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HSPT Math : Fractions

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #51 : Fractions

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

Possible Answers:

$\frac{5}{8}$

$\frac{5}{12}$

$\frac{12}{5}$

$\frac{4}{8}$

$\frac{4}{15}$

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 #8 : How To Multiply Fractions

What is the product of the two fractions below?

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

Possible Answers:

$\frac{7}{10}$

$\frac{6}{10}$

$\frac{14}{40}$

$\frac{10}{7}$

$\frac{27}{40}$

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 #52 : Fractions

Raise to the fourth power.

Possible Answers:

-4,096

65,536

-65,536

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 #342 : Concepts

Evaluate:

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

Possible Answers:

$13\frac{8}{9}$

$42\frac{2}{3}$

$14 \frac{1}{3}$

$11\frac{2}{3}$

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:

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

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

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

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

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

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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Example Question #51 : Fractions

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

Possible Answers:

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

$-\frac{32}{243}$

$\frac{32}{243}$

$\frac{243} {32}$

$-\frac{243} {32}$

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 #54 : Fractions

Raise to the fifth power.

Possible Answers:

-78,125

cannot be raised to the fifth power.

16,807

78,125

-16,807

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 #55 : Fractions

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

Possible Answers:

$\$62.99$

$\$10,160$

The correct answer is not given among the other choices.

$\$629.92$

$\$1,016$

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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HSPT Math : Fractions

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #51 : Fractions

Example Question #8 : How To Multiply Fractions

Example Question #52 : Fractions

Example Question #342 : Concepts

Example Question #1 : Multiplicative Inverse Property

Example Question #1011 : Numbers And Operations

Example Question #51 : Fractions

Example Question #54 : Fractions

Example Question #55 : Fractions

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

All HSPT Math Resources

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