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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 #891 : Hspt Mathematics

$\frac{1}{6}* \frac{1}{6}=$

Possible Answers:

$\frac{1}{6}$

$\frac{1}{36}$

$\frac{1}{12}$

$\frac{2}{12}$

Correct answer:

$\frac{1}{36}$

Explanation:

Multiply the numerators and the denominators:

$\frac{1}{6}*\frac{1}{6}=\frac{1}{36}$

Answer: $\frac{1}{36}$

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Example Question #892 : Hspt Mathematics

What is the simplest form of the result:

$\frac{1}{x^3}\times \frac{3x}{2x^2}\times \frac{4x^4}{3}$

Possible Answers:

$\frac{2}{x}$

Correct answer:

Explanation:

In order to multiply fractions, we can simply multiply straight across:

$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$

So we can write:

$\frac{1}{x^3}\times \frac{3x}{2x^2}\times \frac{4x^4}{3}=\frac{1\times 3x\times 4x^4}{x^3\times 2x^2\times 3}$

$\frac{12x^5}{6x^5}=\frac{12}{6}=2$

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Example Question #893 : Hspt Mathematics

Simplify

$\frac{3}{5}\times \frac{2}{6}\times \frac{3}{7}$

Possible Answers:

$\frac{1}{12}$

$\frac{24}{35}$

$\frac{3}{35}$

$\frac{4}{35}$

$\frac{6}{35}$

Correct answer:

$\frac{3}{35}$

Explanation:

In order to multiply fractions, we can simply multiply straight across:

$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$

So we can write:

$\frac{3}{5}\times \frac{2}{6}\times \frac{3}{7}=\frac{3\times 2\times 3}{5\times 6\times 7}$

$=\frac{18}{210}$

Divide it by the least common factor (i.e. 6) to simplify:

$\frac{18}{210}=\frac{3}{35}$

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Example Question #894 : Hspt Mathematics

$\frac{1}{4}\times \frac{2}{6}-\frac{1}{8}=?$

Possible Answers:

$-\frac{1}{24}$

$\frac{2}{17}$

$\frac{45}{24}$

$\frac{1}{4}$

$\frac{1}{24}$

Correct answer:

$-\frac{1}{24}$

Explanation:

In this problem we need to follow our order of operations; in this case we need to multiply before we subtract fractions.

To multiply fractions we just need to multiply the numerator by the numerator and the denominator by the denominator. In this case $1\times 2$ (the numerators of the fractions being multiplied) and $4\times 6$ (the denominators) giving us

$\frac{2}{24}$

We then rewrite our equation.

$\frac{2}{24}-\frac{1}{8}=?$

In order to subtract fractions, we must have a common denominator. To do this we need to find a common multiple of 24 and 8. In this case, the 8 nicely goes into 24 three times, so we will only need to multiply one of our fractions to have common denominators.

To do this we must multiply one-eighth three times like this...

$\frac{3}{3}\left(-\frac{1}{8}\right)=-\frac{3}{24}$

Remember that if you are multiplying a fraction, you must multiply both the numerator and the denominator in order to obtain a multiple of your original factor.

Lastly subtract.

$\frac{2}{24}-\frac{3}{24}=-\frac{1}{24}$

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Example Question #895 : Hspt Mathematics

Solve:

$\frac{2}{5}\times \frac{3}4=$

Possible Answers:

$\frac{5}{9}$

$\frac{8}{15}$

$\frac{3}{10}$

$\frac{6}{5}$

Correct answer:

$\frac{3}{10}$

Explanation:

$\frac{2}{5}\times \frac{3}{4}=\frac{2\times3}{5\times4}=\frac{6}{20}=\frac{3}{10}$

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Example Question #896 : Hspt Mathematics

Multiply the fractions:

$\frac{2}{4}*\frac{5}{7}=$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{5}$

$\frac{5}{14}$

Correct answer:

$\frac{5}{14}$

Explanation:

To multiply fractions, multiply both numerators on top and both denominators on the bottom.

$\frac{2}{4}*\frac{5}{7}=\frac{2*5}{4*7}=\frac{10}{28}$

Then, reduce to simplest form by removing any common factors:

$\frac{10}{28}=\frac{10\div2}{28\div2}=\frac{5}{14}$

Answer: $\frac{5}{14}$

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Example Question #897 : Hspt Mathematics

Solve:

$\small \frac{3}{10}\times \frac{16}{15}=$

Possible Answers:

$\small \frac{8}{25}$

$\small \small \frac{9}{32}$

$\small \frac{19}{25}$

$\small \frac{41}{30}$

$\frac{19}{150}$

Correct answer:

$\small \frac{8}{25}$

Explanation:

$\small \frac{3}{10}\times \frac{16}{15}=\frac{48}{150}=\frac{8}{25}$

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Example Question #898 : Hspt Mathematics

Solve for y:

$\frac{3}{2y}=\frac{6}{x}$

Possible Answers:

$\frac{x}{4}$

$\frac{1}{2}$

$\frac{x}{3}$

Correct answer:

$\frac{x}{4}$

Explanation:

In order to solve for y, cross multiplication must be used. Appyling cross multiplication, we get:

$\frac{3}{2y}=\frac{6}{x}$

12y=3x

Next, we divide each side by 12.

This results in $y=\frac{x}{4}$

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Example Question #305 : Arithmetic

On Monday, Marsha saw a sweater that she wanted to buy. It was 15 dollars. She went back the next day and saw that it was only 10 dollars. Which of the following is a sale that the store could have been running, explaining the reduced price on the sweater?

Possible Answers:

percent off

$\frac{2}{5}$ off

$\frac{1}{3}$ off

percent off

Correct answer:

$\frac{1}{3}$ off

Explanation:

Given that the sweater's price was reduced by 5 dollars, this is a one third reduction because one third of 15 dollars is 5 dollars. 15 dollars minus 5 dollars is equal to 10 dollars.

Thus, the correct answer is:

$\frac{1}{3}$ off

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Example Question #899 : Hspt Mathematics

$\frac{4^{^{2}}+\left ( 12-4 \right )}{2}$

Possible Answers:

Correct answer:

Explanation:

In order to solve:

First, solve the exponent equation within the numerator portion of the fraction:

$\small \small \frac{4^{2} + \left ( 12-4 \right )}{2}=$

Then, solve the equation within the parentheses:

$\small \small \frac{16+8}{2}=$

Then, solve the entire equation in the numerator portion and divide the numerator by the denominator.

$\small \small \frac{24}{2}=12$

Answer: 12

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #891 : Hspt Mathematics

Example Question #892 : Hspt Mathematics

Example Question #893 : Hspt Mathematics

Example Question #894 : Hspt Mathematics

Example Question #895 : Hspt Mathematics

Example Question #896 : Hspt Mathematics

Example Question #897 : Hspt Mathematics

Example Question #898 : Hspt Mathematics

Example Question #305 : Arithmetic

Example Question #899 : Hspt Mathematics

All HSPT Math Resources

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