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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1003 : Numbers And Operations

Multiply:

$0.58 \times 8.3$

Possible Answers:

4.814

4.2164

0.4814

0.42164

4.6574

Correct answer:

4.814

Explanation:

First, multiply the numbers, ignoring the decimal points:

$58 \times 83 = 4814$

Since the two factors in the original product have three digits to the right of the decimal points between them, position the decimal point in the product such that three digits are at its right. The result, therefore, is

4.814

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Example Question #6 : How To Multiply Fractions

Multiply: $6.73 \times 0.006$

Possible Answers:

0.04308

0.4038

0.04038

0.438

0.0438

Correct answer:

0.04038

Explanation:

First, remove the decimal points, multiplying as follows:

$673 \times 6 = 4 038$

Between them, the two factors have five digits to the right of their decimal points, so position the decimal point in the product so that there are five digits to the right. This will require placing a zero in front as a placeholder, so the final result is

$6.73 \times 0.006 = 0.04038$

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Example Question #1001 : Numbers And Operations

Find $\frac{3}{5}\cdot \frac{7}{9}$ .

Possible Answers:

$\frac{7}{5}$

$\frac{15}{7}$

$\frac{3}{5}$

$\frac{7}{15}$

Correct answer:

$\frac{7}{15}$

Explanation:

To find the product of two fractions, multiply the numerators together and then multiply the denominators together.

$\frac{3}{5}\cdot \frac{7}{9}=\frac{21}{45}$ , which can be reduced to $\frac{7}{15}$ .

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Example Question #1002 : Numbers And Operations

Find $\frac{5}{7}\cdot \frac{3}{4}=$ .

Possible Answers:

$\frac{2}{3}$

$\frac{5}{7}$

$\frac{15}{28}$

$\frac{20}{21}$

Correct answer:

$\frac{15}{28}$

Explanation:

To find the product of two fractions, multiply the numerators together and then multiply the denominators together.

$\frac{5}{7}\cdot \frac{3}{4}=\frac{15}{28}$

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Example Question #341 : Arithmetic

$\frac{1}{3} \times \frac{4}{5}=?$

Possible Answers:

$\frac{5}{12}$

$\frac{12}{5}$

$\frac{4}{15}$

$\frac{5}{8}$

$\frac{4}{8}$

Correct answer:

$\frac{4}{15}$

Explanation:

Multiply the numerators together, and then multiply the denominators together:

$\frac{1}{3} \times \frac{4}{5}=\frac{1\times 4}{3\times 5}=\frac{4}{15}$

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Example Question #1003 : Numbers And Operations

What is the product of the two fractions below?

$\frac{4}{5}\cdot\frac{7}{8}$

Possible Answers:

$\frac{14}{40}$

$\frac{27}{40}$

$\frac{6}{10}$

$\frac{7}{10}$

$\frac{10}{7}$

Correct answer:

$\frac{7}{10}$

Explanation:

To solve for this expression, first multiple the numerators, and then multiply the demonators.

$\frac{4}{5}\cdot\frac{7}{8}$

$\frac{4\times7}{5\times8}$

$\frac{28}{40}$

Simplify the fraction by removing a common factor.

$\frac{28\div4}{40\div4}=\frac{7}{10}$

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Example Question #342 : Arithmetic

Raise to the fourth power.

Possible Answers:

-65,536

65,536

-4,096

4,096

Correct answer:

4,096

Explanation:

To raise a negative number to an even-numbered power, raise its absolute value to that power:

$(-8)^{4}= 8^{4} = 8 \times 8 \times 8 \times 8 = 4,096$

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Example Question #1672 : Ssat Middle Level Quantitative (Math)

Evaluate:

$15 - \left ( \frac{2}{3} \times 3 - \frac{4}{3}\right )$

Possible Answers:

$13\frac{8}{9}$

$42\frac{2}{3}$

$11\frac{2}{3}$

$14 \frac{1}{3}$

Correct answer:

$14 \frac{1}{3}$

Explanation:

By the order of operations, carry out the operations in parentheses first; since there is a multiplication and a subtraction present, carry them out in that order. Finally, carry out the remaining subtraction:

$15 - \left ( \frac{2}{3} \times 3 - \frac{4}{3}\right )$

$= 15 - \left ( 2- \frac{4}{3}\right )$

$= 15 - \frac{2}{3}$

$= 14 \frac{1}{3}$

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Example Question #1 : Multiplicative Inverse Property

Which of the following statements demonstrates the inverse property of multiplication?

Possible Answers:

None of the examples in the other responses demonstrates the inverse property of multiplication.

$\frac{6}{7} \times\frac{1}{4} = \frac{1}{4} \times \frac{6}{7}$

$\frac{6}{7} \times\left ( \frac{1}{4} \times \frac{3}{8} \right ) =\left ( \frac{6}{7} \times\frac{1}{4} \right ) \times \frac{3}{8}$

$\frac{6}{7} \times \frac{7}{6} = 1$

$\frac{6}{7} \times 1 = \frac{6}{7}$

Correct answer:

$\frac{6}{7} \times \frac{7}{6} = 1$

Explanation:

The inverse property of multiplication states that for every real number, a number exists, called the multiplicative inverse, such that the number and its inverse have product 1. Of the statements given, only

$\frac{6}{7} \times \frac{7}{6} = 1$

demonstrates this property.

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Example Question #1011 : Numbers And Operations

Raise $- \frac{3}{2}$ to the fourth power.

Possible Answers:

$\frac{16} {81}$

$- \frac{16}{81}$

$\frac{81}{16}$

$\frac{16}{81}$

Correct answer:

$\frac{81}{16}$

Explanation:

To raise a negative number to an even-numbered power, raise its absolute value to that power. Also, to raise a fraction to a power, raise its numerator and its denominator to that power. Combine these ideas as follows:

$\left (- \frac{3}{2} \right )^{4} = \left( \frac{3}{2}\right )^{4} = \frac{3^{4} }{2^{4} } = \frac{ 3 \times 3\times 3 \times 3 }{ 2 \times 2 \times 2 \times 2 } \right ) = \frac{81}{16}$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1003 : Numbers And Operations

Example Question #6 : How To Multiply Fractions

Example Question #1001 : Numbers And Operations

Example Question #1002 : Numbers And Operations

Example Question #341 : Arithmetic

Example Question #1003 : Numbers And Operations

Example Question #342 : Arithmetic

Example Question #1672 : Ssat Middle Level Quantitative (Math)

Example Question #1 : Multiplicative Inverse Property

Example Question #1011 : Numbers And Operations

All HSPT Math Resources

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