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Basic Arithmetic : Addition with Fractions

Study concepts, example questions & explanations for Basic Arithmetic

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Example Questions

Example Question #1721 : Mathematical Relationships And Basic Graphs

Add these fractions:

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

Possible Answers:

$\frac{39}{42}$ $\displaystyle \frac{39}{42}$

$\frac{41}{42}$ $\displaystyle \frac{41}{42}$

$\frac{43}{42}$ $\displaystyle \frac{43}{42}$

$\frac{20}{21}$ $\displaystyle \frac{20}{21}$

Correct answer:

$\frac{41}{42}$ $\displaystyle \frac{41}{42}$

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.

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

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

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

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

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Example Question #43 : Fractions

Add these fractions:

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

Possible Answers:

$\frac{31}{35}$ $\displaystyle \frac{31}{35}$

$\frac{30}{35}$ $\displaystyle \frac{30}{35}$

$\frac{29}{35}$ $\displaystyle \frac{29}{35}$

$\frac{28}{35}$ $\displaystyle \frac{28}{35}$

Correct answer:

$\frac{29}{35}$ $\displaystyle \frac{29}{35}$

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.

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

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

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

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

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Basic Arithmetic : Addition with Fractions

Study concepts, example questions & explanations for Basic Arithmetic

All Basic Arithmetic Resources

Example Questions

Example Question #1721 : Mathematical Relationships And Basic Graphs

Example Question #43 : Fractions

All Basic Arithmetic Resources

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