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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #43 : Fractions

Add these fractions:

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

Possible Answers:

$\frac{21}{35}$

$\frac{29}{35}$

$\frac{34}{35}$

$\frac{31}{35}$

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 #3 : Subtraction With Fractions

Subtract these fractions:

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

Possible Answers:

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

$\frac{1}{6}$

$\frac{2}{9}$

$\frac{1}{9}$

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 #1 : Subtraction With Fractions

Subtract these fractions:

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

Possible Answers:

$\frac{11}{12}$

$\frac{5}{12}$

$\frac{7}{15}$

$\frac{9}{12}$

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 #44 : Fractions

Add these fractions:

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

Possible Answers:

$\frac{39}{42}$

$\frac{20}{21}$

$\frac{43}{42}$

$\frac{41}{42}$

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:

$\frac{7}{12}$

$\frac{5}{12}$

$\frac{7}{6}$

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

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 #46 : Fractions

Add these fractions:

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

Possible Answers:

$\frac{30}{35}$

$\frac{31}{35}$

$\frac{28}{35}$

$\frac{29}{35}$

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:

$\frac{1}{2}$

$\frac{7}{10}$

$\frac{1}{3}$

$\frac{3}{5}$

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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Example Question #9 : Subtraction With Fractions

Subtract these fractions:

$\frac{3}{7}-\frac{1}{4}$

Possible Answers:

$\frac{9}{28}$

$\frac{11}{28}$

$\frac{3}{14}$

$\frac{5}{28}$

Correct answer:

$\frac{5}{28}$

Explanation:

To solve this we need to first find common denominators. We do that by multiplying the first fraction by 4 over 4 and the second fraction by 7 over 7.

$\frac{3}{7}*\frac{4}{4}=\frac{12}{28}$

$\frac{1}{4}*\frac{7}{7}=\frac{7}{28}$

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

$\frac{12}{28}-\frac{7}{28}=\frac{5}{28}$

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Example Question #10 : Subtraction With Fractions

Subtract these fractions:

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

Possible Answers:

$\frac{1}{36}$

$\frac{1}{17}$

$\frac{1}{72}$

$\frac{1}{24}$

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 #233 : Basic Arithmetic

Subtract these fractions:

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

Possible Answers:

$\frac{11}{21}$

$\frac{3}{7}$

$\frac{12}{21}$

$\frac{10}{21}$

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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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #43 : Fractions

Example Question #3 : Subtraction With Fractions

Example Question #1 : Subtraction With Fractions

Example Question #44 : Fractions

Example Question #12 : Adding And Subtracting Fractions

Example Question #46 : Fractions

Example Question #13 : Adding And Subtracting Fractions

Example Question #9 : Subtraction With Fractions

Example Question #10 : Subtraction With Fractions

Example Question #233 : Basic Arithmetic

All Algebra II Resources

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