Question

1. find the answers.

a. \\(\

$$\begin{align}72,536\\\\49,875\\\\63,299\\\\+\\ 7,847\\end{align}$$

\\) b. \\(\

$$\begin{align}\\$381.25\\\\-295.29\\end{align}$$

\\) c. \\(\

$$\begin{align}632\\\\\\times508\\end{align}$$

\\) d. \\(399\overline{)170,772}\\)
e. \\(\

$$\begin{align}6\\frac{1}{3}\\\\9\\frac{1}{4}\\\\ + 4\\frac{5}{6}\\end{align}$$

\\) f. \\(\

$$\begin{align}3\\frac{2}{3}\\\\ - 1\\frac{5}{6}\\end{align}$$

\\) g. \\(3\frac{1}{3}\times1\frac{7}{8}=\underline{\quad\quad}\\) h. \\(1\frac{3}{7}\div\frac{9}{14}=\underline{\quad\quad}\\)
i. \\(\

$$\begin{align}9.02\\\\17.859\\\\ + 6.423\\end{align}$$

\\) j. \\(\

$$\begin{align}8.1\\\\ - 7.2954\\end{align}$$

\\) k. \\(\

$$\begin{align}.17\\\\\\times2.3\\end{align}$$

\\) l. \\(5.49\overline{)19.764}\\) m. \\(2^6=\underline{\quad\quad}\\)

1. write the equivalent decimal.

a. \\(53\\%=\underline{\quad\quad}\\) b. \\(5\frac{1}{5}\\%=\underline{\quad\quad}\\) c. \\(\frac{1}{8}=\underline{\quad\quad}\\) d. \\(\frac{3}{4}\\%=\underline{\quad\quad}\\) e. \\(840\\%=\underline{\quad\quad}\\)

1. find the percentages.

a. \\(81\\%\text{ of }3,600\\) \\(\underline{\quad\quad}\\) b. \\(500\\%\text{ of }18\\) \\(\underline{\quad\quad}\\) c. \\(2\frac{1}{4}\\%\text{ of }6,000\\) \\(\underline{\quad\quad}\\)

1. find the percent of increase or decrease.

a. was \\(\\$60\\) now \\(\\$50\\) b. had 50 found 15 c. yesterday \\(\\$100\\) today \\(\\$95\\)

Explanation:

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Problem 1

a. Step1: Sum the four numbers

$72,536 + 49,875 + 63,299 + 7,847 = 193,557$

b. Step1: Subtract the values

$\$381.25 - \$295.29 = \$85.96$

c. Step1: Multiply the two numbers

$632 \times 508 = 321,056$

d. Step1: Divide the numbers

$\frac{170,772}{399} = 428$

e. Step1: Convert to improper fractions

$6\frac{1}{3} = \frac{19}{3}$, $9\frac{1}{4} = \frac{37}{4}$, $4\frac{5}{6} = \frac{29}{6}$

e. Step2: Find common denominator (12)

$\frac{76}{12} + \frac{111}{12} + \frac{58}{12} = \frac{245}{12} = 20\frac{5}{12}$

f. Step1: Convert to improper fractions

$3\frac{2}{3} = \frac{11}{3}$, $1\frac{5}{6} = \frac{11}{6}$

f. Step2: Subtract fractions

$\frac{22}{6} - \frac{11}{6} = \frac{11}{6} = 1\frac{5}{6}$

g. Step1: Convert to improper fractions

$3\frac{1}{5} = \frac{16}{5}$, $1\frac{7}{8} = \frac{15}{8}$

g. Step2: Multiply fractions

$\frac{16}{5} \times \frac{15}{8} = 6$

h. Step1: Convert to improper fractions

$1\frac{3}{7} = \frac{10}{7}$, $\frac{9}{14}$ stays as is

h. Step2: Divide (multiply by reciprocal)

$\frac{10}{7} \times \frac{14}{9} = \frac{20}{9} = 2\frac{2}{9}$

i. Step1: Sum the decimals

$9.02 + 17.859 + 6.423 = 33.302$

j. Step1: Subtract the decimals

$8.1 - 7.2954 = 0.8046$

k. Step1: Multiply the decimals

$0.17 \times 2.3 = 0.391$

l. Step1: Divide the decimals

$\frac{19.764}{5.49} = 3.6$

m. Step1: Calculate the exponent

$2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$
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Problem 2

a. Step1: Convert % to decimal

$53\% = \frac{53}{100} = 0.53$

b. Step1: Convert mixed % to decimal

$5\frac{1}{5}\% = 5.2\% = \frac{5.2}{100} = 0.052$

c. Step1: Convert fraction to decimal

$\frac{1}{8} = 0.125$

d. Step1: Convert fraction % to decimal

$\frac{3}{4}\% = 0.75\% = \frac{0.75}{100} = 0.0075$

e. Step1: Convert % to decimal

$840\% = \frac{840}{100} = 8.4$
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Problem 3

a. Step1: Calculate percentage

$0.81 \times 3,600 = 2,916$

b. Step1: Calculate percentage

$5.00 \times 18 = 90$

c. Step1: Convert mixed % to decimal

$2\frac{1}{4}\% = 2.25\% = 0.0225$

c. Step2: Calculate percentage

$0.0225 \times 6,000 = 135$
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Problem 4

a. Step1: Find amount of decrease

$\$60 - \$50 = \$10$

a. Step2: Calculate % decrease

$\frac{10}{60} \times 100\% \approx 16.67\%$ decrease

b. Step1: Find new total

$50 + 15 = 65$

b. Step2: Calculate % increase

$\frac{15}{50} \times 100\% = 30\%$ increase

c. Step1: Find amount of decrease

$\$100 - \$95 = \$5$

c. Step2: Calculate % decrease

$\frac{5}{100} \times 100\% = 5\%$ decrease

Answer:

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Problem 1

a. $193,557$
b. $\$85.96$
c. $321,056$
d. $428$
e. $20\frac{5}{12}$
f. $1\frac{5}{6}$
g. $6$
h. $2\frac{2}{9}$
i. $33.302$
j. $0.8046$
k. $0.391$
l. $3.6$
m. $64$
---

Problem 2

a. $0.53$
b. $0.052$
c. $0.125$
d. $0.0075$
e. $8.4$
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Problem 3

a. $2,916$
b. $90$
c. $135$
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Problem 4

a. $\approx16.67\%$ decrease
b. $30\%$ increase
c. $5\%$ decrease