ISEE Middle Level Math : How to multiply fractions

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

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Example Questions

Example Question #21 : How To Multiply Fractions

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

Possible Answers:

\displaystyle \frac{32}{243}

\displaystyle \frac{243} {32}

\displaystyle -\frac{32}{243}

\displaystyle - \frac{3}{2} cannot be raised to the fifth power.

\displaystyle -\frac{243} {32}

Correct answer:

\displaystyle -\frac{243} {32}

Explanation:

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:

\displaystyle \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}

Example Question #22 : How To Multiply Fractions

Solve for \displaystyle x in this equation:

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

Possible Answers:

\displaystyle \frac{10}{27}

\displaystyle \frac{5}{27}

\displaystyle \frac{10}{29}

\displaystyle \frac{27}{10}

\displaystyle \frac{1}{3}

Correct answer:

\displaystyle \frac{10}{27}

Explanation:

To solve for \displaystyle x, we need to cross multiply.

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

\displaystyle 2\times5=9\times3x

\displaystyle 10=27x

Divide both sides by 27 to isolate the variable.

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

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

 

Example Question #21 : How To Multiply Fractions

Which of the answer choices is equal to \displaystyle \frac{63}{9}\cdot\frac{3}{2}?

Possible Answers:

\displaystyle 12

\displaystyle 11\frac{1}{2}

\displaystyle 10\frac{1}{2}

\displaystyle 10

Correct answer:

\displaystyle 10\frac{1}{2}

Explanation:

The expression, \displaystyle \frac{63}{9}\cdot\frac{3}{2} is equal to:

\displaystyle (63\div9)\cdot\frac{3}{2}

This is equal to:

\displaystyle 7\cdot \frac{3}{2}

This equals:

\displaystyle \frac{21}{2}=10\frac{1}{2}

Example Question #24 : How To Multiply Fractions

Find the product. 

\displaystyle \frac{2}{7}\times \frac{5}{9}

Possible Answers:

\displaystyle \frac{10}{63}

\displaystyle \frac{7}{16}

\displaystyle \frac{18}{35}

\displaystyle \frac{10}{42}

Correct answer:

\displaystyle \frac{10}{63}

Explanation:

To multiply fractions, simply multiply the first numerator by the second numerator and the first denominator by the second denominator.  Simply when necessary. 

\displaystyle 2\times5=10

\displaystyle 7\times9=63

\displaystyle \frac{2}{7}\times \frac{5}{9}=\frac{10}{63}

Example Question #25 : How To Multiply Fractions

What is \displaystyle \frac{1}{5} of \displaystyle \frac{7}{6}?

Possible Answers:

\displaystyle \frac{7}{30}

\displaystyle \frac{7}{6}

\displaystyle \frac{6}{30}

\displaystyle \frac{7}{5}

\displaystyle \frac{8}{11}

Correct answer:

\displaystyle \frac{7}{30}

Explanation:

To find the answer, you must multiple the fractions together.  

When multiplying fractions, all you have to do is multiple the numerators together and the denominators together.  

So 

\displaystyle 1*7=7 

and 

\displaystyle 5*6=30 

giving us 

\displaystyle \frac{7}{30}.

Example Question #21 : How To Multiply Fractions

\displaystyle \frac{6}{7}*\frac{1}{9}=x?

Possible Answers:

\displaystyle \frac{1}{10}

\displaystyle \frac{2}{21}

\displaystyle \frac{7}{18}

\displaystyle \frac{2}{3}

\displaystyle \frac{1}{11}

Correct answer:

\displaystyle \frac{2}{21}

Explanation:

To multiply fractions, you must multiple the numerators and denominators.  

So 

\displaystyle 6*1=6 

and 

\displaystyle 9*7=63.  

Your final answer is \displaystyle \frac{6}{63}=\frac{3\cdot 2}{3\cdot 21}=\frac{2}{21}.

Example Question #212 : Fractions

Solve for \displaystyle x

\displaystyle \frac{5}{6}*\frac{3}{4}=x

Possible Answers:

\displaystyle \frac{8}{10}

\displaystyle \frac{4}{5}

\displaystyle \frac{1}{3}

\displaystyle \frac{8}{24}

\displaystyle \frac{5}{8}

Correct answer:

\displaystyle \frac{5}{8}

Explanation:

To multiply fractions, you multiply the numerators

\displaystyle 5*3=15 

and multiply the denominators

\displaystyle 6*4=24 

to get,

 \displaystyle \frac{15}{24}.  

They each have a common factor of \displaystyle 3 so it reduces down to \displaystyle \frac{5}{8} by dividing each.

Example Question #361 : Numbers And Operations

Multiply the following:

\displaystyle \frac{2}{3} \cdot \frac{1}{3}

Possible Answers:

\displaystyle \frac{3}{6}

\displaystyle \frac{2}{9}

\displaystyle \frac{2}{3}

\displaystyle \frac{3}{3}

\displaystyle \frac{1}{3}

Correct answer:

\displaystyle \frac{2}{9}

Explanation:

When multiplying fractions, we will first multiply the numerators, then we will multiply the denominators.

So, given the fractions

\displaystyle \frac{2}{3} \cdot \frac{1}{3}

when multiplying, we will get

\displaystyle \frac{2}{3} \cdot \frac{1}{3} = \frac{2 \cdot 1}{3 \cdot 3}

\displaystyle \frac{2}{3} \cdot \frac{1}{3} = \frac{2}{9}

Example Question #1251 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Simplify the following expression:

\displaystyle \frac{4}{5}*\frac{8}{9}

 

Possible Answers:

\displaystyle \frac{32}{63}

\displaystyle \frac{32}{45}

\displaystyle \frac{11}{21}

\displaystyle \frac{40}{63}

Correct answer:

\displaystyle \frac{32}{45}

Explanation:

Simplify the following expression:

\displaystyle \frac{4}{5}*\frac{8}{9}

To multiply fractions, simply multiply across the top and bottom:

\displaystyle \frac{4}{5}*\frac{8}{9}=\frac{4*8}{5*9}=\frac{32}{45}

Now, we cannot simplify our answer, so our answer remains:

\displaystyle \frac{32}{45}

Example Question #361 : Numbers And Operations

Simplify the following:

\displaystyle \frac{2}{3} \cdot \frac{4}{5}

Possible Answers:

\displaystyle \frac{6}{8}

\displaystyle \frac{120}{15}

\displaystyle \frac{4}{15}

\displaystyle \frac{8}{15}

\displaystyle \frac{22}{15}

Correct answer:

\displaystyle \frac{8}{15}

Explanation:

When we multiply fractions, we first multiply the numerators, then we multiply the denominators.  We do not need to find common denominators when multiplying.  So in

\displaystyle \frac{2}{3} \cdot \frac{4}{5}

we will multiply.  We get

\displaystyle \frac{2 \cdot 4}{3 \cdot 5}

\displaystyle \frac{8}{15}

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