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PSAT Math : Arithmetic

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Example Questions

Example Question #1 : Decimal Operations

At the store, green fabric costs $4.53 a yard. How much does 3.8 yards of green fabric cost? (Round to two decimal places.)

Possible Answers:

$17.21

$17.13

$17.31

$17.12

$17.22

Correct answer:

$17.21

Explanation:

This is a simple multiplication problem involving decimals. Simply multiply 4.53 by 3.8:

$\small 4.53*3.8 = 17.214$

Now, round to the nearest two decimal places, giving an answer of 17.21.

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Example Question #4 : How To Multiply Decimals

Find the product. Round to the nearest hundredths place.

$10.18 53\times 53.22$

Possible Answers:

541.8

532.64

541.78

542

500

Correct answer:

541.78

Explanation:

The hundredths place is the position two places to the right of the decimal. Our product is $10.18 \times 53.22 = 541.7796$ . Rounding to the hundredths place results in 541.78 .

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Example Question #1 : Decimal Operations

simplify: 0.2 ÷ 0.04

Possible Answers:

0.02

0.005

0.05

Correct answer: 5

Explanation:

0.2 ÷ 0.04 <- easiest way to approach is to move the decimal to the right (the same amount of spaces on each side) so that the decimal disappears

since 0.04 has 2 spaces and 0.2 only has 1, move the decimal 2 spaces to the right on each side

0.2 ÷ 0.04 = 20 ÷ 4 = 5

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Example Question #1 : Decimal Operations

If the cost of 20 equally priced pencils cost $5.80, then at the same rate what is the greatest number of pencils you can purchase for $50?

Possible Answers:

173

150

172

172.41

200

Correct answer:

172

Explanation:

Remeber for this problem that you cannot spend more than $50. First find the price of each pencil by 5.80/20 = 29 cents. And then use this to do 50/0.29 = 172.41. So the greatest number of pencils you can purchase for $50 is 172 pencils.

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Example Question #2 : Decimal Operations

Charlie has charges on his credit card of $63.70, $37.32, and $81.78. If he pays down half his bill at once, and then pays the rest in four equal monthly installments, how much is each monthly installment?

Possible Answers:

$\$25.00$

$\$25.32$

$\$22.85$

$\$23.05$

$\$21.78$

Correct answer:

$\$22.85$

Explanation:

Adding all the charges together and dividing by 2 yields $91.40. Dividing this by 4 yields a monthly installment of $22.85.

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Example Question #3 : Decimal Operations

Simplify:

$\frac{0.004}{0.0005}$

Possible Answers:

0.8

0.08

0.008

Correct answer:

Explanation:

Multiply both the numerator and denominator by some power of 10 to get rid of the decimals; in this case, multiply both by 10,000.

$\frac{0.004}{0.0005}\cdot \frac{10,000}{10,000}=\frac{40}{5}=8$

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Example Question #501 : Arithmetic

Which number has 2.8 as its reciprocal?

Possible Answers:

$-\frac{5}{1 4}$

-2.8

$\frac{5}{1 4}$

-8.2

8.2

Correct answer:

$\frac{5}{1 4}$

Explanation:

The number that has 2.8 as its reciprocal is, in return, the reciprocal of 2.8.

$2.8 = \frac{28}{10} = \frac{28 \div 2}{10 \div 2} = \frac{14}{5}$

The reciprocal of this can be found by switching the numerator and the denominator. This is $\frac{5}{1 4}$ .

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Example Question #6 : How To Divide Decimals

23 grams of sodium are equal to $6.022 \times 10^{23}$ atoms. How many atoms comprise one milligram of sodium?

(Select the closest answer)

Possible Answers:

$1.39 \times 10 ^{20}$

$2.62 \times 10^{17}$

$2.62 \times 10^{19}$

$1.39 \times 10 ^{19}$

$2.62 \times 10^{18}$

Correct answer:

$2.62 \times 10^{19}$

Explanation:

23 grams are equal to 23,000 milligrams, so to find the number of atoms in one milligram, divide:

$=\frac{ 6.022 \times 10^{23} }{ 23,000}$

$=\frac{ 6.022 \times 10^{23} }{ 2.3 \times 10 ^{4} }$

$= \frac{ 6.022 }{ 2.3 } \cdot \frac{ 10^{23} }{ 10 ^{4} }$

$=2.62 \times 10^{19}$

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Example Question #1 : How To Subtract Decimals

Round the answer to the nearest tenth.

0.57-2.657=

Possible Answers:

-2.11

-2.1

-2.05

-2.0

2.0

Correct answer:

-2.1

Explanation:

0.57 - 2.657 = -2.087

Don't forget the negative sign!

This number then rounds to -2.1.

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Example Question #2 : How To Subtract Decimals

Simplify:

-0.5+1.2-(0.6+0.1)

Possible Answers:

-0.2

-2.4

0.2

Correct answer:

Explanation:

Start by simplifying within the parentheses:

-0.5+1.2-(0.6+0.1)

-0.5+1.2-(0.7)

Then add/subtract each number

0.7-0.7 = 0

When you finish simplifying, the answer is 0.

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PSAT Math : Arithmetic

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : Decimal Operations

Example Question #4 : How To Multiply Decimals

Example Question #1 : Decimal Operations

Example Question #1 : Decimal Operations

Example Question #2 : Decimal Operations

Example Question #3 : Decimal Operations

Example Question #501 : Arithmetic

Example Question #6 : How To Divide Decimals

Example Question #1 : How To Subtract Decimals

Example Question #2 : How To Subtract Decimals

All PSAT Math Resources

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