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HSPT Math : Concepts

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 #371 : Arithmetic

$\frac{1}{2}\div\frac{3}{8}=$

Possible Answers:

$\frac{3}{4}$

$\frac{3}{16}$

$5\tfrac{1}{3}$

$\frac{1}{2}$

$1\tfrac{1}{3}$

Correct answer:

$1\tfrac{1}{3}$

Explanation:

When dividing fractions, first find the reciprocal of the second fraction and change the problem to multiplication:

$\frac{1}{2}\div\frac{3}{8}\rightarrow\frac{1}{2}\times\frac{8}{3}$

You then treat the problem like any other multiplication problem and multiply straight across.

$\frac{1}{2}\times\frac{8}{3}=\frac{8}{6}$

Since the numerator is larger than the denominator, we know our answer will be greater than 1.

$\frac{8}{6} \rightarrow 1\tfrac{2}{6}$

6 divides into 8 one time, with 2 remaining. The 2 remains on top of the 6 as the numerator. This answer can still be reduced; however, as 2 and 6 are both evenly divisible by 2.

$1\tfrac{2}{6}\rightarrow1\tfrac{1}{3}$

Your final answer is $1\tfrac{1}{3}$

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Example Question #372 : Arithmetic

$\dpi{100} \frac{\frac{1}{2}\times \frac{1}{3}}{\frac{1}{9}}=$

Possible Answers:

$\dpi{100} \frac{1}{9}$

$\dpi{100} \frac{2}{3}$

$\dpi{100} \frac{1}{54}$

$\dpi{100} \frac{3}{2}$

Correct answer:

$\dpi{100} \frac{3}{2}$

Explanation:

First multiply the fraction in the numerator.

$\dpi{100} \frac{1}{2}\times \frac{1}{3}=\frac{1\times 1}{2\times 3}=\frac{1}{6}$

Now we have $\dpi{100} \frac{\frac{1}{6}}{\frac{1}{9}}$

Never divide fractions. We multiply the numerator by the reciprocal of the denominator.

$\dpi{100} \frac{\frac{1}{6}}{\frac{1}{9}}=\frac{1}{6}\div \frac{1}{9}=\frac{1}{6}\times \frac{9}{1}=\frac{1\times 9}{6\times 1}=\frac{9}{6}=\frac{3}{2}$

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Example Question #373 : Arithmetic

Which of these expressions is the greatest?

Possible Answers:

Twenty percent of one fourth

Twenty-five percent of one fifth

One fourth of 0.2

All of these expressions are equivalent

One fifth of 0.25

Correct answer:

All of these expressions are equivalent

Explanation:

The easiest way to see that all four are equivalent is to convert each to a decimal product, noting that twenty percent and one-fifth are equal to 0.2 , and twenty-five percent and one fourth are equal to 0.25 .

One fourth of 0.2: $\frac{1}{4}*0.2=\frac{1}{4}*\frac{2}{10}=\frac{2}{40}=\frac{1}{20}$

One fifth of 0.25: $\frac{1}{5}*0.25=\frac{1}{5}*\frac{25}{100}=\frac{25}{500}=\frac{5}{100}=\frac{1}{20}$

Twenty-five percent of one fifth: $*\frac{1}{5}=\frac{25}{100}*\frac{1}{5}=\frac{25}{500}=\frac{1}{20}$

Twenty percent of one fourth: $*\frac{1}{4}=\frac{20}{100}*\frac{1}{4}=\frac{20}{400}=\frac{1}{20}$

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Example Question #1162 : Ssat Middle Level Quantitative (Math)

How many times does $\frac{1}{4}$ go into $\frac{3}{4}$ ?

Possible Answers:

121

Correct answer:

Explanation:

This problem can be solved by dividing $\frac{3}{4}$ by $\frac{1}{4}$ . First, simplify $\frac{3}{4}$ into $\frac{67}{4}$ , then divide by $\frac{1}{4}$ .

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Example Question #373 : Concepts

Solve: $\frac{3}{\frac{1}{9}+1}$

Possible Answers:

$\frac{27}{10}$

$\frac{10}{3}$

$\frac{17}{10}$

$\frac{4}{3}$

Correct answer:

$\frac{27}{10}$

Explanation:

Add the terms in denominator: $\frac{3}{\frac{1}{9}+1}$

$\frac{3}{\frac{1}{9}+1} = \frac{3}{\frac{1}{9}+\frac{9}{9}} = \frac{3}{\frac{10}{9}}$

Simplify the complex fraction.

$\frac{3}{\frac{10}{9}}= 3\div \frac{10}{9} = 3 \times \frac{9}{10} = \frac{27}{10}$

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Example Question #374 : Arithmetic

Which of the following is true of $\frac{17}{37}$ ?

Possible Answers:

$0.46<\frac{17}{37}< 0.47$

$0.48<\frac{17}{37}< 0.49$

$0.45 <\frac{17}{37}< 0.46$

$0.47<\frac{17}{37}< 0.48$

Correct answer:

$0.45 <\frac{17}{37}< 0.46$

Explanation:

Divide 17 by 37:

Division

The quotient falls between 0.45 and 0.46, so

$0.45 <\frac{17}{37}< 0.46$ .

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Example Question #375 : Arithmetic

$\frac{3}{7}$ is the square root of what number?

Possible Answers:

$\frac{9}{7}$

$\frac{6}{7}$

$\frac{9}{49}$

$\frac{3}{14}$

Correct answer:

$\frac{9}{49}$

Explanation:

The square root of a number is the number which, when squared - multiplied by itself - yields that number as its result. Therefore, $\frac{3}{7}$ is the square root of

$\frac{3}{7} \times \frac{3}{7} = \frac{3 \times 3 }{7 \times 7} = \frac{9}{49}$

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Example Question #83 : Fractions

Define an operation $\bigstar$ on the real numbers as follows:

$a \bigstar b = \frac{a-1}{b-2}$

Which of the following is an undefined quantity?

Possible Answers:

$3 \bigstar 0$

$2 \bigstar 1$

$1 \bigstar 4$

$3 \bigstar 2$

Correct answer:

$3 \bigstar 2$

Explanation:

$a \bigstar b = \frac{a-1}{b-2}$ ; since the divisor in a division expression cannot be equal to 0, it cannot hold that

b - 2 =0 , or

b= 2 .

In other words, $a \bigstar b$ is undefined if and only if b= 2 .

The only choice in which this holds is $3 \bigstar 2$ .

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Example Question #376 : Arithmetic

Which of the following is the square root of 0.36?

Possible Answers:

$\frac{18}{25}$

$\frac{9}{50}$

$\frac{3}{50}$

$\frac{3}{5}$

Correct answer:

$\frac{3}{5}$

Explanation:

$0.36 = \frac{36}{100} = \frac{36 \div 4}{100 \div 4} = \frac{9}{25}$

The square root of 0.36 is therefore the square root of $\frac{9}{25}$ . The square root of a fraction whose numerator and denominator are both perfect squares can be found as follows:

$\sqrt{\frac{9}{25} } = \frac{\sqrt{9}}{\sqrt{25}} = \frac{3}{5}$

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Example Question #377 : Arithmetic

Solve:

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

Possible Answers:

$\frac{34}{35}$

$\frac{5}{6}$

$\frac{6}{7}$

$\frac{32}{35}$

Correct answer:

$\frac{32}{35}$

Explanation:

To multiple fractions, you just multiply the numerators together and the denominators together.

This gives you

4*8=32 as a numerator

and

5*7=35 as a denominator.

Your final answer would be $\frac{32}{35}$ .

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All HSPT Math Resources

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #371 : Arithmetic

Example Question #372 : Arithmetic

Example Question #373 : Arithmetic

Example Question #1162 : Ssat Middle Level Quantitative (Math)

Example Question #373 : Concepts

Example Question #374 : Arithmetic

Example Question #375 : Arithmetic

Example Question #83 : Fractions

Example Question #376 : Arithmetic

Example Question #377 : Arithmetic

All HSPT Math Resources

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