How to multiply and divide decimals - HSPT Math

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Question

If Exam 1 is worth 25% of the total grade, Exam 2 is worth 25% and Exam 3 is worth 50%, what is Dave’s final grade?

Answer

Final Grade = Exam1 * 0.25 + Exam 2 * 0.25 + Exam3 * 0.50 =

960.25 + 700.25 + 85*0.5 =

24 + 17.5 + 42.5 = 84

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Question

A car has gas mileage of 46 miles per gallon. Assume that gas costs $3.90 per gallon. What would be the total cost of gas if the car traveled 1,150 miles?

Answer

First find out how many gallons of gas the car consumed while traveling 1150 miles. This can be found out like so:

1150 miles x gallons/46 miles = 25 gallons

Multiplying 25 by $3.90 yields $97.50.

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Question

Kevin is looking at the blueprint of the house he is building. The scale is 1 inch = 5 feet. On paper, the master bedroom is 2.5 inches by 3 inches. What is the actual size of the bedroom?

Answer

The given dimensions must be multiplied by 5, so 2.5 inches becomes 12.5 feet, and 3 inches becomes 15 feet.

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Question

If , approximately how many inches are in one meter?

Answer

and $100\ cm=1\ m$

Using the factor-label method we get the following equation.

$\frac{1; meter}{1}\frac{100 ; cm}{1 ; m}\frac{1 ; in}{2.5; cm} = 40 ; in$

We treat the units as if they are numbers, and can cancel the units from the fractions.

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Question

What is 48,570 in scientific notation?

Answer

Convert to scientific notation by creating a number that is greater than or equal to 1 AND less than 10 AND includes the same digits as the original number. Remove all zeros before the first natural number and after the last natural number.

So, we have 48,570.

Now we move the decimal to create our number between 1 and 10.

4.8570

We have one zero after the last natural number, which is 7. Remove that.

4.857

Now we must multiply that number by 10 to a certain power. We choose our power by how many places the decimal must move to get our original number. In this case, the decimal would have to move 4 places to the right.

4.857

48.57

485.7

48,570.

So our final answer is $\dpi{100} 4.857\times 10^{4}$

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Question

You bought a dozen eggs marked at and received change from . What is the percent of sales tax?

Answer

Set the equation up as

Solve for , which equals $\frac{2.45}{2.29}$

or

Therefore the percent sales tax is:

$(1.0698-1) \times 100=6.98% \approx 7%$

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Question

Multiply: $\frac{3}{4}\times \frac{3}{2}$

Answer

To multiply, there is no need to solve for a least common denominator. Simply multiply the numerator with the numerator and the denominators together.

$\frac{3}{4}\times \frac{3}{2}= \frac{9}{8}$

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Question

Multiply: $24 \times 0.3$

Answer

Multiply the terms as is, ignoring the decimal.

$24\times 3 = 72$

Since there is one decimal from the original problem, the decimal place is one unit from the right. Therefore, the final answer must have a decimal one unit to from the right.

The answer is .

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Question

Above is the menu at the concession stand at a school carnival.

David wants to buy some chicken strips for himself and his companions. He wants six strips, his brother Mickey wants five strips, his girlfriend Vickie wants three, and Mickey's girlfriend Jenny wants five. Since the concession stand only sells the strips in orders of four, he has decided to just purchase as many orders as it takes to feed the entire group. How much will he spend on enough orders of strips to satisfy the group?

(No tax is charged, since this is a school event)

Answer

The group wants a total of strips; since

$19 \div 4 = 4 \textup{ R }3$ ,

Dave will need to purchase five orders of strips (he cannot purchase a partial order). This will cost him

$$3.99 \times 5 = $19.95$ .

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Question

An aircraft's cruising speed is miles per hour. How far will it travel in $1\frac{1}{4}$ hours?

Answer

The formula to calculate distance is $d =\frac{r}{t}$ where represents rate of speed and represents time.

In this problem, mph., and $t= 1\frac{1}{4}$ hours.

Convert the $1\frac{1}{4}$ to an improper fraction:

$1\frac{1}{4} = \frac{(4\times 1)+1}{4} =\frac{5}{4}$

To solve, multiply.

$d = \frac{340}{1} \times\frac{5}{4}$

$d = \frac{1700}{4}$

miles.

At its cruising speed of mph, the aircraft will travel miles in $1\frac{1}{4}$ hours.

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Question

Evaluate

$0.5\ast0.05\ast1.5$

Answer

First, $0.5\ast0.05=0.025$

Then, $0.025\ast1.5=0.0375$

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Question

Answer

When multiplying decimals you ignore the decimals and multiply the two numbers like you would normally.

Then count the total number of decimal places to the right of the decimal of the original numbers.

Move the decimal from the whole number answer you just received to the left the same number of times as the total decimal places to the right of the numbers before you multiplied them.

Therefore the answer is

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Question

A watch originally cost $55.00. If it is on sale for 20% off, what is the sale price of the watch?

Answer

To solve:

First, find what is 20% of 55 by multiplying:

$\small 55\cdot .20=11$

Then, subtract 20% (11) from the original price:

$\small 55-11=44$

The final sale price will be $44.00.

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Question

Which is largest?

a. 30% of 150

b. 20% of 300

c. 40% of 60

d. 10% of 400

Answer

To solve:

First find the corresponding percentage of each multiple choice answer,

a) $\small 150\cdot .30= 45$

b) $\small 300\cdot .20= 60$

c) $\small 60\cdot .40= 24$

d) $\small 400\cdot .10= 40$

Then, compare the amounts and select which amount is the largest:

b) 60

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Question

Divide:

$320 \div 0.004$

Answer

Examine the divisor 0.004. To make this a whole number, the decimal point needs to be moved three places right. Do this to both 0.004 and 320, adding an implied decimal point after the latter first:

$320.000 \div 0.004 \Rightarrow 320000. \div 4$

Now perform this division:

$320,000. \div 4 = 80,000$

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Question

Evaluate: $0.3^{5}$

Answer

$0.3^{5} = 0.3 \cdot 0.3\cdot 0.3\cdot 0.3\cdot 0.3$

First, multiply, ignoring the decimal points:

$3 \cdot 3\cdot 3\cdot 3\cdot 3 = 243$

Put a decimal point after the number:

Since there were five digits total (one per factor) left of the decimal points, move the decimal point in the product left five places, inserting zeroes as needed:

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Question

Express 1.14 as a fraction in lowest terms.

Answer

The fraction has its last nonzero digit in the hundredths place, so write the number, without the decimal point, over 100. Then reduce.

$\frac{114}{100} = \frac{114\div 2}{100\div 2} = \frac{57}{50}$

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Question

Express 450,000,000,000 in scientific notation.

Answer

To rewrite a very large number in scientific notation:

Write the number with the decimal point after it (it is implied to be at that location).

Move the decimal point left as many places as needed until it follows the first nonzero digit, which here is the four. Count the number of places it is moved - here it will be eleven places.

The number formed is , which will be placed in front; 11, the number of places counted, will be the exponent. The number, in scientific notation, will be $4.5 \times 10^{11}$ .

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Question

How do you write $\frac{1}{5}$ as a percent?

Answer

$\frac{1}{5}$ is equal to $\frac{20}{100}$ , which is 20%.

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Question

Express $\frac{8}{15}$ as a decimal.

Answer

Divide 8 by 15:

$\frac{8}{15} = 8 \div 15 = 0.5333...$

The 3 repeats, so the correct choice is $0.5\overline{3}$ .

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