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Algebra II : Adding and Subtracting Fractions

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Example Questions

Example Question #4482 : Algebra Ii

Subtract the fractions: $\frac{5}{9}-\frac{1}{3}-\frac{5}{12}$

Possible Answers:

$-\frac{1}{4}$

$\frac{7}{36}$

$-\frac{7}{36}$

$-\frac{23}{36}$

$\frac{1}{4}$

Correct answer:

$-\frac{7}{36}$

Explanation:

Determine the least common denominator by writing out the multiples for each term.

9-[9,18,27,36]

3-[3,6,9,12,15,18,21,24,27,30,33,36]

12-[12,24,36]

The least common denominator is 36.

Convert all fractions.

$\frac{5}{9}-\frac{1}{3}-\frac{5}{12} = \frac{5(4)}{9(4)}-\frac{1(12)}{3(12)}-\frac{5(3)}{12(3)}$

Simplify the right side.

$\frac{20}{36}-\frac{12}{36}-\frac{15}{36}$

Subtract the numerators. The denominator remains the same.

The answer is: $-\frac{7}{36}$

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Example Question #122 : Adding And Subtracting Fractions

Add the fractions: $\frac{1}{4}+\frac{3}{8}+\frac{1}{12}$

Possible Answers:

$\frac{17}{48}$

$\frac{17}{12}$

$\frac{2}{3}$

$\frac{17}{24}$

$\frac{19}{48}$

Correct answer:

$\frac{17}{24}$

Explanation:

In order to add the fractions, we will need to determine the least common denominator. Write out the multiples of the denominators.

4-[4,8,12,16,20,24]

8-[8,16,24]

12-[12,24]

The LCD is 24. Convert the fractions.

$\frac{1(6)}{4(6)}+\frac{3(3)}{8(3)}+\frac{1(2)}{12(2)}=\frac{ 6}{24}+\frac{9}{24}+\frac{2}{24}$

Combine the numerators, but do not change the denominators.

The answer is: $\frac{17}{24}$

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Example Question #121 : Adding And Subtracting Fractions

Solve: $\frac{3}{5}-\frac{2}{7} -\frac{1}{2}$

Possible Answers:

$\frac{13}{35}$

$-\frac{13}{35}$

$\frac{2}{13}$

$\frac{4}{35}$

$-\frac{13}{70}$

Correct answer:

$-\frac{13}{70}$

Explanation:

Identify the least common denominator.

(5)(7)(2) =70

Convert the fractions.

$\frac{3}{5}-\frac{2}{7} -\frac{1}{2} =\frac{3(7)(2)}{5(7)(2)}-\frac{2(5)(2)}{7(5)(2)} -\frac{1(5)(7)}{2(5)(7)}$

Simplify the terms.

$\frac{42}{70}-\frac{20}{70}-\frac{35}{70} = -\frac{13}{70}$

The answer is: $-\frac{13}{70}$

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Example Question #151 : Fractions

Add the following fractions: $\frac{1}{5x}+\frac{3}{7}+\frac{10}{x^2}$

Possible Answers:

$\textup{The answer is not given.}$

$\frac{2}{5x^2}$

$\frac{2}{5}x^2$

$\frac{15x^2+7x+350}{35x^2}$

$\frac{15x^2+7x}{35x^2+350}$

Correct answer:

$\frac{15x^2+7x+350}{35x^2}$

Explanation:

Determine the least common denominator.

The first two denominators do not have an x^2 . After all denominators have an x^2 term, the coefficients of the three denominators are: 5,7,1

The least common denominator would be: 35x^2

Convert all fractions.

$\frac{1}{5x}+\frac{3}{7}+\frac{10}{x^2}=\frac{1(7x)}{5x(7x)}+\frac{3(5x^2)}{7(5x^2)}+\frac{10(35)}{x^2 (35)}$

Simplify the fractions.

The answer is: $\frac{15x^2+7x+350}{35x^2}$

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Example Question #4493 : Algebra Ii

Add the fractions: $\frac{4}{9}+\frac{1}{3}+\frac{5}{6}$

Possible Answers:

$\textup{The answer is not given.}$

$\frac{17}{9}$

$\frac{29}{18}$

$\frac{3}{13}$

$\frac{19}{18}$

Correct answer:

$\frac{29}{18}$

Explanation:

To add the fractions we need the least common denominator. Write the multiples for each denominator.

9-[9,18]

3-[3,6,9,12,15,18]

6-[6,12,18]

Convert the fractions with a denominator of 18, since this is the least common denominator.

$\frac{4}{9}+\frac{1}{3}+\frac{5}{6}=\frac{4(2)}{9(2)}+\frac{1(6)}{3(6)}+\frac{5(3)}{6(3)}$

Simplify the fractions.

$\frac{8}{18}+\frac{6}{18}+\frac{15}{18} = \frac{29}{18}$

The answer is: $\frac{29}{18}$

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Example Question #4494 : Algebra Ii

Subtract: $\frac{3}{27}-\frac{9}{30}-\frac{12}{60}$

Possible Answers:

$-\frac{7}{8}$

$-\frac{1}{3}$

$-\frac{7}{18}$

$\textup{The answer is not given.}$

$-\frac{7}{15}$

Correct answer:

$-\frac{7}{18}$

Explanation:

In order to subtract the fractions, we should reduce all the fractions first.

$\frac{3}{27}-\frac{9}{30}-\frac{12}{60} = \frac{1}{9}-\frac{3}{10}-\frac{1}{5}$

Convert the reduced fractions to a common denominator. By visualization, the common denominator is 90, since this value is divisible by all three numbers.

$\frac{1(10)}{9(10)}-\frac{3(9)}{10(9)}-\frac{1(18)}{5(18)}$

Simplify the top and bottom.

$\frac{10}{90}-\frac{27}{90}-\frac{18}{90} = -\frac{35}{90}$

Reduce this fraction.

$-\frac{35}{90} = -\frac{7\times 5}{18\times 5} = -\frac{7}{18}$

The answer is: $-\frac{7}{18}$

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Example Question #122 : Adding And Subtracting Fractions

Add the fractions: $\frac{8}{11}+\frac{1}{66}$

Possible Answers:

$\frac{9}{11}$

$\frac{49}{66}$

$\frac{3}{22}$

$\frac{9}{77}$

$\textup{The answer is not given.}$

Correct answer:

$\frac{49}{66}$

Explanation:

Change the first fraction so that both fractions have the same denominator.

Multiply the first fraction by $\frac{6}{6}$ in order to change the fraction.

$\frac{8}{11}(\frac{6}{6})+\frac{1}{66} = \frac{48}{66}+\frac{1}{66} = \frac{49}{66}$

The answer is: $\frac{49}{66}$

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Example Question #122 : Adding And Subtracting Fractions

Add the fractions: $\frac{2}{3}+\frac{8}{9}+2\frac{1}{6}$

Possible Answers:

$\frac{23}{9}$

$\frac{17}{9}$

$\frac{41}{12}$

$\frac{67}{18}$

$\frac{35}{18}$

Correct answer:

$\frac{67}{18}$

Explanation:

Change the mixed fraction to an improper fraction.

$1\frac{1}{6} = \frac{6(2)+1}{6} = \frac{13}{6}$

Rewrite the expression.

$\frac{2}{3}+\frac{8}{9}+\frac{13}{6}$

Convert all of the terms to common denominator. A common denominator is 18 since this value is divisible by all denominators given.

$\frac{2(6)}{3(6)}+\frac{8(2)}{9(2)}+\frac{13(3)}{6(3)}$

Simplify all the terms.

$\frac{12}{18}+\frac{16}{18}+\frac{39}{18} = \frac{67}{18}$

The answer is: $\frac{67}{18}$

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Example Question #4497 : Algebra Ii

Compute the fractions: $\frac{7}{2}-\frac{3}{8}+\frac{3}{4}$

Possible Answers:

$\frac{31}{4}$

$\frac{9}{8}$

$\frac{31}{8}$

$\frac{9}{4}$

Correct answer:

$\frac{31}{8}$

Explanation:

Convert the fractions to a common denominator.

The least common denominator is eight.

$\frac{7(4)}{2(4)}-\frac{3}{8}+\frac{3(2)}{4(2)} = \frac{28}{8}-\frac{3}{8}+\frac{6}{8}$

Find the sum now that the denominators are equal.

The answer is: $\frac{31}{8}$

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Example Question #121 : Adding And Subtracting Fractions

Add the fractions: $\frac{7}{4}+\frac{9}{8}+\frac{1}{12}$

Possible Answers:

$\frac{11}{8}$

$\frac{71}{12}$

$\frac{11}{3}$

$\frac{71}{24}$

$\textup{The answer is not given.}$

Correct answer:

$\frac{71}{24}$

Explanation:

Determine the least common denominator. Write out the multiples of each denominator.

4-[4,8,12,16,20,24]

8-[8,16,24]

12-[12,24]

Convert all fractions to a common denominator of 24.

$\frac{7}{4}+\frac{9}{8}+\frac{1}{12} = \frac{7(6)}{4(6)}+\frac{9(3)}{8(3)}+\frac{1(2)}{12(2)}$

Simplify the fractions.

$\frac{42}{24}+\frac{27}{24}+\frac{2}{24} = \frac{71}{24}$

The answer is: $\frac{71}{24}$

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Algebra II : Adding and Subtracting Fractions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #4482 : Algebra Ii

Example Question #122 : Adding And Subtracting Fractions

Example Question #121 : Adding And Subtracting Fractions

Example Question #151 : Fractions

Example Question #4493 : Algebra Ii

Example Question #4494 : Algebra Ii

Example Question #122 : Adding And Subtracting Fractions

Example Question #122 : Adding And Subtracting Fractions

Example Question #4497 : Algebra Ii

Example Question #121 : Adding And Subtracting Fractions

All Algebra II Resources

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