How to multiply fractions - ISEE Middle Level Math

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Question

Evaluate:

$-3.6 \cdot (-0.07)$

Answer

The product of two negative numbers is the (positive) product of theie absolute values.

$-3.6 \cdot (-0.07) = +(3.6 \cdot 0.07) = 3.6 \cdot 0.07$

There are a total of three digits to the right of the two decimal points. Therefore, the product can be calculated by multiplying 36 by 7, then placing the decimal point so that there are three digits at right.

$36 \cdot 7 = 252 \Rightarrow 3.6 \cdot 0.07 = 0.252$

This is the correct choice.

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Question

Solve:

$\frac{2}{5}\times\frac{7}{8}=$

Answer

$\frac{2}{5}\times\frac{7}{8}=\frac{2\times7}{5\times8}=\frac{14}{40}=\frac{7}{20}$

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Question

Multiply:

$4.3 \times 3.7$

Answer

First, multiply the numbers, ignoring the decimal points:

$43 \times 37 = 1591$

Since the two factors in the original product have two digits to the right of the decimal points between them, position the decimal point in the product such that two digits are at its right. The result, therefore, is

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Question

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

Answer

Multiply the numerators and then denominators:

$\frac{2}{5}* \frac{2}{5}=\frac{4}{25}$

Answer:

$\frac{4}{25}$

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Question

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

Answer

Multiply the numerators then denominators:

$\frac{4}{5}* \frac{2}{3}=\frac{8}{15}$

Answer: $\frac{8}{15}$

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Question

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

Answer

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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Question

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

Answer

Multiply the numerators and the denominators:

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

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

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Question

Simplify

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

Answer

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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Question

What is the simplest form of the result:

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

Answer

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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Question

Solve:

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

Answer

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

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Question

Solve:

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

Answer

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

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Question

Multiply the fractions:

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

Answer

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

$\frac{2}{4}\frac{5}{7}=\frac{25}{4*7}=\frac{10}{28}$

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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Question

Solve for y:

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

Answer

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

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

Next, we divide each side by 12.

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

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Question

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?

Answer

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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Question

Solve for in this equation:

$\frac{2}{3x}=\frac{9}{5}$

Answer

To solve for , we need to cross multiply.

$\frac{2}{3x}=\frac{9}{5}$

$2\times5=9\times3x$

Divide both sides by 27 to isolate the variable.

$\frac{10}{27}=x$

The fraction cannot be reduced, making this our final answer.

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Question

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)?

Answer

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

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

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Question

Evaluate:

$20 - 7.5 \times 3 - 1.2$

Answer

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

$20 - 7.5 \times 3 - 1.2$

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

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Question

Evaluate:

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

Answer

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:

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

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

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

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

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Question

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

Answer

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:

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

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Question

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

Answer

To raise a negative number to an odd-numbered power, raise its absolute value to that power, then make the sign negative. Also, to raise a fraction to a power, raise its numerator and its denominator to that power. Combine these ideas as follows:

$\left (- \frac{3}{2} \right )^{5} = - \left ( \frac{3}{2}\right )^{5} = - \left ( \frac{3^{5}} {2^{5}} \right ) = - \left ( \frac{3 \times 3 \times 3\times 3 \times 3 }{2\times 2 \times 2 \times 2 \times 2 } \right ) = -\frac{243}{32}$

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