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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #941 : Hspt Mathematics

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

Possible Answers:

$\frac{32}{243}$

$\frac{243} {32}$

$-\frac{32}{243}$

$- \frac{2}{3}$ cannot be raised to the fifth power.

$-\frac{243} {32}$

Correct answer:

$-\frac{32}{243}$

Explanation:

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

$\left (- \frac{2}{3} \right )^{5} = - \left ( \frac{2}{3} \right )^{5} = - \left ( \frac{2^{5} }{3^{5} } \right ) = - \left ( \frac{2\times 2 \times 2 \times 2 \times 2 }{3 \times 3 \times 3\times 3 \times 3 } \right ) = -\frac{32}{243}$

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Example Question #344 : Arithmetic

Raise to the fifth power.

Possible Answers:

-78,125

-16,807

78,125

16,807

cannot be raised to the fifth power.

Correct answer:

-16,807

Explanation:

To raise a negative number to an odd-numbered power, raise its absolute value to that power, then make the sign negative:

$\left ( -7\right )^{5} = - \left ( 7^{5}\right ) = -(7 \times 7 \times 7 \times 7 \times 7) = - 16,807$

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Example Question #345 : Arithmetic

One euro is worth approximately $1.27. For how much American money can a French tourist expect to exchange 800 euros?

Possible Answers:

$\$62.99$

$\$1,016$

The correct answer is not given among the other choices.

$\$629.92$

$\$10,160$

Correct answer:

$\$1,016$

Explanation:

One Euro is equivalent to $1.27, so multiply the number of euros - 800 - by this conversion factor.

$\$1.27 \times 800 = \$ 1,016$

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Example Question #1676 : Ssat Middle Level Quantitative (Math)

Evaluate:

$\left (20 - 7.5 \right )\times 3 - 1.2$

Possible Answers:

36.3

- 3.7

-1.3

6.5

22.5

Correct answer:

36.3

Explanation:

By the order of operations, carry out the operation in parentheses, which is the leftmost subtraction, then the multiplication, then the rightmost subtraction:

$\left (20 - 7.5 \right )\times 3 - 1.2$

$= 12.5 \times 3 - 1.2$

= 37.5 - 1.2

= 36.3

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Example Question #1016 : Numbers And Operations

Evaluate:

$20 - 7.5 \times\left ( 3 - 1.2 \right )$

Possible Answers:

-1.3

22.5

36.3

- 3.7

6.5

Correct answer:

6.5

Explanation:

By the order of operations, carry out the operation in parentheses, which is the rightmost subtraction, then the multiplication, then the leftmost subtraction:

$20 - 7.5 \times\left ( 3 - 1.2 \right )$

$= 20 - 7.5 \times 1.8$

= 20 - 13.5

= 6.5

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Example Question #3 : Multiplicative Identity Property

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

Possible Answers:

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

$\frac{2}{3} \times \frac{5}{7} = \frac{5}{7} \times \frac{2}{3}$

$\frac{2}{3} \times 1 = \frac{2}{3}$

$\frac{2}{3} \times \frac{3}{2} = 1$

$\left (\frac{2}{3} \times \frac{5}{7} \right ) \times \frac{6}{11} = \frac{2}{3} \times\left ( \frac{5}{7} \times \frac{6}{11} \right )$

Correct answer:

$\frac{2}{3} \times 1 = \frac{2}{3}$

Explanation:

The identity property of multiplication states that there is a number 1, called the multiplicative identity, that can be multiplied by any number to obtain that number. Of the four statements,

$\frac{2}{3} \times 1 = \frac{2}{3}$

demonstrates this property.

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Example Question #942 : Hspt Mathematics

is larger than 0. Which of the following could be equal to $3 \times Z$ ?

II. $2\frac{2}{7}$

III.

Possible Answers:

I, II and III

II only

III only

I and II

I only

Correct answer:

I, II and III

Explanation:

All of the answers can be divided by 3 to yield an answer larger than zero. In fact, any positive number would be a viable answer.

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Example Question #943 : Hspt Mathematics

Express the quotient as a fraction in lowest terms:

$5 \frac{3}{5} \div 4 \frac{1}{5}$

Possible Answers:

$1 \frac{1}{4}$

$\frac{4}{5}$

$1 \frac{1}{3}$

$1 \frac{3}{4}$

$\frac{3}{4}$

Correct answer:

$1 \frac{1}{3}$

Explanation:

Rewrite the mixed fractions as improper fractions, change to a multiplication by inverting the second, cross-cancel, and multiply across:

$5 \frac{3}{5} \div 4 \frac{1}{5} = \frac{28}{5 } \div \frac{21}{5 } = \frac{28}{5 } \cdot \frac{5}{21 }= \frac{4}{1 } \cdot \frac{1}{3 }= \frac{4}{3 }$

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Example Question #944 : Hspt Mathematics

Express the quotient as a fraction in lowest terms:

$4 \frac{1}{5} \div 5 \frac{3}{5}$

Possible Answers:

$\frac{5}{7}$

$\frac{6}{7}$

$1 \frac{1}{4}$

$\frac{3}{4}$

$1 \frac{1}{3}$

Correct answer:

$\frac{3}{4}$

Explanation:

Rewrite the mixed fractions as improper fractions, change to a multiplication by inverting the second, cross-cancel, and multiply across:

$4 \frac{1}{5} \div 5 \frac{3}{5} = \frac{21}{5} \div \frac{28}{5} = \frac{21}{5} \cdot \frac{5}{28} = \frac{3}{1} \cdot \frac{1}{4} = \frac{3}{4}$

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Example Question #945 : Hspt Mathematics

Evaluate:

$\frac{12}{5} \div \frac{4}{25}$

Possible Answers:

$\frac{1}{15}$

$\frac{5}{3}$

$\frac{3}{5}$

$\frac{8}{25}$

Correct answer:

Explanation:

Multiply by the reciprocal, cross-cancel, then multiply numerators and denominators:

$\frac{12}{5} \div \frac{4}{25} = \frac{12}{5} \times \frac{25}{4} = \frac{3}{1} \times \frac{5}{1} = \frac{15}{1} = 15$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #941 : Hspt Mathematics

Example Question #344 : Arithmetic

Example Question #345 : Arithmetic

Example Question #1676 : Ssat Middle Level Quantitative (Math)

Example Question #1016 : Numbers And Operations

Example Question #3 : Multiplicative Identity Property

Example Question #942 : Hspt Mathematics

Example Question #943 : Hspt Mathematics

Example Question #944 : Hspt Mathematics

Example Question #945 : Hspt Mathematics

All HSPT Math Resources

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