Question

Change the decimal to a fraction. Reduce the fraction if possible. a. 0.578 b. 3.5 c. 2.73 d. 0.4211 Change the fraction to a decimal. a. 6⁄100 b. 43⁄100 c. 3⁄10 d. 4 23⁄1,000 Calculate the equivalent decimals for the following fractions. a. 1⁄4 b. 2⁄5 c. 2⁄3 d. 3⁄4 Perform the indicated operation. a. 18.67 + 3.456 + 0.2 + 3.21 b. 3.256 + 4.21 + 3.009 + 0.35 c. 7 – 3.06 d. 62.98 – 3.555 e. 5.3 × 12 f. 4.35 × 2.11 g. 56⁄0.7 h. 5.6⁄7 The distance around a circle is called the circumference. The distance across a circle is called the diameter. To find the circumference of any circle, multiply the diameter of the circle by 3.14. Calculate the circumference of a circle with a diameter of 4.79 feet. A college student has taken a summer job to help pay his tuition. In one week he earned the following amounts. Monday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . $45.98 Tuesday. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49.65 Wednesday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.49 Thursday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.22 Friday. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55.61 What was his average daily earning for that week? (Remember, to find an average, add all the daily amounts together, then divide by the number of days.) On your way home from work you stop at a fruit stand where apples are selling for 88 cents/lb. If you have $6.00 with you, how many pounds of apples can you buy (to the nearest whole pound)? A plant foreman wanted to know how many hours had been spent on a particular project. He asked his supervisors to report the hours worked by each department. Here’s the information he received. Department A. . . . . . . . . . . . . . . . . . . . . . . . . . .202.5 hours Department B . . . . . . . . . . . . . . . . . . . . . . . . . . 212 3⁄4 hours Department C . . . . . . . . . . . . . . . . . . . . . . . . . .198.25 hours Department D. . . . . . . . . . . . . . . . . . . . . . . . . . .215 1⁄5 hours Calculate the total number of hours spent on this project by all four departments. (Hint: Change all the hours to either decimals or fractions before adding.) Can you multiply these decimals in your head? You should be able to do it very quickly. Can you figure out the trick? 26.9 × 52.8 × 100.1 × 0.00 × 999.9632 = ? As the manager of an auto repair shop, you decide to compile some statistics on the cars you service. Last week your shop serviced 72 cars. On 12 of these cars you replaced the muffler. Express this as a percent of cars serviced that needed mufflers. The state where you live has a 6% sales tax. If you purchase a car for $9,800, what will you pay, including tax? (This is a two-step problem.) The win-loss record for a football team is 15 wins and 9 losses. What percent of their games did they win? Paula receives a salary of $320 per week plus a 6% commission on her sales. What are her total earnings for a week when her sales are $3,800? A particular lawn mower is on sale at two different stores. The original price at both stores was $130. Watson’s Garden Shop is advertising the mower for 50% off. Hartman’s Home Center reduced the mower 40%, and then took an additional 15% off the reduced price. Which lawn mower is the better deal? How much would 2 3⁄4 pound of hamburger cost at $4.99 per pound? (Hint: First change the mixed number 2 3⁄4 to a decimal.)

Answer 1

QUESTION 1a

We want to change $0.578$ to a fraction in the simplest form.

We need repeatedly multiply by multiples of 10, until we obtain an integer(the least integer). We then divide by the same value that we used to multiply to get,

$0.578=\frac{0.578\times 1000}{1000}$

This implies that,

$0.578=\frac{578}{1000}$

$0.578=\frac{289\times 2}{500\times 2}$

We cancel out the common factors to get,

$0.578=\frac{289}{500}$

QUESTION 1b

We want to convert $3.5$ to a fraction in the simplest form.

We need repeatedly multiply by multiples of 10, until we obtain an integer(the least integer). We then divide by the same value that we used to multiply to get,

$3.5=\frac{3.5\times 10}{10}$

This implies that,

$3.5=\frac{35}{10}$

$3.5=\frac{7\times 5}{2\times 5}$

We cancel out the common factors to get,

$3.5=\frac{7}{2}$

Or as mixed numbers, we have

$3.5=3\frac{1}{2}$

QUESTION 1c

We want to convert $2.73$ to a fraction in the simplest form.

We need repeatedly multiply by multiples of 10, until we obtain an integer(the least integer). We then divide by the same value that we used to multiply to get,

$2.73=\frac{2.73\times 100}{100}$

This implies that,

$2.73=\frac{273}{100}$

Or as mixed numbers, we have

$2.73=2\frac{73}{100}$

QUESTION 1d

We want to change $0.4211$ to a fraction in the simplest form.

We need repeatedly multiply by multiples of 10, until we obtain an integer(the least integer). We then divide by the same value that we used to multiply to get,

$0.4211=\frac{0.4211\times 10000}{10000}$

This implies that,

$0.4211=\frac{4211}{10000}$

Question 2a

We want to convert $\frac{6}{10}$ into decimal.

This fraction is having a denominator of 10 so we just have to move the decimal point back once to get,

$\frac{6}{10}=0.6$

Check attachment for long division.

QUESTION 2b

We want to convert $\frac{43}{100}$ into decimal.

This fraction is having a denominator of 100 so we just have to move the decimal point back twice to get,

$\frac{43}{100}=0.43$

Check attachment for long division.

QUESTION 2c

We want to change $\frac{3}{10}$ into decimal.

This fraction is having a denominator of 10 so we just have to move the decimal point back once to get,

$\frac{3}{10}=0.3$

Check attachment for long division.

QUESTION 2d

The given fraction is $\frac{423}{1000}$.

This fraction is having a denominator of 1000 so we just have to move the decimal point back three times to obtain,

$\frac{423}{1000}=0.423$

Check attachment for long division.

QUESTION 3a

The given fraction is $\frac{1}{4}$.

We can make the denominator 100 by multiplying both the numerator and the denominator by $25$ to obtain,

$\frac{1}{4} =\frac{1\times 25}{4\times 25}$

This implies that,

$\frac{1}{4} =\frac{25}{100}$

We move the decimal point back twice to obtain,

$\frac{1}{4} =0.25$

See attachment for long division

QUESTION 3b

The given fraction is $\frac{2}{5}$.

We can make the denominator 10 by multiplying both the numerator and the denominator by $2$ to obtain,

$\frac{2}{5} =\frac{2\times 2}{5\times 2}$

This implies that,

$\frac{2}{5} =\frac{4}{10}$

We move the decimal point back twice to obtain,

$\frac{2}{5} =0.4$

See attachment for long division

QUESTION 3c

We want to change $\frac{2}{3}$ into decimals.

We use long division as shown in the attachment to obtain;

$\frac{2}{3}=0.66...$

QUESTION 3d

The given fraction is $\frac{3}{4}$.

We can make the denominator 100 by multiplying both the numerator and the denominator by $25$ to obtain,

$\frac{3}{4} =\frac{3\times 25}{4\times 25}$

This implies that,

$\frac{3}{4} =\frac{75}{100}$

We move the decimal point back twice to obtain,

$\frac{3}{4} =0.75$

QUESTION 4a

We want to simplify

$18.67+3.465+0.2+3.21$

We arrange to obtain,

 $18.670$

  $3.465$

  $0.200$

+ $3.210$

----------------------------

 $25.545$

----------------------------

QUESTION 4b

We want to simplify

$3.56+4.21+3.009+0.35$

We rearrange and carry out the operation as follows;

$3.256$

$4.210$

$3.009$

+$0.350$

----------------------

$10.825$

-----------------------

QUESTION 4c

We want to simplify

$7-3.06$

We rearrange and perform the operation as follows;

$7.00$

-$3.06$

--------------------

$3.94$

--------------------

QUESTION 4d

We want to simplify,

$62.98-3.555$

We rearrange and carry out the operations as follows;

$62.980$

$-3.555$

---------------------

$59.425$

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QUESTION 4e

We want to simplify the product;

$5.3\times 12$

$=\frac{53}{10}\times 12$

$=\frac{636}{10}$

$=63.6$

The rest of the solutions will be in the attachment