \frac{31}{4} \times -\frac{5}{3} = \frac{31 \times -5}{4 \times 3} = \frac{-155}{12}
   \]

So, the product is \( \frac{-155}{12} \).

You can leave the result as an improper fraction, or convert it into a mixed number:
   \[
   \frac{-155}{12} = -12 \frac{11}{12}
   \]

### Final Answer: 
\[
\frac{-155}{12} \text{ or } -12 \frac{11}{12}
\]

Do you want more details or have any questions? 

Here are some related questions for practice:
1. What is the product of \( 5 \frac{1}{2} \times -3 \frac{1}{4} \)?
2. How do you simplify \( \frac{-124}{5} \)?
3. Can you convert \( 8 \frac{2}{7} \) to an improper fraction?
4. What is \( -2 \frac{3}{5} + 4 \frac{1}{4} \)?
5. What is the reciprocal of \( \frac{31}{4} \)?

**Tip:** Always convert mixed numbers to improper fractions before performing operations like multiplication or division.

This page explains how to multiply the mixed numbers 7 3/4 and -1 2/3 by converting them into improper fractions. The step-by-step solution provides clear instructions for converting mixed numbers and performing fraction multiplication, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation