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Algebra II : Fractions

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Example Questions

Example Question #7 : Subtraction With Fractions

Subtract these fractions:

$\frac{1}{8}-\frac{1}{9}$

Possible Answers:

$\frac{1}{36}$

$\frac{1}{17}$

$\frac{1}{24}$

$\frac{1}{72}$

Correct answer:

$\frac{1}{72}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 9 over 9 and the second fraction by 8 over 8.

$\frac{1}{8}*\frac{9}{9}=\frac{9}{72}$

$\frac{1}{9}*\frac{8}{8}=\frac{8}{72}$

Subtract the numerators of these fractions to get the final answer.

$\frac{9}{72}-\frac{8}{72}=\frac{1}{72}$

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Example Question #41 : Operations With Fractions

Subtract these fractions:

$\frac{6}{7}-\frac{1}{3}$

Possible Answers:

$\frac{3}{7}$

$\frac{12}{21}$

$\frac{10}{21}$

$\frac{11}{21}$

Correct answer:

$\frac{11}{21}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 3 over 3 and the second fraction by 7 over 7.

$\frac{6}{7}*\frac{3}{3}=\frac{18}{21}$

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

Subtract the numerators of these fractions to get the final answer.

$\frac{18}{21}-\frac{7}{21}=\frac{11}{21}$

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Example Question #21 : Adding And Subtracting Fractions

$\frac{9x}{x-1}-\frac{4+x}{3x-3}$

Possible Answers:

$\frac{13x-2)}{3(x-1)}$

$\frac{2(13x-2)}{3(x-1)}$

$\frac{2(13x-2)}{3(x)}$

$\frac{2(13x-2)}{(x-1)}$

$\frac{2(x-2)}{3(x-1)}$

Correct answer:

$\frac{2(13x-2)}{3(x-1)}$

Explanation:

To solve this problem, first identify the common denominator, which happens to be: 3x-3. Therefore, you just need to offset the first fraction so that it becomes $\frac{9x(3)}{(x-1)(3)}$ . Then, combine the numerators, remembering that there is a subtraction sign: 9x(3)-(4+x)=27x-4-x=26x-4 . Put that over the denominator so that you have: $\frac{26x-4}{3x-3}$ . I'd factor to make sure you can't simplify anymore: $\frac{2(13x-2)}{3(x-1)}$ . It turns out you can't so this is your final answer.

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Example Question #22 : Adding And Subtracting Fractions

$\frac{2}{x+1}-\frac{3}{x-5}$

Possible Answers:

$\frac{x-13}{(x+1)(x-5)}$

$\frac{-x-13}{(x+1)(x-5)}$

$\frac{-x-13}{(x-5)}$

$\frac{x+13}{(x+1)(x-5)}$

$\frac{-x-13}{(x-5)}$

Correct answer:

$\frac{-x-13}{(x+1)(x-5)}$

Explanation:

To combine these two fractions, you must first identify the common denominator. In this case, it's the product of the two denominators (x+1)(x-5) . Then, multiply each of the numerators by their missing piece of the denominator: $\frac{2(x-5)}{(x+1)(x-5)}-\frac{3(x+1)}{(x-5)(x+1)}$ . Now, you can combine the numerators to get: $\frac{2x-10-3x-3}{(x+1)(x-5)}$ . Simplify and combine like terms to get: $\frac{-x-13}{(x+1)(x-5)}$ .

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Example Question #23 : Adding And Subtracting Fractions

Simplify: $\frac{1+3}{\frac{2}{3+2}} + \frac{1}{2}$

Possible Answers:

$1\frac{1}{8}$

$10\frac{1}{2}$

$\frac{3}{7}$

$2\frac{1}{5}$

$\frac{9}{10}$

Correct answer:

$10\frac{1}{2}$

Explanation:

Simplify the complex fraction $\frac{1+3}{\frac{2}{3+2}}$ first.

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

Rewrite the complex fraction using a division sign.

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

Turn the division sign to a multiplication sign and take the reciprocal of the second term. Simplify.

$4 \div \frac{2}{5} = 4\times \frac{5}{2} = \frac{20}{2} = 10$

Add this number with the second term.

$\frac{1+3}{\frac{2}{3+2}} + \frac{1}{2} = 10+\frac{1}{2} = 10\frac{1}{2}$

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Example Question #51 : Fractions

Add: $\frac{3}{ab} + \frac{a+3}{a}$

Possible Answers:

$\frac{6+a}{a^2b}$

$\frac{a+6b}{ab}$

$\frac{3+ab+3b}{ab}$

$\frac{ab+6b}{ab}$

$\frac{6+a+b}{ab}$

Correct answer:

$\frac{3+ab+3b}{ab}$

Explanation:

In order to add the numerators of the fractions, we need to find the least common denominator.

The least common denominator is:

We will need to multiply the numerator and denominator by to match the denominators of both fractions.

$\frac{3}{ab} + \frac{b\left (a+3 \right )}{ab}$

Simplify the fraction.

$\frac{3}{ab} + \frac{b\left (a+3 \right )}{ab} = \frac{3}{ab}+\frac{ab+3b}{ab}$

Combine the two fractions.

The answer is: $\frac{3+ab+3b}{ab}$

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Example Question #24 : Adding And Subtracting Fractions

Solve: $\frac{1}{3} -\frac{2}{5}+\frac{1}{4}$

Possible Answers:

$\frac{7}{60}$

$\frac{21}{50}$

$\frac{11}{60}$

$\frac{11}{30}$

Correct answer:

$\frac{11}{60}$

Explanation:

Find the least common denominator. One method is to multiply all three uncommon denominators together.

$3 \times 5 \times 4 = 60$

Rewrite the fractions. For each fraction, multiply the numerator with what was multiplied on the denominator to get the least common denominator.

$\frac{1}{3} -\frac{2}{5}+\frac{1}{4} = \frac{20}{60}- \frac{24}{60}+ \frac{15}{60}$

Add the numerators. The denominators do not change.

$\frac{20}{60}- \frac{24}{60}+ \frac{15}{60} = \frac{11}{60}$

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Example Question #52 : Fractions

Add the following fractions: $\frac{3}{2}+ \frac{4}9{}$

Possible Answers:

$\frac{35}{18}$

$\frac{16}{9}$

$\frac{7}{18}$

$\frac{7}{11}$

$\frac{2}{3}$

Correct answer:

$\frac{35}{18}$

Explanation:

In order to add the fractions, we must find a least common denominator.

Multiply the denominators together.

$2 \times 9 =18$

Reconvert the fractions.

$\frac{3}{2}+ \frac{4}{9} = \frac{27}{18}+ \frac{8}{18} = \frac{35}{18}$

The answer is: $\frac{35}{18}$

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Example Question #53 : Fractions

Perform the following operation:

$\frac{5}{16}+\frac{3}{8}$

Possible Answers:

$\frac{11}{16}$

$\frac{8}{16}$

$\frac{15}{16}$

$\frac{11}{8}$

Correct answer:

$\frac{11}{16}$

Explanation:

Perform the following operation:

$\frac{5}{16}+\frac{3}{8}$

To start, we will need a common denominator. In this case, let's use 16, because it is the smallest possible common denominator.

$\frac{3}{8}*\frac{2}{2}=\frac{6}{16}$

Next, simply add across the top and we have our answer!

$\frac{5}{16}+\frac{6}{16}=\frac{11}{16}$

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Example Question #31 : Adding And Subtracting Fractions

Add the fractions: $\frac{2}{x-3}+\frac{1}{x+2}$

Possible Answers:

$\frac{x+1}{(x-3)(x+2)}$

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

$\frac{x+1}{(x+2)(x-3)}$

$\frac{3x+1}{(x-3)(x+2)}$

$\frac{3x+1}{x-6}$

Correct answer:

$\frac{3x+1}{(x-3)(x+2)}$

Explanation:

$\frac{2}{x-3}+\frac{1}{x+2}$

To add fractions we must find a common denominator. In this example we do so by multiplying each side by the denominator of the other fraction:

$\frac{x+2}{x+2}*\frac{2}{x-3}+\frac{1}{x+2}*\frac{x-3}{x-3}$

Add the numerators:

$\frac{2(x+2)+x-3}{(x-3)(x+2)}\rightarrow \mathbf{\frac{3x+1}{(x-3)(x+2)}}$

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Algebra II : Fractions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #7 : Subtraction With Fractions

Example Question #41 : Operations With Fractions

Example Question #21 : Adding And Subtracting Fractions

Example Question #22 : Adding And Subtracting Fractions

Example Question #23 : Adding And Subtracting Fractions

Example Question #51 : Fractions

Example Question #24 : Adding And Subtracting Fractions

Example Question #52 : Fractions

Example Question #53 : Fractions

Example Question #31 : Adding And Subtracting Fractions

All Algebra II Resources

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