Question

homework problems (problems are done on notebook paper.)

1. 10 is what percent of 12? (nearest whole percent)
2. 28% of $990
3. 1\frac{1}{4}% of 1,680
4. 32²
5. \longdiv{47.25}{2.1}
6. \frac{9}{10} \times \frac{5}{8}
7. \frac{2}{3} \times \frac{6}{7}
8. \frac{5}{9} \div 1\frac{1}{3}
9. \frac{5}{12} = \frac{}{15}
10. 5.23 g = \underline{\quad\quad} dag
11. subtract 7%, 59%, and 6\frac{2}{3}% respectively from 100%.
12. order 5%,.1, \frac{3}{8}, \frac{2}{3}, and.25 from least to greatest.
13. find the rate of commission if the sale is $2,000 and the commission is $400.

Explanation:

Step1: Calcular 10% de 12

$\frac{10}{12} \times 100 \approx 83.33\%$
Redondear al entero más cercano: $83\%$

Step2: Calcular 28% de $990$

$0.28 \times 990 = 277.2$

Step3: Calcular $1\frac{1}{4}\%$ de 1,680

$1\frac{1}{4}\% = 1.25\% = 0.0125$
$0.0125 \times 1680 = 21$

Step4: Calcular $32^2$

$32 \times 32 = 1024$

Step5: Realizar la división $47.25 \div 2.1$

$\frac{47.25}{2.1} = 22.5$

Step6: Multiplicar las fracciones $\frac{9}{10} \times \frac{5}{8}$

$\frac{9 \times 5}{10 \times 8} = \frac{45}{80} = \frac{9}{16}$

Step7: Multiplicar las fracciones $\frac{2}{3} \times \frac{6}{7}$

$\frac{2 \times 6}{3 \times 7} = \frac{12}{21} = \frac{4}{7}$

Step8: Dividir $\frac{5}{9} \div 1\frac{1}{3}$

$1\frac{1}{3} = \frac{4}{3}$, así que $\frac{5}{9} \div \frac{4}{3} = \frac{5}{9} \times \frac{3}{4} = \frac{15}{36} = \frac{5}{12}$

Step9: Resolver la proporción $\frac{5}{12} = \frac{15}{x}$

$5x = 15 \times 12 \implies x = \frac{180}{5} = 36$

Step10: Convertir 5.23 g a dag

1 dag = 10 g, así que $5.23 \div 10 = 0.523$ dag

Step11: Restar los porcentajes de 100%

• $100\% - 7\% = 93\%$
• $100\% - 59\% = 41\%$
• $100\% - 6\frac{2}{3}\% = 93\frac{1}{3}\%$

Step12: Ordenar de menor a mayor

Convertir todos a decimales:

• $5\% = 0.05$
• $0.1 = 0.1$
• $\frac{3}{8} = 0.375$
• $\frac{2}{3} \approx 0.667$
• $0.25 = 0.25$

Orden: $5\%, 0.1, 0.25, \frac{3}{8}, \frac{2}{3}$

Step13: Calcular la tasa de comisión

$\text{Tasa} = \frac{\text{Comisión}}{\text{Venta}} \times 100 = \frac{400}{2000} \times 100 = 20\%$

Answer:

1. $83\%$
2. $\$277.2$
3. $21$
4. $1024$
5. $22.5$
6. $\frac{9}{16}$
7. $\frac{4}{7}$
8. $\frac{5}{12}$
9. $36$
10. $0.523$
11. $93\%$, $41\%$, $93\frac{1}{3}\%$
12. $5\%, 0.1, 0.25, \frac{3}{8}, \frac{2}{3}$
13. $20\%$