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SSAT Upper Level Math : Rational Numbers

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #5 : How To Find A Complex Fraction

Simplify:

$\frac{3\frac{1}{2}-2\frac{1}{5}}{4\frac{3}{4}}$

Possible Answers:

The correct answer is not given among the other responses.

$\frac{7}{25}$

$\frac{5}{19}$

$\frac{27}{100}$

$\frac{9}{23}$

Correct answer:

The correct answer is not given among the other responses.

Explanation:

$\frac{3\frac{1}{2}-2\frac{1}{5}}{4\frac{3}{4}}$

$=\left ( 3\frac{1}{2}-2\frac{1}{5} \right )\div 4\frac{3}{4}}$

$= \left ( \frac{7}{2}- \frac{11}{5} \right ) \div \frac{19}{4}$

$= \left ( \frac{35}{10}- \frac{22}{10} \right ) \times \frac{4}{19}$

$= \frac{13}{10} \times \frac{4}{19}$

$= \frac{13}{5} \times \frac{2}{19}$

$= \frac{26}{95}$

This is not among the given responses.

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Example Question #81 : Rational Numbers

Simplify:

$\frac{3\frac{1}{2}+2\frac{1}{5}}{4\frac{3}{4}}$

Possible Answers:

$1\frac{1}{6}$

$1\frac{2}{5}$

$1\frac{1}{5}$

$1\frac{1}{4}$

$1\frac{3}{5}$

Correct answer:

$1\frac{1}{5}$

Explanation:

$\frac{3\frac{1}{2}+2\frac{1}{5}}{4\frac{3}{4}}$

$=\left ( 3\frac{1}{2}+2\frac{1}{5} \right )\div 4\frac{3}{4}}$

$= \left ( \frac{7}{2}+ \frac{11}{5} \right ) \div \frac{19}{4}$

$= \left ( \frac{35}{10}+ \frac{22}{10} \right ) \times \frac{4}{19}$

$= \frac{57}{10} \times \frac{4}{19}$

$= \frac{3}{5} \times \frac{2}{1}$

$= \frac{6}{5} = 1\frac{1}{5}$

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Example Question #4 : How To Find A Complex Fraction

Simplify, writing as a proper fraction.

$\frac{2\tfrac{1}{4}}{5\tfrac{2}{5}}$

Possible Answers:

$\frac{5}{9}$

$\frac{2}{5}$

$\frac{7}{12}$

$\frac{5}{12}$

$\frac{3}{10}$

Correct answer:

$\frac{5}{12}$

Explanation:

Remember that that fraction bar is just a division symbol. Rewrite as a division, rewrite those mixed fractions as improper fractions, then rewrite as as a multiplication by the reciprocal of the second fraction.

$\frac{2\tfrac{1}{4}}{5\tfrac{2}{5}} = 2\tfrac{1}{4} \div 5\tfrac{2}{5} = \frac{9}{4} \div \frac{27}{5} = \frac{9}{4} \cdot \frac{5}{27} = \frac{1}{4} \cdot \frac{5}{3}= \frac{5}{12}$

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Example Question #1211 : Ssat Upper Level Quantitative (Math)

Simplify.

$\frac{2}{x^2}-\frac{4}{x}$

Possible Answers:

$\frac{4}{x}$

$\frac{x^2-x}{2}$

$\frac{-2}{x^2-x}$

$\frac{2-4x}{x^2}$

$\frac{2}{x^2}$

Correct answer:

$\frac{2-4x}{x^2}$

Explanation:

Find the least common denominator which is x^2 .

Just multiply the right fraction top and bottom by .

$\frac{2}{x^2}-\frac{4\cdot x}{x \cdot x}=\frac{2}{x^2}-\frac{4x}{x^2}$

Finally, subtract.

Answer should be,

$\frac{2-4x}{x^2}$ .

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Example Question #2 : How To Subtract Complex Fractions

Simplify.

$\frac{x^2-5x+6}{x^2+2x-8}-\frac{x^2-5x-6}{x^2+x-12}$

Possible Answers:

$\frac{-1}{x+4}$

$\frac{2x-4}{x+4}$

$\frac{x-5}{x+4}$

$\frac{-5}{x+4}$

$\frac{5}{x+4}$

Correct answer:

$\frac{-1}{x+4}$

Explanation:

Lets try to factor. Remember, we need to find two terms that are factors of the c term that add up to the b term.

$\frac{(x-2)(x-3)}{(x-2)(x+4)}-\frac{(x-3)(x-2)}{(x-3)(x+4)}$

Next cancel out the like terms.

$\frac{x-3}{x+4}-\frac{x-2}{x+4}$

Now combine the numerator. Remember to distribute the negative sign.

This is the final answer:

$\frac{-1}{x+4}$ .

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Example Question #3 : How To Subtract Complex Fractions

Simplify.

$1-\frac{3}{x-3}$

Possible Answers:

$\frac{3}{x-3}$

$\frac{x-6}{x-3}$

$\frac{x+6}{x-3}$

$\frac{1}{x-3}$

Correct answer:

$\frac{x-6}{x-3}$

Explanation:

Turn the into a fraction that has a common denominator with the other fraction. To do this multiply $1 \cdot \frac{x-3}{x-3}$ .

This results in the following expression:

$\frac{x-3}{x-3}-\frac{3}{x-3}$

With the same denominator, just subtract and remember to distribute the negative sign.

The final answer is

$\frac{x-6}{x-3}$ .

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Example Question #4 : How To Subtract Complex Fractions

Solve and simplify.

$\frac{x^2-9}{x+3}-\frac{x^2-16}{x+4}$

Possible Answers:

$\frac{1}{x^2+7x+12}$

$\frac{x^2+7}{x^2+7x+12}$

$\frac{2x}{x^2+7x+12}$

$\frac{7}{x^2+7x+12}$

Correct answer:

Explanation:

Lets try to reduce the fraction. When factoring a difference of squares, the form is (x-a)(x+a) . When you foil, the middle terms cancel out.

So when doing that, we have:

$\frac{(x-3)(x+3)}{(x+3)}-\frac{(x-4)(x+4)}{(x+4)}$ .

Cancel out like terms and we get this:

(x-3)-(x-4) .

Distribute the negative sign and we should get .

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Example Question #82 : Rational Numbers

Solve for .

$\frac{1}{\sqrt{x}}-\frac{1}{2\sqrt{x}}=2$

Possible Answers:

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

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

$\frac{1}{16}$

Correct answer:

$\frac{1}{16}$

Explanation:

First find the least common denominator. That will be $2\sqrt{x}$ .

Multiply top and bottom of the left fraction by .

$\frac{1}{\sqrt{x}}\cdot \frac{2}{2}=\frac{2}{2\sqrt{x}}$

Then subtract the numerator and then cross-multiply to get this:

$\frac{2}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}=2\rightarrow 2-1=2(2\sqrt{x}) \rightarrow 1=4\sqrt{x}$

Then combine like terms. To get rid of the square root,

$\frac{1}{4}=\sqrt{x}$ square both sides to get $\left(\frac{1}{4}\right)^2=\frac{1}{16}$ as the final answer.

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Example Question #1 : How To Subtract Complex Fractions

Solve for .

$\frac{5}{x-2}-\frac{2}{x+2}=1$

Possible Answers:

Both and .

Correct answer:

Both and .

Explanation:

Find the least common denominator which is x^2-4 . Then multiply the left fraction numerator by x+2 and multiply the right numerator by x-2 inorder for each fraction to share the common denominator.

$\frac{5(x+2)}{x^2-4}-\frac{2(x-2)}{x^2-4}=1$

Distribute and be careful of the negative sign.

$\frac{5x+10-2x+4}{x^2-4}=1$

Cross-multiply and create the quadratic equation.

x^2-3x-18=0

Lets factor. Remember, we need to find two terms that are factors of the c term that add up to the b term.

(x-6)(x+3)=0

x=6 , x=-3

If you check these answers back into the question, none of the fractions are undefined so these are the final answers.

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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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SSAT Upper Level Math : Rational Numbers

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #5 : How To Find A Complex Fraction

Example Question #81 : Rational Numbers

Example Question #4 : How To Find A Complex Fraction

Example Question #1211 : Ssat Upper Level Quantitative (Math)

Example Question #2 : How To Subtract Complex Fractions

Example Question #3 : How To Subtract Complex Fractions

Example Question #4 : How To Subtract Complex Fractions

Example Question #82 : Rational Numbers

Example Question #1 : How To Subtract Complex Fractions

Example Question #7 : How To Subtract Complex Fractions

All SSAT Upper Level Math Resources

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