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Common Core: 5th Grade Math : Add Fractions with Unlike Denominators

Study concepts, example questions & explanations for Common Core: 5th Grade Math

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Example Questions

Example Question #1 : Add Fractions With Unlike Denominators

$\frac{1}{4}+\frac{1}{2}$

Possible Answers:

$\frac{1}{2}$

$\frac{2}{6}$

$\frac{3}{4}$

$\frac{1}{3}$

$\frac{2}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

$\frac{1}{4}+\frac{1}{2}$

In order to solve this problem, we first have to find common denominators.

$\frac{1}{2}\times\frac{2}{2}=\frac{2}{4}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{1}{4}+\frac{2}{4}=\frac{3}{4}$

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Example Question #2 : Add Fractions With Unlike Denominators

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

Possible Answers:

$\frac{7}{20}$

$\frac{1}{7}$

$\frac{8}{10}$

$\frac{2}{7}$

$\frac{7}{10}$

Correct answer:

$\frac{7}{10}$

Explanation:

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

In order to solve this problem, we first have to find common denominators.

$\frac{1}{5}\times\frac{2}{2}=\frac{2}{10}$

$\frac{1}{2}\times \frac{5}{5}=\frac{5}{10}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{2}{10}+\frac{5}{10}=\frac{7}{10}$

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Example Question #3 : Add Fractions With Unlike Denominators

$\frac{1}{3}+\frac{2}{5}$

Possible Answers:

$\frac{3}{8}$

$\frac{2}{8}$

$\frac{15}{11}$

$\frac{11}{15}$

$\frac{11}{30}$

Correct answer:

$\frac{11}{15}$

Explanation:

$\frac{1}{3}+\frac{2}{5}$

In order to solve this problem, we first have to find common denominators.

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

$\frac{2}{5}\times\frac{3}{3}=\frac{6}{15}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{5}{15}+\frac{6}{15}=\frac{11}{15}$

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Example Question #4 : Add Fractions With Unlike Denominators

$\frac{1}{2}+\frac{2}{7}$

Possible Answers:

$\frac{3}{9}$

$\frac{11}{14}$

$\frac{11}{28}}$

$\frac{14}{11}$

$\frac{1}{3}$

Correct answer:

$\frac{11}{14}$

Explanation:

$\frac{1}{2}+\frac{2}{7}$

In order to solve this problem, we first have to find common denominators.

$\frac{1}{2}\times\frac{7}{7}=\frac{7}{14}$

$\frac{2}{7}\times\frac{2}{2}=\frac{4}{14}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{7}{14}+\frac{4}{14}=\frac{11}{14}$

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Example Question #5 : Add Fractions With Unlike Denominators

$\frac{3}{4}+\frac{1}{3}=$

Possible Answers:

$\frac{7}{4}$

$\frac{13}{24}$

$1\frac{1}{12}$

$\frac{12}{13}$

$\frac{4}{7}$

Correct answer:

$1\frac{1}{12}$

Explanation:

$\frac{3}{4}+\frac{1}{3}$

In order to solve this problem, we first have to find common denominators.

$\frac{3}{4}\times\frac{3}{3}=\frac{9}{12}$

$\frac{1}{3}\times\frac{4}{4}=\frac{4}{12}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{9}{12}+\frac{4}{12}=\frac{13}{12}$

$\frac{13}{12}=1\frac{1}{12}$ because can go into one time, with one left over.

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Example Question #6 : Add Fractions With Unlike Denominators

$\frac{5}{6}+\frac{2}{4}$

Possible Answers:

$\frac{24}{16}$

$\frac{12}{16}$

$1\frac{1}{3}$

$\frac{7}{10}$

$\frac{16}{24}$

Correct answer:

$1\frac{1}{3}$

Explanation:

$\frac{5}{6}+\frac{2}{4}$

In order to solve this problem, we first have to find common denominators.

$\frac{5}{6}\times\frac{2}{2}=\frac{10}{12}$

$\frac{2}{4}\times\frac{3}{3}=\frac{6}{12}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{10}{12}+\frac{6}{12}=\frac{16}{12}$

$\frac{16}{12}=1\frac{4}{12}=1\frac{1}{3}$ because and go into one time with four left over. $\frac{4}{12}$ can be reduced to $\frac{1}{3}$ by dividing the numerator and the denominator by

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Example Question #7 : Add Fractions With Unlike Denominators

Solve the following:

$\frac{2}{3}+\frac{1}{7}$

Possible Answers:

$\frac{17}{42}$

$\frac{16}{21}$

$\frac{1}{5}$

$\frac{17}{21}$

$\frac{3}{10}$

Correct answer:

$\frac{17}{21}$

Explanation:

$\frac{2}{3}+\frac{1}{7}$

In order to solve this problem, we first have to find common denominators.

$\frac{2}{3}\times\frac{7}{7}=\frac{14}{21}$

$\frac{1}{7}\times\frac{3}{3}=\frac{3}{21}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{14}{21}+\frac{3}{21}=\frac{17}{21}$

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Example Question #8 : Add Fractions With Unlike Denominators

Solve:

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

Possible Answers:

$\frac{5}{6}$

$1\frac{1}{6}$

$\frac{3}{5}$

$\frac{6}{7}$

$\frac{7}{12}$

Correct answer:

$1\frac{1}{6}$

Explanation:

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

In order to solve this problem, we first have to find common denominators.

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

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

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{4}{6}+\frac{3}{6}=\frac{7}{6}$

$\frac{7}{6}=1\frac{1}{6}$ because can go into one time with $\frac{1}{6}$ left over.

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Example Question #9 : Add Fractions With Unlike Denominators

Solve:

$\frac{1}{4}+\frac{4}{8}$

Possible Answers:

$\frac{3}{4}$

$\frac{8}{6}$

$\frac{5}{12}$

$\frac{12}5{}$

$\frac{1}{2}$

Correct answer:

$\frac{3}{4}$

Explanation:

$\frac{1}{4}+\frac{4}{8}$

In order to solve this problem, we first have to find common denominators.

$\frac{1}{4}\times\frac{2}{2}=\frac{2}{8}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{2}{8}+\frac{4}{8}=\frac{6}{8}$

$\frac{6}{8}\div\frac{2}{2}=\frac{3}{4}$

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Example Question #10 : Add Fractions With Unlike Denominators

Solve:

$\frac{4}6{+\frac{3}{8}}$

Possible Answers:

$\frac{1}{2}$

$\frac{25}{48}$

$1\frac{1}{24}$

$\frac{7}{14}$

$\frac{24}{25}$

Correct answer:

$1\frac{1}{24}$

Explanation:

$\frac{4}6{+\frac{3}{8}}$

In order to solve this problem, we first have to find common denominators.

$\frac{4}{6}\times\frac{4}{4}=\frac{16}{24}$

$\frac{3}{8}\times\frac{3}{3}=\frac{9}{24}$

Now that we have common denominators, we can add the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{16}{24}+\frac{9}{24}=\frac{25}{24}$

$\frac{25}{24}=1\frac{1}{24}$ because can go into one time with left over.

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Common Core: 5th Grade Math : Add Fractions with Unlike Denominators

Study concepts, example questions & explanations for Common Core: 5th Grade Math

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #1 : Add Fractions With Unlike Denominators

Example Question #2 : Add Fractions With Unlike Denominators

Example Question #3 : Add Fractions With Unlike Denominators

Example Question #4 : Add Fractions With Unlike Denominators

Example Question #5 : Add Fractions With Unlike Denominators

Example Question #6 : Add Fractions With Unlike Denominators

Example Question #7 : Add Fractions With Unlike Denominators

Example Question #8 : Add Fractions With Unlike Denominators

Example Question #9 : Add Fractions With Unlike Denominators

Example Question #10 : Add Fractions With Unlike Denominators

All Common Core: 5th Grade Math Resources

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