Multiplying and Dividing Fractions - Algebra 2

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Question

Simplify $\frac{3}{6}$\cdot$\frac{12}{4}$ .

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Answer

The problem can be made easier by first simplifying each fraction: $\frac{3}{6}$=\frac{1}{2}$ and $\frac{12}{4}$=\frac{3}{1}$ .

This brings our new problem to $\frac{1}{2}$\cdot$\frac{3}{1}$ .

Now, the numerators are multiplied by each other then the denomenators are multiplied by each other: $\frac{1\cdot3}{2\cdot1}$=\frac{3}{2}$ .

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Question

Simplify $\frac{5}{3}$\div$\frac{7}{6}$ .

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Answer

To solve, we must turn the division problem into a multiplication problem by "flipping" the second fraction (dividing by a fraction is the same as multiplying by its reciprocal):

$\frac{5}{3}$\div$\frac{7}{6}$=\frac{5}{3}$\cdot$\frac{6}{7}$ .

Then, we multiply the numerators followed by the denomenators:

$\frac{5\cdot6}{3\cdot7}$=\frac{30}{21}$ .

Lastly, the fraction must be simplified by a factor of 3:

$\frac{30}{21}$=\frac{10}{7}$ , which gives us our final answer.

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Question

Solve the following equation to find .

$\frac{2}{3}$x=\frac{4}{15}$+\frac{3}{15}$

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Answer

The first step in solving this equation is to add the fractions, giving us:

$\frac{2}{3}$x=\frac{7}{15}$

To solve for , we need to divide both sides by $\frac{2}{3}$ .

Remember: When we divide a number by a fraction, we "switch" (find the reciprocal) of the fraction and mulitply it to the number.

$\bigg($\frac{3}{2}$\bigg)\bigg($\frac{2}{3}$\bigg)x=\bigg($\frac{7}{15}$\bigg) \bigg($\frac{3}{2}$\bigg)$

The right side of the equation cancels out leaving alone:

$x=\frac{7\times 3}{15\times 2}$=\frac{21}{30}$$

Notice: Both the numerator and denominator are divisble by so we can simplify this further.

$x=\frac{7}{10}$$

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Question

Multiply:

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Answer

To multiply fractions, just multiply the numerators, then the denominators, and then simplify.

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Question

Multiply:

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Answer

To multiply fractions, multiply the numerators and denominators together, then simplify.

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Question

Multiply:

$\left($\frac{4}{5}$x\right)\cdot \left($\frac{6}{13}$y\right)$

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Answer

Multiply the numerators and denominators. Then, simplify.

$($\frac{4}{5}$x)($\frac{6}{13}$y)=($\frac{4x}{5}$)($\frac{6y}{13}$)=\frac{24xy}{65}$$

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Question

Multiply:

$\left($\frac{15}{7x}$\right)\cdot $\left($\frac{12x^2$}{5}\right)$

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Answer

Multiply the numerators and denominators, then simplify.

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Question

Simplify:

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Answer

In order to divide fractions, you need to multiply the first fraction by the reciprocal of the second one.

Now, multiply the numerators and denominators together, then simplify.

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Question

Simplify:

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Answer

To divid fractions, you need to multiply the first fraction by the reciprocal of the second.

Now, multiply the numerators and denominators together, then simplify.

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Question

Simplify:

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Answer

To divide fractions, you need to multiply the first fraction by the reciprocal of the second.

Now, multiply the numerators and denominators, then simplify.

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Question

Evaluate: $\frac{7}{6}$\div 2$\frac{3}{8}$

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Answer

Change all the fractions to improper fractions.

$\frac{7}{6}$\div 2$\frac{3}{8}$=\frac{7}{6}$\div $\frac{19}{8}$

Convert the division sign to a multiplication sign, but flip the second term. Simplify.

$\frac{7}{6}$\times $\frac{8}{19}$= $\frac{7}{3}$\times $\frac{4}{19}$= $\frac{28}{57}$

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Question

Divide and simplify:

$\frac{2}{11}$\div $\frac{9}{22}$ .

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Answer

Multiplying fractions is a two-step process. First, you must flip the second fraction (make it its reciprocal) and then set up the equation as a multiplication problem:

$$\frac{2}{11}$\cdot $\frac{22}${}9$ .

Then, cross-reduce: 11 goes into both 11 and 22, so you can take that out so it looks like:

$\frac{2}{1}$\cdot $\frac{2}{9}$ .

Then, multiply straight across so that you get $$\frac{4}${}9$ .

You can't simplify any further, so that's your answer!

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Question

Multiply and simplify:

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Answer

Before multiplying straight across, I would start with some cross-reducing. Look diagonally and see what can be simplified.

Between and , you can take out a

Between and , you can take out a .

The simplified version looks like:

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Question

Multiply these fractions:

$\frac{5}{12}$*$\frac{3}{7}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{5}{12}$$\frac{3}{7}$=\frac{53}{12*7}$=\frac{15}{84}$

Simply the fraction to get the final answer:

$\frac{15}{84}$\div $\frac{3}{3}$=\frac{5}{28}$

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Question

Multiply these fractions:

$\frac{7}{9}$*$\frac{1}{14}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{7}{9}$$\frac{1}{14}$=\frac{71}{9*14}$=\frac{7}{126}$

Simply the fraction to get the final answer:

$\frac{7}{126}$\div $\frac{7}{7}$=\frac{1}{18}$

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Question

Multiply these fractions:

$\frac{2}{3}$*$\frac{5}{6}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{2}{3}$$\frac{5}{6}$=\frac{25}{3*6}$=\frac{10}{18}$

Simply the fraction to get the final answer:

$\frac{10}{18}$\div $\frac{2}{2}$=\frac{5}{9}$

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Question

Multiply these fractions:

$\frac{1}{2}$*$\frac{2}{3}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{1}{2}$$\frac{2}{3}$=\frac{12}{2*3}$=\frac{2}{6}$

Simply the fraction to get the final answer:

$\frac{2}{6}$\div $\frac{2}{2}$=\frac{1}{3}$

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Question

Multiply these fractions:

$\frac{5}{7}$*$\frac{1}{3}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{5}{7}$$\frac{1}{3}$=\frac{51}{7*3}$=\frac{5}{21}$

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Question

Multiply these fractions:

$\frac{4}{9}$*$\frac{3}{7}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{4}{9}$$\frac{3}{7}$=\frac{43}{9*7}$=\frac{12}{63}$

Simply the fraction to get the final answer:

$\frac{12}{63}$\div $\frac{3}{3}$=\frac{4}{21}$

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Question

Multiply these fractions:

$\frac{8}{9}$*$\frac{3}{4}$

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Answer

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{8}{9}$$\frac{3}{4}$=\frac{83}{9*4}$=\frac{24}{36}$

Simplify the fraction to get the final answer:

$\frac{24}{36}$\div $\frac{6}{6}$=\frac{4}{6}$\div $\frac{2}{2}$=\frac{2}{3}$

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