How to multiply and divide decimals - HSPT Math

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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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Question

Andrew has completed 80% of the race. If the race is 5000 meters, how far along is Andrew?

Answer

Multiply the length of the race by the percentage accomplished by Andrew:

$5000 \ast .80= 4000$

Answer: Andrew has completed 4000 meters of the race.

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Question

Which is less?

a. 60% of 10

b. 20% of 40

c. 30% of 20

d. 10% of 50

Answer

Find the amounts by multiplying each number to the percentage rate:

$a. 10 \ast .60=6$

$b. 40 \ast .20=8$

$c. 20 \ast .30=6$

$d. 50 \ast .10=5$

Compare the amounts to find the least. The answer is D.

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Question

Anita is sewing a quilt made of 120 patches. She has sewn together 84 patches already. What percentage of the quilt has Anita sewn?

Answer

Divide 84 by the entire amount of patches 120 to find the percentage completed.

$84 \div 120= .70$

The answer is Anita has completed 70% of the quilt.

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Question

A round trip flight is on sale for \$425.00. If the flight originally costs \$500.00, what percentage was it reduced by?

Answer

Subtract the sale price from the original price:

Divide that amount by the original price to find the percentage of the sale.

$75 \div 500=.15$

Answer: The flight was reduced by 15%.

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Question

Phil filled up 25 balloons for a party. By the end of the night, only 15 balloons were left; the rest had popped. What percentage of balloons popped throughout the party?

Answer

Subtract to find the amount of balloons that popped.

Then, divide $10\div 25=.4$

The answer: 40% of the balloons popped.

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Question

A pair of sneakers is on sale for 20% off the original price of \$120.00. What is the sale price of the sneakers?

Answer

First, multiply 120 by 0.20.

Subtract that amount from the original price:

Answer: The sneaker's sale price is \$96.00

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Question

Carolina needs to complete a 600-word essay for a test she is taking. If she has already written 445 words, what percentage of the essay has she completed? (Round to the nearest percent.)

Answer

Divide the number of words completed by the number of words needed:

$445 \div 600=0.74$

Answer: Carolina has completed 74% of the essay.

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Question

Jacob is shopping for a snowboard. He has a 20% off coupon. How much will he pay for the snowboard if it is currently priced at \$279.00?

Answer

First, multiply:

Then, subtract that amount from the original price:

Answer: Jacob will pay \$223.80 using his coupon.

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Question

Gavin is shopping for a bar-b-que grill. If he has a 30% off coupon, how much will he save if the grill is currently priced at \$669.00?

Answer

Multiply:

Answer: Gavin will save \$200.70 by using the coupon.

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Question

Lola is shopping for a set of dishes. If the set she likes is on sale for 40% off, how much will she pay if it originally cost \$310.00?

Answer

First, multiply:

Then, subtract that amount from the original price:

Answer: Lola will pay \$186.00 for the set of dishes.

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