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SSAT Upper Level Math : Complex Fractions

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #7 : How To Subtract Complex Fractions

Solve for .

$\frac{2}{x-1}-\frac{2}{x+1}=\left | 2\right |$

Possible Answers:

$-\sqrt{3}$

$\sqrt{3}$

$\pm\sqrt{3}$

Correct answer:

$\pm\sqrt{3}$

Explanation:

Find the least common denominator which is x^2-1 . Then multiply the left fraction numerator by x+1 and multiply the right numerator by x-1 in order to make each fraction share the common denominator.

$\frac{2(x+1)}{x^2-1}-\frac{2(x-1)}{x^2-1}=\left | 2\right |$

Distribute and be careful of the negative sign.

$\frac{2x+2-2x+2}{x^2-1}=\left | 2\right |$

Simplify the numerator and cross multiply. Because there is an absolute value bar, we need to split this expression into two different equations.

Equation one:

2(x^2-1)=4

2x^2-2=4

2x^2=6

x^2=3

$x=\pm \sqrt{3}$ By inspection, these values pass and don't violate the fractions being undefined.

Equation two:

-2(x^2-1)=4

-2x^2+2=4

-2x^2=2

x^2=-1

x=i This answer is imaginary and not in the choices leaving $\pm \sqrt{3}$ as the answers.

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Example Question #1 : How To Divide Complex Fractions

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

Possible Answers:

$\frac{6}{5}$

$\frac{8}{15}$

$\frac{5}{6}$

$\frac{4}{5}$

Correct answer:

$\frac{5}{6}$

Explanation:

Keep in mind that the main fraction line just means "divide."

So then,

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

Now, divide this like any other fraction.

$\frac{2}{3}\div\frac{4}{5}=\frac{2}{3}\times\frac{5}{4}=\frac{10}{12}=\frac{5}{6}$

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Example Question #2 : How To Divide Complex Fractions

$\frac{\frac{4}{3}}{6}=?$

Possible Answers:

$\frac{1}{8}$

$\frac{3}{4}$

$\frac{7}{8}$

$\frac{2}{9}$

Correct answer:

$\frac{2}{9}$

Explanation:

Remember that the main line in the fraction means "divide."

Then,

$\frac{\frac{4}{3}}{6}=\frac{4}{3}\div6$

Now, divide this like you would divide any other fraction.

$\frac{4}{3}\div6=\frac{4}{3}\times\frac{1}{6}=\frac{4}{18}=\frac{2}{9}$

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Example Question #3 : How To Divide Complex Fractions

$\frac{\frac{9}{10}}{\frac{5}{2}}=?$

Possible Answers:

$\frac{9}{25}$

$\frac{11}{15}$

$\frac{4}{5}$

$\frac{25}{9}$

Correct answer:

$\frac{9}{25}$

Explanation:

Remember that the main line in the fraction means "divide."

Now,

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

Divide these two fractions.

$\frac{9}{10}\div\frac{5}{2}=\frac{9}{10}\times\frac{2}{5}=\frac{18}{50}=\frac{9}{25}$

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Example Question #2 : How To Divide Complex Fractions

$\frac{\frac{8}{9}}{\frac{1}{2}}=?$

Possible Answers:

$\frac{13}{9}$

$\frac{9}{16}$

$\frac{16}{9}$

$\frac{10}{9}$

Correct answer:

$\frac{16}{9}$

Explanation:

The main fraction line means "divide."

Rewrite the complex fraction:

$\frac{\frac{8}{9}}{\frac{1}{2}}=\frac{8}{9}\div\frac{1}{2}$

Divide these fractions.

$\frac{8}{9}\div\frac{1}{2}=\frac{8}{9}\times\frac{2}{1}=\frac{16}{9}$

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Example Question #4 : How To Divide Complex Fractions

$\frac{\frac{12}{13}}{\frac{1}{4}}=?$

Possible Answers:

$\frac{48}{13}$

$\frac{37}{13}$

$\frac{12}{5}$

$\frac{13}{48}$

Correct answer:

$\frac{48}{13}$

Explanation:

The main fraction line means "divide."

Rewrite the complex fractions as thus:

$\frac{\frac{12}{13}}{\frac{1}{4}}=\frac{12}{13}\div\frac{1}{4}$

Now, divide these two fractions.

$\frac{12}{13}\div\frac{1}{4}=\frac{12}{13}\times\frac{4}{1}=\frac{48}{13}$

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Example Question #5 : How To Divide Complex Fractions

$\frac{\frac{7}{8}}{\frac{5}{4}}=?$

Possible Answers:

$\frac{10}{7}$

$\frac{4}{7}$

$\frac{4}{5}$

$\frac{7}{10}$

Correct answer:

$\frac{7}{10}$

Explanation:

The main fraction line means "divide." Rewrite the complex fraction as thus:

$\frac{\frac{7}{8}}{\frac{5}{4}}=\frac{7}{8}\div\frac{5}{4}$

Divide these two fractions.

$\frac{7}{8}\div\frac{5}{4}=\frac{7}{8}\times\frac{4}{5}=\frac{28}{40}=\frac{7}{10}$

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Example Question #6 : How To Divide Complex Fractions

$\frac{\frac{12}{11}}{\frac{5}{2}}=?$

Possible Answers:

$\frac{5}{11}$

$\frac{55}{24}$

$\frac{24}{55}$

$\frac{11}{5}$

Correct answer:

$\frac{24}{55}$

Explanation:

The main line in a fraction means "divide." Rewrite the complex fraction as thus:

$\frac{\frac{12}{11}}{\frac{5}{2}}=\frac{12}{11}\div\frac{5}{2}$

Now, divide the fractions.

$\frac{12}{11}\div\frac{5}{2}=\frac{12}{11}\times\frac{2}{5}=\frac{24}{55}$

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Example Question #3 : How To Divide Complex Fractions

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

Possible Answers:

$\frac{5}{9}$

$\frac{5}{6}$

$\frac{6}{5}$

$\frac{12}{7}$

Correct answer:

$\frac{6}{5}$

Explanation:

The main line in a fraction means "divide." Rewrite the complex fraction as thus:

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

Now, divide the fractions.

$\frac{3}{2}\div\frac{5}{4}=\frac{3}{2}\times\frac{4}{5}=\frac{12}{10}=\frac{6}{5}$

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Example Question #8 : How To Divide Complex Fractions

$\frac{\frac{1}{8}}{\frac{7}{8}}=?$

Possible Answers:

$\frac{3}{5}$

$\frac{9}{56}$

$\frac{1}{7}$

Correct answer:

$\frac{1}{7}$

Explanation:

The main line in a fraction means "divide." Rewrite the complex fraction as thus:

$\frac{\frac{1}{8}}{\frac{7}{8}}=\frac{1}{8}\div\frac{7}{8}$

Now, divide these fractions.

$\frac{1}{8}\div\frac{7}{8}=\frac{1}{8}\times\frac{8}{7}=\frac{8}{56}=\frac{1}{7}$

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SSAT Upper Level Math : Complex Fractions

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #7 : How To Subtract Complex Fractions

Example Question #1 : How To Divide Complex Fractions

Example Question #2 : How To Divide Complex Fractions

Example Question #3 : How To Divide Complex Fractions

Example Question #2 : How To Divide Complex Fractions

Example Question #4 : How To Divide Complex Fractions

Example Question #5 : How To Divide Complex Fractions

Example Question #6 : How To Divide Complex Fractions

Example Question #3 : How To Divide Complex Fractions

Example Question #8 : How To Divide Complex Fractions

All SSAT Upper Level Math Resources

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