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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 #361 : Concepts

Which of the following yields the largest number?

Possible Answers:

$\frac{1}{3}-\frac{1}{6}$

$\frac{1}{3}\div\frac{1}{6}$

$\frac{1}{3}+\frac{1}{6}$

$\frac{1}{3}\times\frac{1}{6}$

Correct answer:

$\frac{1}{3}\div\frac{1}{6}$

Explanation:

When dividing by a fraction between 0 and 1, the answer will always get larger. In this case it is larger than simply adding the two fractions together.

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Example Question #1153 : Ssat Middle Level Quantitative (Math)

Divide: $1.2 \div 64$

Possible Answers:

0.1875

0.00768

0.0768

0.001875

0.01875

Correct answer:

0.01875

Explanation:

Simply use the long division process. The quotient will be:

$12 \div 64 = 0.01875$

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Example Question #14 : How To Divide Fractions

Simplify:

$\frac{4\frac{1}{2} }{\frac{3}{10}}$

Possible Answers:

$1 \frac {4}{5}$

$\frac {5}{9}$

$\frac {1}{15}$

Correct answer:

Explanation:

Rewrite as a division and evaluate:

$\frac{4\frac{1}{2} }{\frac{3}{10}}$

$= 4\frac{1 }{2} \div \frac{3}{10}$

$= \frac{1 + 4 \times 2}{2} \div \frac{3}{10}$

$= \frac{9}{2} \div \frac{3}{10}= \frac{9}{2} \times \frac{10}{3}= \frac{3}{1} \times \frac{5}{1}= \frac{15}{1} = 15$

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Example Question #366 : Arithmetic

Simplify:

$\frac{5 \frac{1}{4}}{1 \frac{5}{9}}$

Possible Answers:

$8 \frac{1}{6}$

$3 \frac{3}{8}$

$\frac{6}{49}$

$\frac{8}{27}$

$5 \frac{9}{20}$

Correct answer:

$3 \frac{3}{8}$

Explanation:

Rewrite as a division, then solve:

$\frac{5 \frac{1}{4}}{1 \frac{5}{9}}$

$= 5 \frac{1}{4} \div 1 \frac{5}{9}$

$= \frac{1 + 5 \times 4}{4} \div \frac{5 + 1 \times 9}{9}$

$= \frac{21}{4} \div \frac{14}{9}$

$= \frac{21}{4} \times \frac{9}{14}$

$= \frac{3}{4} \times \frac{9}{2}$

$= \frac{3 \times 9}{4 \times 2} = \frac{27}{8} = 3 \frac{3}{8}$

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Example Question #491 : Numbers And Operations

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

Possible Answers:

$\frac{3}{4}$

$5\tfrac{1}{3}$

$\frac{1}{2}$

$1\tfrac{1}{3}$

$\frac{3}{16}$

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 #1101 : Ssat Upper Level Quantitative (Math)

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

Possible Answers:

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

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

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

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

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 #1 : How To Multiply

Which of these expressions is the greatest?

Possible Answers:

One fifth of 0.25

One fourth of 0.2

Twenty-five percent of one fifth

All of these expressions are equivalent

Twenty percent of one fourth

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 #372 : Concepts

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 #372 : Concepts

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

Possible Answers:

$\frac{17}{10}$

$\frac{27}{10}$

$\frac{10}{3}$

$\frac{4}{3}$

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 #371 : Concepts

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

Possible Answers:

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

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

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

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

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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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #361 : Concepts

Example Question #1153 : Ssat Middle Level Quantitative (Math)

Example Question #14 : How To Divide Fractions

Example Question #366 : Arithmetic

Example Question #491 : Numbers And Operations

Example Question #1101 : Ssat Upper Level Quantitative (Math)

Example Question #1 : How To Multiply

Example Question #372 : Concepts

Example Question #372 : Concepts

Example Question #371 : Concepts

All HSPT Math Resources

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