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Common Core: 5th Grade Math : Number & Operations with Fractions

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

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Example Questions

Example Question #773 : Fractions

Emily is trying out for the track team this year. On Monday she ran $\displaystyle 12$ laps. On Tuesday she runs $2\tfrac{1}{3}$ $\displaystyle 2\tfrac{1}{3}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$26\frac{1}{3}\ laps$ $\displaystyle 26\frac{1}{3}\ laps$

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

$28\frac{1}{3}\ laps$ $\displaystyle 28\frac{1}{3}\ laps$

$28\ laps$ $\displaystyle 28\ laps$

$24\frac{1}{3}\ laps$ $\displaystyle 24\frac{1}{3}\ laps$

Correct answer:

$28\ laps$ $\displaystyle 28\ laps$

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.

$2\frac{1}{3}=\frac{7}{3}$ $\displaystyle 2\frac{1}{3}=\frac{7}{3}$

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

$\frac{12}{1}\times\frac{7}{3}=\frac{84}{3}$ $\displaystyle \frac{12}{1}\times\frac{7}{3}=\frac{84}{3}$

Finally, reduce to find your final answer.

$\frac{84}{3}=28$ $\displaystyle \frac{84}{3}=28$

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Example Question #774 : Fractions

Emily is trying out for the track team this year. On Monday she ran $\displaystyle 15$ laps. On Tuesday she runs $2\tfrac{1}{3}$ $\displaystyle 2\tfrac{1}{3}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$10\frac{1}{3}\ laps$ $\displaystyle 10\frac{1}{3}\ laps$

$30\frac{1}{3}\ laps$ $\displaystyle 30\frac{1}{3}\ laps$

$10\frac{1}{2}\ laps$ $\displaystyle 10\frac{1}{2}\ laps$

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

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

Correct answer:

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

Explanation:

$2\frac{1}{3}=\frac{7}{3}$ $\displaystyle 2\frac{1}{3}=\frac{7}{3}$

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

$\frac{15}{1}\times\frac{7}{3}=\frac{105}{3}$ $\displaystyle \frac{15}{1}\times\frac{7}{3}=\frac{105}{3}$

Finally, reduce to find your final answer.

$\frac{105}{3}=35$ $\displaystyle \frac{105}{3}=35$

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Example Question #775 : Fractions

Emily is trying out for the track team this year. On Monday she ran $\displaystyle 21$ laps. On Tuesday she runs $2\tfrac{1}{3}$ $\displaystyle 2\tfrac{1}{3}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$42\frac{1}{3}\ laps$ $\displaystyle 42\frac{1}{3}\ laps$

$49\ laps$ $\displaystyle 49\ laps$

$42\ laps$ $\displaystyle 42\ laps$

$42\frac{1}{2}\ laps$ $\displaystyle 42\frac{1}{2}\ laps$

$47\frac{1}{3}\ laps$ $\displaystyle 47\frac{1}{3}\ laps$

Correct answer:

$49\ laps$ $\displaystyle 49\ laps$

Explanation:

$2\frac{1}{3}=\frac{7}{3}$ $\displaystyle 2\frac{1}{3}=\frac{7}{3}$

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

$\frac{21}{1}\times\frac{7}{3}=\frac{147}{3}$ $\displaystyle \frac{21}{1}\times\frac{7}{3}=\frac{147}{3}$

Finally, reduce to find your final answer.

$\frac{147}{3}=49$ $\displaystyle \frac{147}{3}=49$

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Example Question #776 : Fractions

Claire is trying out for the track team this year. On Monday she ran $\displaystyle 12$ laps. On Tuesday she runs $1\tfrac{2}{3}$ $\displaystyle 1\tfrac{2}{3}$ times as many laps as she did on Monday. How many laps does she run on

Possible Answers:

$12\frac{2}{3}\ laps$ $\displaystyle 12\frac{2}{3}\ laps$

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

$36\frac{2}{3}\ laps$ $\displaystyle 36\frac{2}{3}\ laps$

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

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

Correct answer:

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

Explanation:

$1\frac{2}{3}=\frac{5}{3}$ $\displaystyle 1\frac{2}{3}=\frac{5}{3}$

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

$\frac{12}{1}\times\frac{5}{3}=\frac{60}{3}$ $\displaystyle \frac{12}{1}\times\frac{5}{3}=\frac{60}{3}$

Finally, reduce to find your final answer.

$\frac{60}{3}=20$ $\displaystyle \frac{60}{3}=20$

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Example Question #777 : Fractions

Claire is trying out for the track team this year. On Monday she ran $\displaystyle 18$ laps. On Tuesday she runs $1\tfrac{2}{3}$ $\displaystyle 1\tfrac{2}{3}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

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

$30\frac{2}{3}\ laps$ $\displaystyle 30\frac{2}{3}\ laps$

$9\frac{1}{3}\ laps$ $\displaystyle 9\frac{1}{3}\ laps$

$9\ laps$ $\displaystyle 9\ laps$

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

Correct answer:

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

Explanation:

$1\frac{2}{3}=\frac{5}{3}$ $\displaystyle 1\frac{2}{3}=\frac{5}{3}$

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

$\frac{18}{1}\times\frac{5}{3}=\frac{90}{3}$ $\displaystyle \frac{18}{1}\times\frac{5}{3}=\frac{90}{3}$

Finally, reduce to find your final answer.

$\frac{90}{3}=30$ $\displaystyle \frac{90}{3}=30$

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Example Question #778 : Fractions

Claire is trying out for the track team this year. On Monday she ran $\displaystyle 22$ laps. On Tuesday she runs $1\tfrac{2}{3}$ $\displaystyle 1\tfrac{2}{3}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$44\ laps$ $\displaystyle 44\ laps$

$36\ laps$ $\displaystyle 36\ laps$

$44\frac{2}{3}\ laps$ $\displaystyle 44\frac{2}{3}\ laps$

$26\frac{1}{3}\ laps$ $\displaystyle 26\frac{1}{3}\ laps$

$36\frac{2}{3}\ laps$ $\displaystyle 36\frac{2}{3}\ laps$

Correct answer:

$36\frac{2}{3}\ laps$ $\displaystyle 36\frac{2}{3}\ laps$

Explanation:

$1\frac{2}{3}=\frac{5}{3}$ $\displaystyle 1\frac{2}{3}=\frac{5}{3}$

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

$\frac{22}{1}\times\frac{5}{3}=\frac{110}{3}$ $\displaystyle \frac{22}{1}\times\frac{5}{3}=\frac{110}{3}$

Finally, reduce to find your final answer.

$\frac{110}{3}=36\frac{2}{3}$ $\displaystyle \frac{110}{3}=36\frac{2}{3}$

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Example Question #779 : Fractions

Molly is trying out for the track team this year. On Monday she ran $\displaystyle 12$ laps. On Tuesday she runs $1\tfrac{2}{5}$ $\displaystyle 1\tfrac{2}{5}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$16\frac{4}{5}\ laps$ $\displaystyle 16\frac{4}{5}\ laps$

$12\frac{2}{5}\ laps$ $\displaystyle 12\frac{2}{5}\ laps$

$16\frac{2}{5}\ laps$ $\displaystyle 16\frac{2}{5}\ laps$

$24\frac{2}{5}\ laps$ $\displaystyle 24\frac{2}{5}\ laps$

$60\ laps$ $\displaystyle 60\ laps$

Correct answer:

$16\frac{4}{5}\ laps$ $\displaystyle 16\frac{4}{5}\ laps$

Explanation:

$1\frac{2}{5}=\frac{7}{5}$ $\displaystyle 1\frac{2}{5}=\frac{7}{5}$

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

$\frac{12}{1}\times\frac{7}{5}=\frac{84}{5}$ $\displaystyle \frac{12}{1}\times\frac{7}{5}=\frac{84}{5}$

Finally, reduce to find your final answer.

$\frac{84}{5}=16\frac{4}{5}$ $\displaystyle \frac{84}{5}=16\frac{4}{5}$

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Example Question #780 : Fractions

Molly is trying out for the track team this year. On Monday she ran $\displaystyle 15$ laps. On Tuesday she runs $1\tfrac{2}{5}$ $\displaystyle 1\tfrac{2}{5}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

$30\frac{1}{5}\ laps$ $\displaystyle 30\frac{1}{5}\ laps$

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

$21\frac{1}{5}\ laps$ $\displaystyle 21\frac{1}{5}\ laps$

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

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

Correct answer:

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

Explanation:

$1\frac{2}{5}=\frac{7}{5}$ $\displaystyle 1\frac{2}{5}=\frac{7}{5}$

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

$\frac{15}{1}\times\frac{7}{5}=\frac{105}{5}$ $\displaystyle \frac{15}{1}\times\frac{7}{5}=\frac{105}{5}$

Finally, reduce to find your final answer.

$\frac{105}{5}=21$ $\displaystyle \frac{105}{5}=21$

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Example Question #781 : Fractions

Molly is trying out for the track team this year. On Monday she ran $\displaystyle 13$ laps. On Tuesday she runs $1\tfrac{2}{5}$ $\displaystyle 1\tfrac{2}{5}$ times as many laps as she did on Monday. How many laps does she run on Tuesday?

Possible Answers:

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

$18\frac{1}{5}\ laps$ $\displaystyle 18\frac{1}{5}\ laps$

$26\frac{1}{5}\ laps$ $\displaystyle 26\frac{1}{5}\ laps$

$26\frac{1}{3}\ laps$ $\displaystyle 26\frac{1}{3}\ laps$

$25\ laps$ $\displaystyle 25\ laps$

Correct answer:

$18\frac{1}{5}\ laps$ $\displaystyle 18\frac{1}{5}\ laps$

Explanation:

$1\frac{2}{5}=\frac{7}{5}$ $\displaystyle 1\frac{2}{5}=\frac{7}{5}$

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

$\frac{13}{1}\times\frac{7}{5}=\frac{91}{5}$ $\displaystyle \frac{13}{1}\times\frac{7}{5}=\frac{91}{5}$

Finally, reduce to find your final answer.

$\frac{91}{5}=18\frac{1}{5}$ $\displaystyle \frac{91}{5}=18\frac{1}{5}$

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Example Question #782 : Fractions

Hannah is trying out for the track team this year. On Monday she ran $\displaystyle 12$ 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:

$24\frac{1}{4}\ laps$ $\displaystyle 24\frac{1}{4}\ laps$

$15\ laps$ $\displaystyle 15\ laps$

$48\ laps$ $\displaystyle 48\ laps$

$15\frac{1}{4}\ laps$ $\displaystyle 15\frac{1}{4}\ laps$

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

Correct answer:

$15\ laps$ $\displaystyle 15\ laps$

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.

$\frac{12}{1}\times\frac{5}{4}=\frac{60}{4}$ $\displaystyle \frac{12}{1}\times\frac{5}{4}=\frac{60}{4}$

Finally, reduce to find your final answer.

$\frac{60}{4}=15$ $\displaystyle \frac{60}{4}=15$

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Common Core: 5th Grade Math : Number & Operations with Fractions

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

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #773 : Fractions

Example Question #774 : Fractions

Example Question #775 : Fractions

Example Question #776 : Fractions

Example Question #777 : Fractions

Example Question #778 : Fractions

Example Question #779 : Fractions

Example Question #780 : Fractions

Example Question #781 : Fractions

Example Question #782 : Fractions

All Common Core: 5th Grade Math Resources

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