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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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All Common Core: 5th Grade Math Resources

7 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{5}{9}$ of an inch and a width of $\frac{1}{2}$ of an inch.

Possible Answers:

$\frac{5}{18}\text{ of an inch}^2$

$\frac{6}{11}\text{ of an inch}^2$

$\frac{9}{28}\text{ of an inch}^2$

$\frac{6}{18}\text{ of an inch}^2$

$\frac{5}{28}\text{ of an inch}^2$

Correct answer:

$\frac{5}{18}\text{ of an inch}^2$

Explanation:

To set up a tiled area model to solve the problem, we use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

5 18

We make the area model by because those are the denominators of our fractions. We shade up and over , because those are the numerators of our fractions. Our answer is a fraction made up of the boxes that are shaded (the numerator) and the total tiles in the area model (the denominator).

$\frac{5}{18}$

Notice that we could have multiplied the numerators of our fractions and the denominators of our fraction to find our answer.

$5\times1=5$

$9\times2=18$

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Example Question #22 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{3}{8}$ of an inch and a width of $\frac{3}{9}$ of an inch.

Possible Answers:

$\frac{9}{72}\text{ of an inch}^2$

$\frac{1}{72}\text{ of an inch}^2$

$\frac{6}{17}\text{ of an inch}^2$

$\frac{9}{17}\text{ of an inch}^2$

$\frac{5}{72}\text{ of an inch}^2$

Correct answer:

$\frac{9}{72}\text{ of an inch}^2$

Explanation:

To set up a tiled area model to solve the problem, we use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

9 72

$\frac{9}{72}$

Notice that we could have multiplied the numerators of our fractions and the denominators of our fraction to find our answer.

$3\times3=9$

$8\times9=72$

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Example Question #24 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

By tiling a rectangle with unit squares, find the area of a rectangle with a length of $\frac{8}{9}$ of an inch and a width of $\frac{1}{2}$ of an inch.

Possible Answers:

$\frac{8}{18}\text{ of an inch}^2$

$\frac{7}{18}\text{ of an inch}^2$

$\frac{9}{18}\text{ of an inch}^2$

$\frac{9}{11}\text{ of an inch}^2$

$\frac{8}{11}\text{ of an inch}^2$

Correct answer:

$\frac{8}{18}\text{ of an inch}^2$

Explanation:

To set up a tiled area model to solve the problem, we use the denominators for the dimensions of our area model, and we use the numerators to fill parts of the area model.

8 18

$\frac{8}{18}$

Notice that we could have multiplied the numerators of our fractions and the denominators of our fraction to find our answer.

$8\times1=8$

$9\times2=18$

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Example Question #361 : Number & Operations With Fractions

A rectangular yard measures $4\ ft\times 7\frac{1}{2}\ ft$ . Which of the following statements is TRUE?

Possible Answers:

The yard's area is the same as the yard's perimeter.

The area of the yard is twice the area of a sandbox that measures $2\ ft\times 3\frac{3}{4}\ ft$ .

Increasing both the width and length of the yard by the same amount will not change the area.

A playground that measures $9\ ft\times 3\ ft$ has the same area as the rectangular yard.

The yard is half the area of a playground that measures $6 ft \times 10 ft$

Correct answer:

The yard is half the area of a playground that measures $6 ft \times 10 ft$

Explanation:

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Example Question #1 : Interpret Multiplication As Scaling: Ccss.Math.Content.5.Nf.B.5

Which of the two quantities is larger?

Quantity A: $4\times9\times7$

Quantity B: $3\times8\times7$

Hint: You do not need to perform the multiplication to find the answer!

Possible Answers:

Quantity A and Quantity B are equal.

Quantity B

Quantity A

Correct answer:

Quantity A

Explanation:

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Example Question #1692 : Ssat Middle Level Quantitative (Math)

Fill in the blank with the correct sign.

$\small 5\times \frac{1}{3}$ __________ $\small 5$

Possible Answers:

$\small =$

$\small >$

$\small <$

Correct answer:

$\small <$

Explanation:

$\small 5\times \frac{1}{3}$ __________ $\small 5$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

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

$\small \frac{5}{3}=1\frac{2}{3}$ Because can go into $\small 5$ only time, and $\small \frac{2}{3}$ is left over.

$\small 1\frac{2}{3}$ __________ $\small 5$

$\small 1\frac{2}{3}<5$

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Example Question #362 : Number & Operations With Fractions

Fill in the blank with the correct sign.

$\small 7\times\frac{3}{4}$ __________ $\small 7$

Possible Answers:

$\small =$

Correct answer:

Explanation:

$\small 7\times\frac{3}{4}$ __________ $\small 7$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over Then we multiply like normal.

$\small \frac{7}{1}\times\frac{3}{4}=\frac{21}{4}$

$\small \frac{21}{4}=5\frac{1}{4}$ Because $\small 4$ can go into $\small 21$ only $\small 5$ times and $\small \frac{1}{4}$ is left over.

$\small 5\frac{1}{4}<7$

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Example Question #363 : Number & Operations With Fractions

Fill in the blank with the correct sign.

$\small 8$ __________ $\small 8\times\frac{1}{5}$

Possible Answers:

$\small =$

$\small >$

$\small <$

Correct answer:

$\small >$

Explanation:

$\small 8$ __________ $\small 8\times\frac{1}{5}$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{8}{1}\times\frac{1}{5}=\frac{8}{5}$

$\small \frac{8}{5}=1\frac{3}{5}$ Because $\small 5$ can go into $\small 8$ only $\small 1$ time and $\small \frac{3}{5}$ is left over.

$\small 8>1\frac{3}{5}$

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Example Question #364 : Number & Operations With Fractions

Fill in the blank with the correct sign.

$\small 2\times\frac{1}{2}$ __________

Possible Answers:

$\small <$

$\small >$

$\small =$

Correct answer:

$\small <$

Explanation:

$\small 2\times\frac{1}{2}$ __________

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

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

$\small \frac{2}{2}=1$ Because can go into an even $\small 1$ time.

$\small 1<2$

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Example Question #1701 : Ssat Middle Level Quantitative (Math)

Fill in the blank with the correct sign.

$\small 9$ __________ $\small \small 9\times\frac{2}{3}$

Possible Answers:

$\small >$

Correct answer:

$\small >$

Explanation:

$\small 9$ __________ $\small \small 9\times\frac{2}{3}$

When we multiply a fraction by a whole number, we first want to make the whole number into a fraction. We do that by putting the whole number over $\small 1.$ Then we multiply like normal.

$\small \frac{9}{1}\times\frac{2}{3}=\frac{18}{3}$

$\small \frac{18}{3}=6$ Because can go into $\small 18$ and even times.

$\small 9>6$

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All Common Core: 5th Grade Math Resources

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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 #21 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

Example Question #22 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

Example Question #24 : Find The Area Of A Rectangle With Fractional Side Lengths By Tiling: Ccss.Math.Content.5.Nf.B.4b

Example Question #361 : Number & Operations With Fractions

Example Question #1 : Interpret Multiplication As Scaling: Ccss.Math.Content.5.Nf.B.5

Example Question #1692 : Ssat Middle Level Quantitative (Math)

Example Question #362 : Number & Operations With Fractions

Example Question #363 : Number & Operations With Fractions

Example Question #364 : Number & Operations With Fractions

Example Question #1701 : Ssat Middle Level Quantitative (Math)

All Common Core: 5th Grade Math Resources

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