Question

multiplying negative rational numbers
find the product of the rational numbers. the answers are mixed up at the bottom of the page. cross out the answers as you complete the problems.

1. $4 \times -\frac{7}{4}$
2. $-\frac{1}{3} \times -9$
3. $\frac{3}{8} \times -\frac{1}{4}$
4. $-2\frac{1}{3} \times \frac{3}{4}$
5. $-\frac{1}{3} \times -1\frac{2}{3}$
6. $-3\frac{6}{7} \times -2\frac{1}{2}$
7. $0.75 \times -\frac{4}{3}$
8. $-0.2 \times -\frac{2}{5}$
9. $-0.35 \times -1\frac{3}{7}$
10. $2.5 \times -3\frac{4}{5}$
11. $0.2 \times -0.45$
12. $-0.25 \times -1.4$
13. $-2.3 \times 6.8$
14. $-3.9 \times 5\frac{5}{9}$
15. $-4.2 \times -6\frac{2}{7}$

answers
$21\frac{2}{3}$, $-15.64$, $-9\frac{1}{2}$, $-3\frac{1}{2}$, $-2\frac{11}{12}$, $-1$, $-\frac{3}{10}$, $-0.09$, $\frac{2}{25}$, $0.35$, $\frac{1}{2}$, $\frac{5}{7}$, $9\frac{2}{7}$, $26\frac{2}{5}$

Explanation:

Let's solve problem 7: \( 0.75 \times -\frac{4}{3} \)

Step 1: Convert decimal to fraction

\( 0.75 = \frac{3}{4} \)

Step 2: Multiply the fractions

\( \frac{3}{4} \times -\frac{4}{3} \)
The 3 in the numerator and 3 in the denominator cancel out, and the 4 in the numerator and 4 in the denominator cancel out. We are left with \( -1 \) (since a positive times a negative is negative).

Step 1: Convert decimal to fraction

\( -0.2 = -\frac{1}{5} \)

Step 2: Multiply the fractions

\( -\frac{1}{5} \times -\frac{3}{5} = \frac{3}{25} \)? Wait, no, wait: \( -0.2 = -\frac{1}{5} \), so \( -\frac{1}{5} \times -\frac{3}{5} = \frac{3}{25} \)? Wait, no, let's check again. Wait, \( -0.2 = -\frac{1}{5} \), so \( -\frac{1}{5} \times -\frac{3}{5} = \frac{3}{25} \)? Wait, but \( 0.2 \) is \( \frac{1}{5} \), so \( -0.2 \) is \( -\frac{1}{5} \). Then multiplying two negatives: \( (-\frac{1}{5}) \times (-\frac{3}{5}) = \frac{3}{25} = 0.12 \). Wait, but let's do it as decimals: \( -0.2 \times -0.6 = 0.12 \), and \( \frac{3}{25} = 0.12 \), so that's correct.
Wait, but the answer choices have \( \frac{2}{25} \)? Wait, maybe I made a mistake. Wait, \( -0.2 \) is \( -\frac{1}{5} \), and \( -\frac{3}{5} \) is \( -0.6 \). So \( (-0.2) \times (-0.6) = 0.12 \), and \( \frac{3}{25} = 0.12 \), but the answer choices have \( \frac{2}{25} = 0.08 \), \( \frac{5}{7} \approx 0.714 \), \( \frac{1}{2} = 0.5 \), etc. Wait, maybe I misread the problem. Let me check again. Problem 8: \( -0.2 \times -\frac{3}{5} \). So \( -0.2 = -\frac{1}{5} \), \( -\frac{3}{5} \) is \( -0.6 \). Multiplying two negatives: \( (-\frac{1}{5}) \times (-\frac{3}{5}) = \frac{3}{25} \). But the answer choices have \( \frac{2}{25} \), \( \frac{5}{7} \), \( \frac{1}{2} \), etc. Wait, maybe the problem is \( -0.2 \times -\frac{2}{5} \)? No, the user wrote \( -\frac{3}{5} \). Wait, maybe I made a mistake. Alternatively, maybe the problem is \( -0.2 \times -\frac{2}{5} \), which would be \( \frac{4}{25} = 0.16 \), but that's not in the choices. Wait, the answer choices include \( \frac{2}{25} \), which is 0.08, \( \frac{5}{7} \approx 0.714 \), \( \frac{1}{2} = 0.5 \), \( \frac{3}{10} = 0.3 \), no. Wait, maybe the original problem is \( -0.2 \times -\frac{2}{5} \). Let's check: \( -0.2 \times -0.4 = 0.08 = \frac{2}{25} \). Ah, maybe a typo in the problem, or I misread the fraction. If it's \( -\frac{2}{5} \) instead of \( -\frac{3}{5} \), then \( -0.2 \times -0.4 = 0.08 = \frac{2}{25} \), which is one of the answer choices. So maybe the problem is \( -0.2 \times -\frac{2}{5} \). So assuming that, let's proceed.

Step 1: Convert decimal to fraction

\( -0.2 = -\frac{1}{5} \)

Step 2: Multiply the fractions

\( -\frac{1}{5} \times -\frac{2}{5} = \frac{2}{25} \)

Answer:

\( -1 \)

Let's solve problem 8: \( -0.2 \times -\frac{3}{5} \)