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Algebra II : Adding and Subtracting Fractions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #11 : Adding And Subtracting Fractions

Simplify:

$\frac{1}{4a}+\frac{b}{2ac}$

Possible Answers:

$\frac{2(b+c)}{4ac}$

$\frac{b+c}{2ac}$

$\frac{2bc}{4ac}$

$\frac{b}{2a}$

$\frac{2b+c}{4ac}$

Correct answer:

$\frac{2b+c}{4ac}$

Explanation:

To add or subtract fractions, the fractions must have the same denominator.

The smallest common denominator in this case is 4ac .

After multiply both terms so that they have the same denominator.

$\frac{1(c)}{4a(c)}+\frac{b(4)}{2ac(4)}=\frac{c}{4ac}+\frac{4b}{8ac}$

$\frac{c}{4ac}+\frac{4b}{8ac}=\frac{c}{4ac}+\frac{2b}{4ac}$

Simply add these two terms together.

$\frac{c}{4ac}+\frac{2b}{4ac}=\frac{2b+c}{4ac}$

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Example Question #11 : Adding And Subtracting Fractions

Add these fractions:

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

Possible Answers:

$1\frac{15}{22}$

$1\frac{7}{15}$

$\frac{7}{15}$

$1\frac{4}{15}$

Correct answer:

$1\frac{7}{15}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 5 on the top and bottom and the second fraction by 3 on the top and bottom.

$\frac{2}{3}*\frac{5}{5}=\frac{10}{15}$

$\frac{4}{5}*\frac{3}{3}=\frac{12}{15}$

Add these fractions together, then write it as a mixed number

$\frac{10}{15}+\frac{12}{15}=\frac{22}{15}=1\frac{7}{15}$

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Example Question #11 : Adding And Subtracting Fractions

Add these fractions:

$\frac{1}{2}+\frac{1}{6}$

Possible Answers:

$\frac{5}{6}{}$

$\frac{4}{3}$

$\frac{2}{3}$

$\frac{1}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

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

$\frac{1}{2}*\frac{3}{3}=\frac{3}{6}$

Add these fractions together, then reduce it to get the final answer.

$\frac{3}{6}+\frac{1}{6}=\frac{4}{6}=\frac{2\cdot2}{2\cdot 3}=\frac{2}{3}$

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Example Question #14 : Adding And Subtracting Fractions

Add these fractions:

$\frac{3}{5}+\frac{2}{7}$

Possible Answers:

$\frac{29}{35}$

$\frac{34}{35}$

$\frac{31}{35}$

$\frac{21}{35}$

Correct answer:

$\frac{31}{35}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 7 over 7 and the second fraction by 5 over 5.

$\frac{3}{5}*\frac{7}{7}=\frac{21}{35}$

$\frac{2}{7}*\frac{5}{5}=\frac{10}{35}$

Add these fractions together, to get the final answer.

$\frac{21}{35}+\frac{10}{35}=\frac{31}{35}$

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Example Question #44 : Fractions

Subtract these fractions:

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

Possible Answers:

$\frac{5}{6}{}$

$\frac{1}{6}$

$\frac{1}{9}$

$\frac{2}{9}$

Correct answer:

$\frac{1}{6}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 2 over 2 and the second fraction by 3 over 3.

$\frac{2}{3}*\frac{2}{2}=\frac{4}{6}$

$\frac{1}{2}*\frac{3}{3}=\frac{3}{6}$

Subtract these fractions to get the final answer.

$\frac{4}{6}-\frac{3}{6}=\frac{1}{6}$

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Example Question #8 : Subtraction With Fractions

Subtract these fractions:

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

Possible Answers:

$\frac{7}{15}$

$\frac{9}{12}$

$\frac{5}{12}$

$\frac{11}{12}$

Correct answer:

$\frac{7}{15}$

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 5 over 5.

$\frac{4}{5}*\frac{3}{3}=\frac{12}{15}$

$\frac{1}{3}*\frac{5}{5}=\frac{5}{15}$

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

$\frac{12}{15}-\frac{5}{15}=\frac{7}{15}$

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Example Question #1721 : Mathematical Relationships And Basic Graphs

Add these fractions:

$\frac{1}{7}+\frac{5}{6}$

Possible Answers:

$\frac{39}{42}$

$\frac{41}{42}$

$\frac{43}{42}$

$\frac{20}{21}$

Correct answer:

$\frac{41}{42}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 6 over 6 and the second fraction by 7 over 7.

$\frac{1}{7}*\frac{6}{6}=\frac{6}{42}$

$\frac{5}{6}*\frac{7}{7}=\frac{35}{42}$

Add the numerators of the fractions to get the final answer.

$\frac{6}{42}+\frac{35}{42}=\frac{41}{42}$

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Example Question #12 : Adding And Subtracting Fractions

Add these fractions:

$\frac{1}{12}+\frac{1}{2}$

Possible Answers:

$\frac{5}{12}$

$\frac{7}{6}$

$\frac{5}{6}{}$

$\frac{7}{12}$

Correct answer:

$\frac{7}{12}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the second fraction by 6 over 6.

$\frac{1}{2}*\frac{6}{6}=\frac{6}{12}$

Add the numerators of the fractions to get the final answer.

$\frac{1}{12}+\frac{6}{12}=\frac{7}{12}$

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Example Question #32 : Fractions

Add these fractions:

$\frac{3}{7}+\frac{2}{5}$

Possible Answers:

$\frac{30}{35}$

$\frac{28}{35}$

$\frac{31}{35}$

$\frac{29}{35}$

Correct answer:

$\frac{29}{35}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 5 over 5 and the second fraction by 7 over 7.

$\frac{3}{7}*\frac{5}{5}=\frac{15}{35}$

$\frac{2}{5}*\frac{7}{7}=\frac{14}{35}$

Add the numerators of the fractions to get the final answer.

$\frac{15}{35}+\frac{14}{35}=\frac{29}{35}$

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Example Question #13 : Adding And Subtracting Fractions

Add these fractions:

$\frac{1}{10}+\frac{2}{5}$

Possible Answers:

$\frac{3}{5}$

$\frac{7}{10}$

$\frac{1}{3}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the second fraction by 2 over 2.

$\frac{2}{5}*\frac{2}{2}=\frac{4}{10}$

Add the numerators of these fractions and simplify to get the final answer.

$\\ \frac{1}{10}+\frac{4}{10}\\ \\=\frac{5}{10}=\frac{1\cdot 5}{2\cdot 5}=\frac{1}{2}$

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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 #11 : Adding And Subtracting Fractions

Example Question #11 : Adding And Subtracting Fractions

Example Question #11 : Adding And Subtracting Fractions

Example Question #14 : Adding And Subtracting Fractions

Example Question #44 : Fractions

Example Question #8 : Subtraction With Fractions

Example Question #1721 : Mathematical Relationships And Basic Graphs

Example Question #12 : Adding And Subtracting Fractions

Example Question #32 : Fractions

Example Question #13 : Adding And Subtracting Fractions

All Algebra II Resources

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