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Common Core: 5th Grade Math : Solve Real World Problems Involving Multiplication of Fractions and Mixed Numbers: CCSS.Math.Content.5.NF.B.6

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All Common Core: 5th Grade Math Resources

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Example Questions

Example Question #261 : How To Multiply Fractions

Hannah is trying out for the track team this year. On Monday she ran $\displaystyle 5$ laps. On Tuesday she runs $1\tfrac{1}{4}$ $\displaystyle 1\tfrac{1}{4}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$10\ laps$ $\displaystyle 10\ laps$

$6\ laps$ $\displaystyle 6\ laps$

$10\frac{3}{4}\ laps$ $\displaystyle 10\frac{3}{4}\ laps$

$6\frac{1}{4}\ laps$ $\displaystyle 6\frac{1}{4}\ laps$

$20\ laps$ $\displaystyle 20\ laps$

Correct answer:

$6\frac{1}{4}\ laps$ $\displaystyle 6\frac{1}{4}\ laps$

Explanation:

First, you need to change the mixed number into an improper fraction. To do this, you multiply the denominator by the whole number, then add the numerator. That number becomes the numerator of your improper fraction. The denominator stays the same.

$1\frac{1}{4}=\frac{5}{4}$ $\displaystyle 1\frac{1}{4}=\frac{5}{4}$

Then put your whole number over $\displaystyle 1$ to make it a fraction, and multiply like normal.

$\frac{5}{1}\times\frac{5}{4}=\frac{25}{4}$ $\displaystyle \frac{5}{1}\times\frac{5}{4}=\frac{25}{4}$

Finally, reduce to find your final answer.

$\frac{25}{4}=6\frac{1}{4}$ $\displaystyle \frac{25}{4}=6\frac{1}{4}$

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Example Question #262 : How To Multiply Fractions

Hannah is trying out for the track team this year. On Monday she ran $\displaystyle 3$ laps. On Tuesday she runs $1\tfrac{1}{4}$ $\displaystyle 1\tfrac{1}{4}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$5\ laps$ $\displaystyle 5\ laps$

$12\frac{1}{4}\ laps$ $\displaystyle 12\frac{1}{4}\ laps$

$12\ laps$ $\displaystyle 12\ laps$

$7\ laps$ $\displaystyle 7\ laps$

$3\frac{3}{4}\ laps$ $\displaystyle 3\frac{3}{4}\ laps$

Correct answer:

$3\frac{3}{4}\ laps$ $\displaystyle 3\frac{3}{4}\ laps$

Explanation:

$1\frac{1}{4}=\frac{5}{4}$ $\displaystyle 1\frac{1}{4}=\frac{5}{4}$

Then put your whole number over $\displaystyle 1$ to make it a fraction, and multiply like normal.

$\frac{3}{1}\times\frac{5}{4}=\frac{15}{4}$ $\displaystyle \frac{3}{1}\times\frac{5}{4}=\frac{15}{4}$

Finally, reduce to find your final answer.

$\frac{15}{4}=3\frac{3}{4}$ $\displaystyle \frac{15}{4}=3\frac{3}{4}$

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Example Question #781 : Fractions

Lauren is trying out for the track team this year. On Monday she ran $\displaystyle 12$ laps. On Tuesday she runs $3\tfrac{1}{4}$ $\displaystyle 3\tfrac{1}{4}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$39\ laps$ $\displaystyle 39\ laps$

$36\frac{1}{4}\ laps$ $\displaystyle 36\frac{1}{4}\ laps$

$34\ laps$ $\displaystyle 34\ laps$

$35\ laps$ $\displaystyle 35\ laps$

$36\frac{3}{4}\ laps$ $\displaystyle 36\frac{3}{4}\ laps$

Correct answer:

$39\ laps$ $\displaystyle 39\ laps$

Explanation:

$3\frac{1}{4}=\frac{13}{4}$ $\displaystyle 3\frac{1}{4}=\frac{13}{4}$

Then put your whole number over $\displaystyle 1$ to make it a fraction, and multiply like normal.

$\frac{12}{1}\times\frac{13}{4}=\frac{156}{4}$ $\displaystyle \frac{12}{1}\times\frac{13}{4}=\frac{156}{4}$

Finally, reduce to find your final answer.

$\frac{156}{4}=39$ $\displaystyle \frac{156}{4}=39$

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Example Question #782 : Fractions

Lauren is trying out for the track team this year. On Monday she ran $\displaystyle 3$ laps. On Tuesday she runs $3\tfrac{1}{4}$ $\displaystyle 3\tfrac{1}{4}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$14\ laps$ $\displaystyle 14\ laps$

$9\frac{1}{4}\ laps$ $\displaystyle 9\frac{1}{4}\ laps$

$12\ laps$ $\displaystyle 12\ laps$

$9\frac{3}{4}\ laps$ $\displaystyle 9\frac{3}{4}\ laps$

$12\frac{1}{4}\ laps$ $\displaystyle 12\frac{1}{4}\ laps$

Correct answer:

$9\frac{3}{4}\ laps$ $\displaystyle 9\frac{3}{4}\ laps$

Explanation:

$3\frac{1}{4}=\frac{13}{4}$ $\displaystyle 3\frac{1}{4}=\frac{13}{4}$

Then put your whole number over $\displaystyle 1$ to make it a fraction, and multiply like normal.

$\frac{3}{1}\times\frac{13}{4}=\frac{39}{4}$ $\displaystyle \frac{3}{1}\times\frac{13}{4}=\frac{39}{4}$

Finally, reduce to find your final answer.

$\frac{39}{4}=9\frac{3}{4}$ $\displaystyle \frac{39}{4}=9\frac{3}{4}$

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Example Question #783 : Fractions

Lauren is trying out for the track team this year. On Monday she ran $\displaystyle 4$ laps. On Tuesday she runs $3\tfrac{1}{4}$ $\displaystyle 3\tfrac{1}{4}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$24\ laps$ $\displaystyle 24\ laps$

$13\ laps$ $\displaystyle 13\ laps$

$16\ laps$ $\displaystyle 16\ laps$

$13\frac{3}{4}\ laps$ $\displaystyle 13\frac{3}{4}\ laps$

$21\ laps$ $\displaystyle 21\ laps$

Correct answer:

$13\ laps$ $\displaystyle 13\ laps$

Explanation:

$3\frac{1}{4}=\frac{13}{4}$ $\displaystyle 3\frac{1}{4}=\frac{13}{4}$

Then put your whole number over $\displaystyle 1$ to make it a fraction, and multiply like normal.

$\frac{4}{1}\times\frac{13}{4}=\frac{52}{4}$ $\displaystyle \frac{4}{1}\times\frac{13}{4}=\frac{52}{4}$

Finally, reduce to find your final answer.

$\frac{52}{4}=13$ $\displaystyle \frac{52}{4}=13$

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Example Question #791 : Fractions

Lauren is trying out for the track team this year. On Monday she ran $\displaystyle 2$ laps. On Tuesday she runs $3\tfrac{1}{4}$ $\displaystyle 3\tfrac{1}{4}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$6\ laps$ $\displaystyle 6\ laps$

$24\ laps$ $\displaystyle 24\ laps$

$26\ laps$ $\displaystyle 26\ laps$

$9\frac{3}{4}\ laps$ $\displaystyle 9\frac{3}{4}\ laps$

$6\frac{1}{2}\ laps$ $\displaystyle 6\frac{1}{2}\ laps$

Correct answer:

$6\frac{1}{2}\ laps$ $\displaystyle 6\frac{1}{2}\ laps$

Explanation:

$3\frac{1}{4}=\frac{13}{4}$ $\displaystyle 3\frac{1}{4}=\frac{13}{4}$

Then put your whole number over $\displaystyle 1$ to make it a fraction, and multiply like normal.

$\frac{2}{1}\times\frac{13}{4}=\frac{26}{4}$ $\displaystyle \frac{2}{1}\times\frac{13}{4}=\frac{26}{4}$

Finally, reduce to find your final answer.

$\frac{26}{4}=6\frac{2}{4}$ $\displaystyle \frac{26}{4}=6\frac{2}{4}$

$\frac{2}{4}\div\frac{2}{2}=\frac{1}{2}$ $\displaystyle \frac{2}{4}\div\frac{2}{2}=\frac{1}{2}$

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

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Example Question #792 : Fractions

Lauren is trying out for the track team this year. On Monday she ran $\displaystyle 10$ laps. On Tuesday she runs $3\tfrac{1}{4}$ $\displaystyle 3\tfrac{1}{4}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$30\ laps$ $\displaystyle 30\ laps$

$32\frac{1}{2}\ laps$ $\displaystyle 32\frac{1}{2}\ laps$

$30\frac{2}{4}\ laps$ $\displaystyle 30\frac{2}{4}\ laps$

$30\frac{3}{4}\ laps$ $\displaystyle 30\frac{3}{4}\ laps$

$32\ laps$ $\displaystyle 32\ laps$

Correct answer:

$32\frac{1}{2}\ laps$ $\displaystyle 32\frac{1}{2}\ laps$

Explanation:

$3\frac{1}{4}=\frac{13}{4}$ $\displaystyle 3\frac{1}{4}=\frac{13}{4}$

Then put your whole number over $\displaystyle 1$ to make it a fraction, and multiply like normal.

$\frac{10}{1}\times\frac{13}{4}=\frac{130}{4}$ $\displaystyle \frac{10}{1}\times\frac{13}{4}=\frac{130}{4}$

Finally, reduce to find your final answer.

$\frac{130}{4}=32\frac{2}{4}$ $\displaystyle \frac{130}{4}=32\frac{2}{4}$

$\frac{2}{4}\div\frac{2}{2}=\frac{1}{2}$ $\displaystyle \frac{2}{4}\div\frac{2}{2}=\frac{1}{2}$

$32\frac{1}{2}$ $\displaystyle 32\frac{1}{2}$

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Example Question #793 : Fractions

Lauren is trying out for the track team this year. On Monday she ran $\displaystyle 7$ laps. On Tuesday she runs $3\tfrac{1}{4}$ $\displaystyle 3\tfrac{1}{4}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$22\frac{1}{4}\ laps$ $\displaystyle 22\frac{1}{4}\ laps$

$22\frac{3}{4}\ laps$ $\displaystyle 22\frac{3}{4}\ laps$

$19\ laps$ $\displaystyle 19\ laps$

$21\frac{3}{4}\ laps$ $\displaystyle 21\frac{3}{4}\ laps$

$21\ laps$ $\displaystyle 21\ laps$

Correct answer:

$22\frac{3}{4}\ laps$ $\displaystyle 22\frac{3}{4}\ laps$

Explanation:

$3\frac{1}{4}=\frac{13}{4}$ $\displaystyle 3\frac{1}{4}=\frac{13}{4}$

Then put your whole number over $\displaystyle 1$ to make it a fraction, and multiply like normal.

$\frac{7}{1}\times\frac{13}{4}=\frac{91}{4}$ $\displaystyle \frac{7}{1}\times\frac{13}{4}=\frac{91}{4}$

Finally, reduce to find your final answer.

$\frac{91}{4}=22\frac{3}{4}$ $\displaystyle \frac{91}{4}=22\frac{3}{4}$

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Example Question #794 : Fractions

A recipe calls for $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ of a cup of flour. If you only want to make half of the recipe, how much flour do you need?

Possible Answers:

$\frac{3}{4}\ cup$ $\displaystyle \frac{3}{4}\ cup$

$\frac{1}{2}\ cup$ $\displaystyle \frac{1}{2}\ cup$

$\frac{1}{8}\ cup$ $\displaystyle \frac{1}{8}\ cup$

$\frac{3}{8}\ cup$ $\displaystyle \frac{3}{8}\ cup$

$\frac{2}{4}\ cup$ $\displaystyle \frac{2}{4}\ cup$

Correct answer:

$\frac{1}{8}\ cup$ $\displaystyle \frac{1}{8}\ cup$

Explanation:

When you cut something in half, you can either divide by $\displaystyle 2$ or multiply by $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ . Remember, when you divide fractions, you actually multiply by the reciprocal. The reciprocal of $\displaystyle 2$ is $\frac{1}{2}$ $\displaystyle \frac{1}{2}$ .

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

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Example Question #795 : Fractions

A recipe calls for $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a cup of flour. If you only want to make half of the recipe, how much flour do you need?

Possible Answers:

$\frac{1}{8}\ cup$ $\displaystyle \frac{1}{8}\ cup$

$\frac{3}{4}\ cup$ $\displaystyle \frac{3}{4}\ cup$

$\frac{1}{4}\ cup$ $\displaystyle \frac{1}{4}\ cup$

$\frac{2}{8}\ cup$ $\displaystyle \frac{2}{8}\ cup$

$\frac{3}{8}\ cup$ $\displaystyle \frac{3}{8}\ cup$

Correct answer:

$\frac{3}{8}\ cup$ $\displaystyle \frac{3}{8}\ cup$

Explanation:

$\frac{3}{4}\times\frac{1}{2}=\frac{3}{8}$ $\displaystyle \frac{3}{4}\times\frac{1}{2}=\frac{3}{8}$

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All Common Core: 5th Grade Math Resources

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Common Core: 5th Grade Math : Solve Real World Problems Involving Multiplication of Fractions and Mixed Numbers: CCSS.Math.Content.5.NF.B.6

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

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #261 : How To Multiply Fractions

Example Question #262 : How To Multiply Fractions

Example Question #781 : Fractions

Example Question #782 : Fractions

Example Question #783 : Fractions

Example Question #791 : Fractions

Example Question #792 : Fractions

Example Question #793 : Fractions

Example Question #794 : Fractions

Example Question #795 : Fractions

All Common Core: 5th Grade Math Resources

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