Question

1. $(-5, -18), (2, 20)$
2. $(2, -4), (7, 15)$

find each product.

1. $1\frac{3}{5} \times -3\frac{1}{5}$
2. $-3\frac{2}{3} \times -3\frac{1}{2}$
3. $2\frac{1}{6} \times -2\frac{5}{6}$
4. $-2\frac{2}{5} \times 1\frac{2}{3}$
5. $7 \times -\frac{5}{3}$
6. $-\frac{1}{2} \times \frac{8}{5}$
7. $-\frac{5}{6} \times -\frac{7}{5}$
8. $\frac{8}{7} \times -\frac{1}{4}$

Explanation:

Problem 31: \( 1\frac{3}{5} \times -3\frac{1}{5} \)

Step 1: Convert mixed numbers to improper fractions

\( 1\frac{3}{5} = \frac{1\times5 + 3}{5} = \frac{8}{5} \)
\( -3\frac{1}{5} = -\frac{3\times5 + 1}{5} = -\frac{16}{5} \)

Step 2: Multiply the improper fractions

\( \frac{8}{5} \times -\frac{16}{5} = -\frac{8\times16}{5\times5} = -\frac{128}{25} = -5\frac{3}{25} \)

Step 1: Convert mixed numbers to improper fractions

\( -3\frac{2}{3} = -\frac{3\times3 + 2}{3} = -\frac{11}{3} \)
\( -3\frac{1}{2} = -\frac{3\times2 + 1}{2} = -\frac{7}{2} \)

Step 2: Multiply the improper fractions (negative times negative is positive)

\( -\frac{11}{3} \times -\frac{7}{2} = \frac{11\times7}{3\times2} = \frac{77}{6} = 12\frac{5}{6} \)

Step 1: Convert mixed numbers to improper fractions

\( 2\frac{1}{6} = \frac{2\times6 + 1}{6} = \frac{13}{6} \)
\( -2\frac{5}{6} = -\frac{2\times6 + 5}{6} = -\frac{17}{6} \)

Step 2: Multiply the improper fractions

\( \frac{13}{6} \times -\frac{17}{6} = -\frac{13\times17}{6\times6} = -\frac{221}{36} = -6\frac{5}{36} \)

Answer:

\( -5\frac{3}{25} \)

Problem 32: \( -3\frac{2}{3} \times -3\frac{1}{2} \)