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:

\(\displaystyle \frac{3}{5}+\frac{2}{7}\)

Possible Answers:

\(\displaystyle \frac{21}{35}\)

\(\displaystyle \frac{29}{35}\)

\(\displaystyle \frac{34}{35}\)

\(\displaystyle \frac{31}{35}\)

Correct answer:

\(\displaystyle \frac{31}{35}\)

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.

\(\displaystyle \frac{3}{5}*\frac{7}{7}=\frac{21}{35}\)

\(\displaystyle \frac{2}{7}*\frac{5}{5}=\frac{10}{35}\)

Add these fractions together, to get the final answer.

\(\displaystyle \frac{21}{35}+\frac{10}{35}=\frac{31}{35}\)

Example Question #12 : Adding And Subtracting Fractions

Subtract these fractions:

\(\displaystyle \frac{2}{3}-\frac{1}{2}\)

Possible Answers:

\(\displaystyle \frac{5}{6}{}\)

\(\displaystyle \frac{1}{9}\)

\(\displaystyle \frac{2}{9}\)

\(\displaystyle \frac{1}{6}\)

Correct answer:

\(\displaystyle \frac{1}{6}\)

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.

\(\displaystyle \frac{2}{3}*\frac{2}{2}=\frac{4}{6}\)

\(\displaystyle \frac{1}{2}*\frac{3}{3}=\frac{3}{6}\)

Subtract these fractions to get the final answer.

\(\displaystyle \frac{4}{6}-\frac{3}{6}=\frac{1}{6}\)

Example Question #1 : Subtraction With Fractions

Subtract these fractions:

\(\displaystyle \frac{4}{5}-\frac{1}{3}\)

Possible Answers:

\(\displaystyle \frac{11}{12}\)

\(\displaystyle \frac{5}{12}\)

\(\displaystyle \frac{7}{15}\)

\(\displaystyle \frac{9}{12}\)

Correct answer:

\(\displaystyle \frac{7}{15}\)

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.

\(\displaystyle \frac{4}{5}*\frac{3}{3}=\frac{12}{15}\)

\(\displaystyle \frac{1}{3}*\frac{5}{5}=\frac{5}{15}\)

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

\(\displaystyle \frac{12}{15}-\frac{5}{15}=\frac{7}{15}\)

Example Question #44 : Fractions

Add these fractions:

\(\displaystyle \frac{1}{7}+\frac{5}{6}\)

Possible Answers:

\(\displaystyle \frac{39}{42}\)

\(\displaystyle \frac{20}{21}\)

\(\displaystyle \frac{43}{42}\)

\(\displaystyle \frac{41}{42}\)

Correct answer:

\(\displaystyle \frac{41}{42}\)

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.

\(\displaystyle \frac{1}{7}*\frac{6}{6}=\frac{6}{42}\)

\(\displaystyle \frac{5}{6}*\frac{7}{7}=\frac{35}{42}\)

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

\(\displaystyle \frac{6}{42}+\frac{35}{42}=\frac{41}{42}\)

 

Example Question #1721 : Mathematical Relationships And Basic Graphs

Add these fractions:

\(\displaystyle \frac{1}{12}+\frac{1}{2}\)

Possible Answers:

\(\displaystyle \frac{7}{6}\)

\(\displaystyle \frac{5}{6}{}\)

\(\displaystyle \frac{7}{12}\)

\(\displaystyle \frac{5}{12}\)

Correct answer:

\(\displaystyle \frac{7}{12}\)

Explanation:

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

\(\displaystyle \frac{1}{2}*\frac{6}{6}=\frac{6}{12}\)

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

\(\displaystyle \frac{1}{12}+\frac{6}{12}=\frac{7}{12}\)

 

Example Question #46 : Fractions

Add these fractions:

\(\displaystyle \frac{3}{7}+\frac{2}{5}\)

Possible Answers:

\(\displaystyle \frac{30}{35}\)

\(\displaystyle \frac{31}{35}\)

\(\displaystyle \frac{28}{35}\)

\(\displaystyle \frac{29}{35}\)

Correct answer:

\(\displaystyle \frac{29}{35}\)

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.

\(\displaystyle \frac{3}{7}*\frac{5}{5}=\frac{15}{35}\)

\(\displaystyle \frac{2}{5}*\frac{7}{7}=\frac{14}{35}\)

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

\(\displaystyle \frac{15}{35}+\frac{14}{35}=\frac{29}{35}\)

Example Question #1722 : Mathematical Relationships And Basic Graphs

Add these fractions:

\(\displaystyle \frac{1}{10}+\frac{2}{5}\)

Possible Answers:

\(\displaystyle \frac{1}{2}\)

\(\displaystyle \frac{3}{5}\)

\(\displaystyle \frac{1}{3}\)

\(\displaystyle \frac{7}{10}\)

Correct answer:

\(\displaystyle \frac{1}{2}\)

Explanation:

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

\(\displaystyle \frac{2}{5}*\frac{2}{2}=\frac{4}{10}\)

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

\(\displaystyle \\ \frac{1}{10}+\frac{4}{10}\\ \\=\frac{5}{10}=\frac{1\cdot 5}{2\cdot 5}=\frac{1}{2}\)

Example Question #9 : Subtraction With Fractions

Subtract these fractions:

\(\displaystyle \frac{3}{7}-\frac{1}{4}\)

Possible Answers:

\(\displaystyle \frac{9}{28}\)

\(\displaystyle \frac{11}{28}\)

\(\displaystyle \frac{3}{14}\)

\(\displaystyle \frac{5}{28}\)

Correct answer:

\(\displaystyle \frac{5}{28}\)

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.

\(\displaystyle \frac{3}{7}*\frac{4}{4}=\frac{12}{28}\)

\(\displaystyle \frac{1}{4}*\frac{7}{7}=\frac{7}{28}\)

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

\(\displaystyle \frac{12}{28}-\frac{7}{28}=\frac{5}{28}\)

Example Question #10 : Subtraction With Fractions

Subtract these fractions:

\(\displaystyle \frac{1}{8}-\frac{1}{9}\)

Possible Answers:

\(\displaystyle \frac{1}{36}\)

\(\displaystyle \frac{1}{17}\)

\(\displaystyle \frac{1}{72}\)

\(\displaystyle \frac{1}{24}\)

Correct answer:

\(\displaystyle \frac{1}{72}\)

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.

\(\displaystyle \frac{1}{8}*\frac{9}{9}=\frac{9}{72}\)

\(\displaystyle \frac{1}{9}*\frac{8}{8}=\frac{8}{72}\)

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

\(\displaystyle \frac{9}{72}-\frac{8}{72}=\frac{1}{72}\)

Example Question #232 : Basic Arithmetic

Subtract these fractions:

\(\displaystyle \frac{6}{7}-\frac{1}{3}\)

Possible Answers:

\(\displaystyle \frac{10}{21}\)

\(\displaystyle \frac{11}{21}\)

\(\displaystyle \frac{3}{7}\)

\(\displaystyle \frac{12}{21}\)

Correct answer:

\(\displaystyle \frac{11}{21}\)

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.

\(\displaystyle \frac{6}{7}*\frac{3}{3}=\frac{18}{21}\)

\(\displaystyle \frac{1}{3}*\frac{7}{7}=\frac{7}{21}\)

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

\(\displaystyle \frac{18}{21}-\frac{7}{21}=\frac{11}{21}\)

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