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ISEE Middle Level Math : How to multiply fractions

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Example Questions

Example Question #11 : How To Multiply Fractions

Multiply the fractions:

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

Possible Answers:

$\displaystyle 10$

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

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

$\displaystyle 28$

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

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 #341 : Numbers And Operations

Solve:

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

Possible Answers:

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

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

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

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

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

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 #342 : Numbers And Operations

Solve for y:

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

Possible Answers:

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

$\displaystyle 4$

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

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

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 #343 : Numbers And Operations

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

$\displaystyle 30$ percent off

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

$\frac{2}{5}$ $\displaystyle \frac{2}{5}$ 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 #344 : Numbers And Operations

One dollar is equal to about 116.76 Japanese yen. For how many yen should a tourist to Japan be able to exchange $3,000 at that rate (nearest whole yen)?

Possible Answers:

$257\textrm{ yen}$ $\displaystyle 257\textrm{ yen}$

$26\textrm{ yen}$ $\displaystyle 26\textrm{ yen}$

$35,028 \textrm{ yen }$ $\displaystyle 35,028 \textrm{ yen }$

$350,280 \textrm{ yen }$ $\displaystyle 350,280 \textrm{ yen }$

$3,503 \textrm{ yen }$ $\displaystyle 3,503 \textrm{ yen }$

Correct answer:

$350,280 \textrm{ yen }$ $\displaystyle 350,280 \textrm{ yen }$

Explanation:

One dollar is equal to 116.76 yen, so multiply $3,000 by this conversion rate to get

$3,000 \times 116.76 = 350,280$ $\displaystyle 3,000 \times 116.76 = 350,280$ yen.

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Example Question #16 : How To Multiply Fractions

Evaluate:

$20 - 7.5 \times 3 - 1.2$ $\displaystyle 20 - 7.5 \times 3 - 1.2$

Possible Answers:

- 3.7 $\displaystyle - 3.7$

6.5 $\displaystyle 6.5$

-1.3 $\displaystyle -1.3$

22.5 $\displaystyle 22.5$

36.3 $\displaystyle 36.3$

Correct answer:

- 3.7 $\displaystyle - 3.7$

Explanation:

By the order of operations, carry out the multiplication first, then the leftmost subtraction, then the rightmost subtraction:

$20 - 7.5 \times 3 - 1.2$ $\displaystyle 20 - 7.5 \times 3 - 1.2$

$\displaystyle = 20 - 22.5 - 1.2$

$\displaystyle = - 2.5 - 1.2$

$= - 2.5 + \left ( - 1.2 \right )$ $\displaystyle = - 2.5 + \left ( - 1.2 \right )$

= - 3.7 $\displaystyle = - 3.7$

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Example Question #11 : How To Multiply Fractions

Raise $\displaystyle -4$ to the fifth power.

Possible Answers:

625 $\displaystyle 625$

$\displaystyle -4$ cannot be raised to the fifth power.

-1,024 $\displaystyle -1,024$

$\displaystyle -625$

1,024 $\displaystyle 1,024$

Correct answer:

-1,024 $\displaystyle -1,024$

Explanation:

To raise a negative number to an odd-numbered power, raise its absolute value to that power, then make the sign negative:

$\left ( -4 \right ) ^{5 } = - \left ( 4^{5}\right ) = - \left ( 4 \times 4 \times 4 \times 4 \times 4\right ) = -1,024$ $\displaystyle \left ( -4 \right ) ^{5 } = - \left ( 4^{5}\right ) = - \left ( 4 \times 4 \times 4 \times 4 \times 4\right ) = -1,024$

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Example Question #12 : How To Multiply Fractions

Raise $\displaystyle -6$ to the fourth power.

Possible Answers:

$\displaystyle -24$

-1,296 $\displaystyle -1,296$

1,296 $\displaystyle 1,296$

-4,096 $\displaystyle -4,096$

4,096 $\displaystyle 4,096$

Correct answer:

1,296 $\displaystyle 1,296$

Explanation:

To raise a negative number to an even-numbered power, raise its absolute value to that power:

$\left ( -6 \right )^{4} = 6 ^{4} = 6 \times 6 \times 6 \times 6 = 1,296$ $\displaystyle \left ( -6 \right )^{4} = 6 ^{4} = 6 \times 6 \times 6 \times 6 = 1,296$

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Example Question #204 : Fractions

Evaluate:

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

Possible Answers:

$13\frac{1}{3}$ $\displaystyle 13\frac{1}{3}$

$18\frac{1}{3}$ $\displaystyle 18\frac{1}{3}$

$44\frac{1}{3}$ $\displaystyle 44\frac{1}{3}$

$12\frac{1}{9}$ $\displaystyle 12\frac{1}{9}$

$11 \frac{2}{3}$ $\displaystyle 11 \frac{2}{3}$

Correct answer:

$11 \frac{2}{3}$ $\displaystyle 11 \frac{2}{3}$

Explanation:

By the order of operations, carry out the operations in parentheses first; since there is a multiplication and an addition present, carry them out in that order. Finally, carry out the subtraction:

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

$= 15 - \left ( 2+ \frac{4}{3}\right )$ $\displaystyle = 15 - \left ( 2+ \frac{4}{3}\right )$

$= 15 - \frac{10}{3}$ $\displaystyle = 15 - \frac{10}{3}$

$= 11 \frac{2}{3}$ $\displaystyle = 11 \frac{2}{3}$

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Example Question #13 : How To Multiply Fractions

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

Possible Answers:

$\frac{16} {81}$ $\displaystyle \frac{16} {81}$

$- \frac{8}{3}$ $\displaystyle - \frac{8}{3}$

$\frac{16}{81}$ $\displaystyle \frac{16}{81}$

$\frac{81}{16}$ $\displaystyle \frac{81}{16}$

$- \frac{16}{81}$ $\displaystyle - \frac{16}{81}$

Correct answer:

$\frac{16}{81}$ $\displaystyle \frac{16}{81}$

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:

$\left (- \frac{2}{3} \right )^{4} = \left( \frac{2}{3} \right )^{4} = \frac{2^{4} }{3^{4} } = \frac{ 2 \times 2 \times 2 \times 2 }{ 3 \times 3\times 3 \times 3 } \right ) = \frac{16}{81}$ $\displaystyle \left (- \frac{2}{3} \right )^{4} = \left( \frac{2}{3} \right )^{4} = \frac{2^{4} }{3^{4} } = \frac{ 2 \times 2 \times 2 \times 2 }{ 3 \times 3\times 3 \times 3 } \right ) = \frac{16}{81}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : How to multiply fractions

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #11 : How To Multiply Fractions

Example Question #341 : Numbers And Operations

Example Question #342 : Numbers And Operations

Example Question #343 : Numbers And Operations

Example Question #344 : Numbers And Operations

Example Question #16 : How To Multiply Fractions

Example Question #11 : How To Multiply Fractions

Example Question #12 : How To Multiply Fractions

Example Question #204 : Fractions

Example Question #13 : How To Multiply Fractions

All ISEE Middle Level Math Resources

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