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HSPT Math : Arithmetic

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Example Questions

Example Question #301 : Arithmetic

Solve:

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

Possible Answers:

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

$\frac{5}{9}$ $\displaystyle \frac{5}{9}$

$\frac{8}{15}$ $\displaystyle \frac{8}{15}$

$\frac{6}{5}$ $\displaystyle \frac{6}{5}$

Correct answer:

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

Explanation:

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

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Example Question #302 : Arithmetic

Multiply the fractions:

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

Possible Answers:

$\displaystyle 10$

$\displaystyle 28$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

Correct answer:

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

Explanation:

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

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

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

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

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

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Example Question #303 : Arithmetic

Solve:

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

Possible Answers:

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

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

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

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

$\frac{19}{150}$ $\displaystyle \frac{19}{150}$

Correct answer:

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

Explanation:

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

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Example Question #304 : Arithmetic

Solve for y:

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

Possible Answers:

$\frac{x}{4}$ $\displaystyle \frac{x}{4}$

$\displaystyle 4$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{x}{3}$ $\displaystyle \frac{x}{3}$

Correct answer:

$\frac{x}{4}$ $\displaystyle \frac{x}{4}$

Explanation:

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

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

12y=3x $\displaystyle 12y=3x$

Next, we divide each side by 12.

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

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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:

$\displaystyle 50$ percent off

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$ off

$\displaystyle 30$ percent off

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$ off

Correct answer:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$ 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:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$ off

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Example Question #1401 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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

Possible Answers:

$\displaystyle 12$

$\displaystyle 36$

$\displaystyle 16$

$\displaystyle 8$

$\displaystyle 0$

Correct answer:

$\displaystyle 12$

Explanation:

In order to solve:

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

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

Then, solve the equation within the parentheses:

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

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

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

Answer: 12

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Example Question #511 : Numbers And Operations

$\small 2 \frac{1}{5} \div 1 \frac{2}{4}=$ $\displaystyle \small 2 \frac{1}{5} \div 1 \frac{2}{4}=$

Possible Answers:

$\small 3 \frac{3}{10}$ $\displaystyle \small 3 \frac{3}{10}$

$\small 2 \frac{1}{10}$ $\displaystyle \small 2 \frac{1}{10}$

$\small 4$ $\displaystyle \small 4$

$\small 1 \frac{7}{15}$ $\displaystyle \small 1 \frac{7}{15}$

Correct answer:

$\small 1 \frac{7}{15}$ $\displaystyle \small 1 \frac{7}{15}$

Explanation:

To solve:

First, turn the mixed fractions into improper fractions.

$\small \small \small \frac{11}{5}\div \frac{6}{4}=$ $\displaystyle \small \small \small \frac{11}{5}\div \frac{6}{4}=$

Then, change the operation to multiplication and flip the second fraction. Solve accordingly and simplify the answer if possible.

$\small \small \frac{11}{5}\cdot \frac{4}{6}=$ $\displaystyle \small \small \frac{11}{5}\cdot \frac{4}{6}=$

The answer is $\small 1\frac{7}{15}$ $\displaystyle \small 1\frac{7}{15}$.

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Example Question #511 : Numbers And Operations

What is $\frac{3}{5}$ $\displaystyle \frac{3}{5}$ divided by $\frac{3}{25}$ $\displaystyle \frac{3}{25}$?

Possible Answers:

$\displaystyle 5$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\displaystyle 3$

$\displaystyle 15$

Correct answer:

$\displaystyle 5$

Explanation:

$\frac{3}{5}\div\frac{3}{25}=\frac{3}{5}\cdo*\frac{25}{3}=5$ $\displaystyle \frac{3}{5}\div\frac{3}{25}=\frac{3}{5}\cdo*\frac{25}{3}=5$

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Example Question #1 : How To Divide Fractions

Evaluate:

$\frac{\frac{2}{7}}{\frac{9}{14}}$ $\displaystyle \frac{\frac{2}{7}}{\frac{9}{14}}$

Possible Answers:

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

$\frac{49}{9}$ $\displaystyle \frac{49}{9}$

$\frac{9}{4}$ $\displaystyle \frac{9}{4}$

$\frac{13}{14}$ $\displaystyle \frac{13}{14}$

$\frac{9}{4 9}$ $\displaystyle \frac{9}{4 9}$

Correct answer:

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

Explanation:

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and multply across:

$\frac{\frac{2}{7}}{\frac{9}{14}}$ $\displaystyle \frac{\frac{2}{7}}{\frac{9}{14}}$ $= \frac{2}{7} \div \frac{9}{14} = \frac{2}{7} \cdot \frac{14}{9} = \frac{2}{1} \cdot \frac{2}{9} = \frac{2\cdot 2}{1\cdot 9} =\frac{4}{9}$ $\displaystyle = \frac{2}{7} \div \frac{9}{14} = \frac{2}{7} \cdot \frac{14}{9} = \frac{2}{1} \cdot \frac{2}{9} = \frac{2\cdot 2}{1\cdot 9} =\frac{4}{9}$

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Example Question #306 : Arithmetic

$\frac{2}{5}\div 2\frac{3}{5}=$ $\displaystyle \frac{2}{5}\div 2\frac{3}{5}=$

Possible Answers:

$\frac{2}{13}$ $\displaystyle \frac{2}{13}$

$\frac{13}{2}$ $\displaystyle \frac{13}{2}$

$1\frac{1}{25}$ $\displaystyle 1\frac{1}{25}$

$2\frac{6}{25}$ $\displaystyle 2\frac{6}{25}$

Correct answer:

$\frac{2}{13}$ $\displaystyle \frac{2}{13}$

Explanation:

First, convert each fraction into an improper fraction

$\frac{2}{5}\div 2\frac{3}{5}=\frac{2}{5}\div \frac{13}{5}=$ $\displaystyle \frac{2}{5}\div 2\frac{3}{5}=\frac{2}{5}\div \frac{13}{5}=$

Then, change the operation to mulitplication and flip the second fraction:

$\frac{2}{5}*\frac{5}{13}=$ $\displaystyle \frac{2}{5}*\frac{5}{13}=$

Reduce and solve accordingly:

Answer: $\frac{2}{13}$ $\displaystyle \frac{2}{13}$

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HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #301 : Arithmetic

Example Question #302 : Arithmetic

Example Question #303 : Arithmetic

Example Question #304 : Arithmetic

Example Question #305 : Arithmetic

Example Question #1401 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #511 : Numbers And Operations

Example Question #511 : Numbers And Operations

Example Question #1 : How To Divide Fractions

Example Question #306 : Arithmetic

All HSPT Math Resources

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