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I can help you solve the math problems from the image you uploaded. The image contains problems related to multiplying and dividing rational numbers. Let's go through the solutions step by step for problem 42. I will show the work for each part:

### Problem 42: Multiply or divide. Show your work.

**a.** \( 52 \times 75 \)
\[
52 \times 75 = 3900
\]

**b.** \( 52 \times (-75) \)
\[
52 \times (-75) = -3900
\]

**c.** \( -2,262 \div (-58) \)
\[
-2,262 \div (-58) = 39
\]
(Dividing two negative numbers gives a positive result.)

**d.** \( \frac{3}{5} \times 4 \)
\[
\frac{3}{5} \times 4 = \frac{12}{5}
\]

**e.** \( -9,908 \div 89 \)
\[
-9,908 \div 89 = -111
\]

**f.** \( -7.77 \div (-0.37) \)
\[
-7.77 \div (-0.37) = 21
\]
(Dividing two negative numbers gives a positive result.)

**g.** \( -34 \times 15 \)
\[
-34 \times 15 = -510
\]

**h.** \( 53.2 \div (-7) \)
\[
53.2 \div (-7) = -7.6
\]

**i.** \( -\frac{2}{3} \div \frac{6}{8} \)
\[
-\frac{2}{3} \div \frac{6}{8} = -\frac{2}{3} \times \frac{8}{6} = -\frac{16}{18} = -\frac{8}{9}
\]

**j.** \( 90 \div 50 \)
\[
90 \div 50 = 1.8
\]

**k.** \( -90 \div (-50) \)
\[
-90 \div (-50) = 1.8
\]
(Dividing two negative numbers gives a positive result.)

**l.** \( -108 \div 24 \)
\[
-108 \div 24 = -4.5
\]

**m.** \( 19.5 \div (-3) \)
\[
19.5 \div (-3) = -6.5
\]

**n.** \( -8.4 \div 6 \)
\[
-8.4 \div 6 = -1.4
\]

**o.** \( 6 \times 2 \frac{1}{2} \)
\[
6 \times 2 \frac{1}{2} = 6 \times \frac{5}{2} = 15
\]

**p.** \( -3 \frac{3}{8} \div (-9) \)
\[
-3 \frac{3}{8} \div (-9) = \left(-\frac{27}{8}\right) \div (-9) = \left(-\frac{27}{8}\right) \times \left(-\frac{1}{9}\right) = \frac{27}{72} = \frac{3}{8}
\]

**q.** \( 4 \times (-1 \frac{1}{4}) \)
\[
4 \times (-1 \frac{1}{4}) = 4 \times -\frac{5}{4} = -5
\]

**r.** \( -2.5 \times 2 \frac{1}{5} \)
\[
-2.5 \times 2 \frac{1}{5} = -2.5 \times \frac{11}{5} = -\frac{27.5}{5} = -5.5
\]

These are the solutions to all parts of problem 42.

Would you like further details on any of the problems or have any questions?

### 5 related questions to expand understanding:
1. How do you multiply and divide fractions effectively?
2. What is the rule for multiplying or dividing negative numbers?
3. How do you convert mixed numbers to improper fractions for easier multiplication or division?
4. How do you approach division involving decimals?
5. What is the significance of multiplying or dividing by negative numbers in real-life scenarios?

### Tip:
When multiplying or dividing fractions, always convert mixed numbers to improper fractions and simplify wherever possible to make calculations easier.

Learn how to multiply and divide rational numbers, including integers, fractions, and negative numbers. This step-by-step solution covers essential math skills, perfect for students in Grades 7-8.

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