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PSAT Math : Arithmetic

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Example Questions

Example Question #491 : Arithmetic

Express as a decimal: $\frac{16}{9}$

Possible Answers:

0.5625

$1.\overline{7}$

$1.6\overline{7}$

1.6

$0.5\overline{6}$

Correct answer:

$1.\overline{7}$

Explanation:

Divide 16 by 9:

Division

The "7" repeats forever, so

$\frac{16}{9} = 1.\overline{7}$

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Example Question #492 : Arithmetic

Express as a decimal: $\frac{9}{16}$

Possible Answers:

0.5625

$1.\overline{7}$

$0.\overline{5}$

$0.5\overline{6}$

1.6

Correct answer:

0.5625

Explanation:

Divide 9 by 16:

Division

$\frac{9}{16} = 0.5625$

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Example Question #493 : Arithmetic

Convert the fraction to a decimal.

$\frac{13}{25}$

Possible Answers:

0.26

0.42

0.52

0.78

0.53

Correct answer:

0.52

Explanation:

We can multiply our numerator and denominator by , which leads to $\frac{52}{100}$ . From here we divide by our denominator, moving the decimal two places to the left.

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Example Question #1 : Decimals

$\frac{1}{10}\times \frac{3}{5}\div \frac{6}{7}= {?}}$

Possible Answers:

0.07

0.04

0.01

0.05

0.10

Correct answer:

0.07

Explanation:

Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.

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Example Question #4 : Decimals With Fractions

Write 0.45 as a fraction.

Possible Answers:

$\frac{11}{20}$

$\frac{3}{4}$

$\frac{9}{20}$

$\frac{2}{5}$

$\frac{5}{9}$

Correct answer:

$\frac{9}{20}$

Explanation:

.45 is equivalent to 45 out of 100, or $\frac{45}{100}$ .

Divide both the numerator and denominator by 5 to simplify the fraction:

$\frac{9}{20}$

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Example Question #5 : Decimals

Express as a fraction: $0.3\overline{4}$

Possible Answers:

$\frac{34}{99}$

$\frac{31}{90}$

$\frac{31}{99}$

$\frac{34}{101}$

$\frac{34}{90}$

Correct answer:

$\frac{31}{90}$

Explanation:

Let $x = 0.3\overline{4} = 0.3444...$

Then

$10 x = 10 \times 0.3444... = 3.444...$

and

$100 x = 100 \times 0.3444... = 34.44...$

Subtract:

100 x = 34.44...

$\underline{10 x = \; \; 3.444...}$

90x = 31

$x = \frac{31}{90}$

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Example Question #1 : How To Multiply Decimals

45.728 x 3.2 = ?

Possible Answers:

14.63296

14632.96

146.3296

146329.6

1463.296

Correct answer:

146.3296

Explanation:

Multiply the numbers out in long format, then move the decimal point over the total number of decimal points in the two numbers (3 in the first, 1 in the second, so 4 total):

45.728 * 3.2 = 91456

91456 + 1371840 = 1,463,296 → 146.3296

Or just count the decimal points in the answer and make sure it's 4.

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Example Question #1 : How To Multiply Decimals

At the farmer's market, oranges are $0.30 each, apples are $0.25 each, bananas are $0.40 each, and tomatoes are $0.60 each. If Scott buys 3 oranges, 7 apples, 4 bananas, and 8 tomatoes, how much does he spend?

Possible Answers:

$7.75

$10.40

$6.80

$11.40

$9.05

Correct answer:

$9.05

Explanation:

To find out how much Scott spends, we need to multiply the quantity of each fruit by its price and add them all up.

3 * $0.30 + 7 * $0.25 + 4 * $0.40 + 8 * $0.60 = $9.05

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Example Question #2 : How To Multiply Decimals

$y=\frac{49}{50}\times0.51\times52$

If is 25% of , what is the closest integer to the value of ?

Possible Answers:

{13}

104

6.5

208

Correct answer:

104

Explanation:

We can approximate the value of y pretty quickly:

y ≈ 1(0.50)(52) = 26

Since y = 0.25x = (1/4)x we know that x = 4y ≈ 4(26) = 104

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Example Question #3 : How To Multiply Decimals

$0.5 \times 0.012 =$

Possible Answers:

0.06

0.6

0.006

0.0006

Correct answer:

0.006

Explanation:

It's much easier to work with whole numbers, so we'll ignore the decimals for the first step: 5 x 12 = 60

Now look at the decimals. To add them back in, think of 60 as 60.0. Now move the decimal point four places to the left: 0.5 x 0.012 = .0060 = .006

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PSAT Math : Arithmetic

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #491 : Arithmetic

Example Question #492 : Arithmetic

Example Question #493 : Arithmetic

Example Question #1 : Decimals

Example Question #4 : Decimals With Fractions

Example Question #5 : Decimals

Example Question #1 : How To Multiply Decimals

Example Question #1 : How To Multiply Decimals

Example Question #2 : How To Multiply Decimals

Example Question #3 : How To Multiply Decimals

All PSAT Math Resources

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