Question

1. \\(\frac{9}{10} = \frac{}{100}\\)\
2. 18 ft. = \\(\underline{\quad\quad}\\) yd.\
3. 3.5 kg = \\(\underline{\quad\quad}\\) cg\
4. \\(\frac{1}{1} \frac{2}{} = \frac{}{6}\\)\
5. \\(\frac{1}{2} \frac{4}{} = \frac{}{8}\\)\
6. reduce \\(\frac{12}{18}\\), \\(\frac{9}{15}\\), \\(\frac{16}{24}\\), \\(\frac{5}{10}\\), and \\(\frac{14}{35}\\) to lowest terms.\
7. round off 0.3762 to the nearest tenth, hundredth, and thousandth.\
8. simplify \\(\frac{25}{15}\\), \\(\frac{18}{12}\\), \\(\frac{9}{6}\\), and \\(\frac{14}{8}\\).\
9. find a 6% commission on sales of $850 and $1,975.\
10. write the greater:.007 or.0669; mi or \\(\overline{v}\\); 17% or \\(\frac{1}{4}\\).\
11. find 15 less than the product of 17 and 4.

Explanation:

Step1: Convert fraction to percent

$\frac{9}{10} = 9 \div 10 = 0.9 = 90\%$

Step2: Convert feet to yards

1 yard = 3 feet, so $18 \div 3 = 6$

Step3: Convert kg to centigrams

1 kg = 100000 cg, so $3.5 \times 100000 = 350000$

Step4: Solve proportion for missing value

$\frac{\frac{1}{2}}{1} = \frac{6}{x} \implies \frac{1}{2}x = 6 \implies x = 12$

Step5: Solve proportion for missing value

$\frac{\frac{1}{4}}{2} = \frac{8}{x} \implies \frac{1}{4}x = 16 \implies x = 64$

Step6: Reduce fractions to lowest terms

• $\frac{12}{18} = \frac{12\div6}{18\div6} = \frac{2}{3}$
• $\frac{9}{15} = \frac{9\div3}{15\div3} = \frac{3}{5}$
• $\frac{16}{24} = \frac{16\div8}{24\div8} = \frac{2}{3}$
• $\frac{5}{10} = \frac{5\div5}{10\div5} = \frac{1}{2}$
• $\frac{14}{35} = \frac{14\div7}{35\div7} = \frac{2}{5}$

Step7: Round decimal to nearest places

• Nearest tenth: $0.3762 \approx 0.4$
• Nearest hundredth: $0.3762 \approx 0.38$
• Nearest thousandth: $0.3762 \approx 0.376$

Step8: Simplify fractions to lowest terms

• $\frac{25}{15} = \frac{25\div5}{15\div5} = \frac{5}{3}$
• $\frac{18}{12} = \frac{18\div6}{12\div6} = \frac{3}{2}$
• $\frac{9}{6} = \frac{9\div3}{6\div3} = \frac{3}{2}$
• $\frac{14}{8} = \frac{14\div2}{8\div2} = \frac{7}{4}$

Step9: Calculate 6% commission for each sale

• For $\$850$: $0.06 \times 850 = 51$
• For $\$1975$: $0.06 \times 1975 = 118.5$

Step10: Compare pairs to find greater value

• $0.0669 > 0.007$
• $\text{MI} = 1000$, $\overline{\text{V}} = 5000$, so $\overline{\text{V}} > \text{MI}$
• $\frac{1}{4} = 25\%$, so $\frac{1}{4} > 17\%$

Step11: Compute product then subtract 15

Product: $17 \times 4 = 68$; $68 - 15 = 53$

Answer:

1. $90\%$
2. $6$
3. $350000$
4. $12$
5. $64$
6. $\frac{2}{3}$, $\frac{3}{5}$, $\frac{2}{3}$, $\frac{1}{2}$, $\frac{2}{5}$
7. Nearest tenth: $0.4$; Nearest hundredth: $0.38$; Nearest thousandth: $0.376$
8. $\frac{5}{3}$, $\frac{3}{2}$, $\frac{3}{2}$, $\frac{7}{4}$
9. $\$51$, $\$118.50$
10. $0.0669$, $\overline{\text{V}}$, $\frac{1}{4}$
11. $53$