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Common Core: 5th Grade Math : Measurement & Data

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

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Example Questions

Example Question #1 : Measurement & Data

What is the area, in meters, of a rectangle that is 200 centimeters long and 5 meters wide?

(1 meter is equivalent to 100 centimeters.)

Possible Answers:

$1000\ cm^2$ $\displaystyle 1000\ cm^2$

$10\ m$ $\displaystyle 10\ m$

$1000\ m^2$ $\displaystyle 1000\ m^2$

$10\ m^2$ $\displaystyle 10\ m^2$

$20\ m^2$ $\displaystyle 20\ m^2$

Correct answer:

$10\ m^2$ $\displaystyle 10\ m^2$

Explanation:

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Example Question #2 : Measurement & Data

How many feet $\displaystyle feet$ are in $72\ inches?$ $\displaystyle 72\ inches?$

Possible Answers:

$\displaystyle 5$

$\displaystyle 8$

$\displaystyle 4$

$\displaystyle 6$

$\displaystyle 7$

Correct answer:

$\displaystyle 6$

Explanation:

To solve this problem we can make proportions.

We know that $1\ foot=12\ inches$ $\displaystyle 1\ foot=12\ inches$, and we can use $\displaystyle x$ has our unknown.

$\frac{1\ foot}{12\ inches}=\frac{x\ feet}{72\ inches}$ $\displaystyle \frac{1\ foot}{12\ inches}=\frac{x\ feet}{72\ inches}$

Next, we want to cross multiply and divide to isolate the $\displaystyle x$ on one side.

$12\ inches\times x\ feet= 1\ foot \times 72\ inches$ $\displaystyle 12\ inches\times x\ feet= 1\ foot \times 72\ inches$

$6\ feet= \frac{1\ foot \times 72\ inches}{12\ inches}$ $\displaystyle 6\ feet= \frac{1\ foot \times 72\ inches}{12\ inches}$

The $\yards$ $\displaystyle \yards$ $\ inches$ $\displaystyle \ inches$ will cancel and we are left with $6\ feet$ $\displaystyle 6\ feet$

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Example Question #3 : Measurement & Data

How many meters $\displaystyle meters$ are in $6\ centimeters?$ $\displaystyle 6\ centimeters?$

Possible Answers:

$\displaystyle 6$

$\displaystyle .06$

$\displaystyle 60$

$\displaystyle .006$

600 $\displaystyle 600$

Correct answer:

$\displaystyle .06$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ $\displaystyle 1\ centimeter= .01\ meters$ and we can use $\displaystyle x$ as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{6\ centimeters}{x\ meters}$ $\displaystyle \frac{1\ centimeter}{.01\ meter}=\frac{6\ centimeters}{x\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times x\ meters=.01\ meter\times 6\ centimeters$ $\displaystyle 1\ centimeter\times x\ meters=.01\ meter\times 6\ centimeters$

$x\ meters=\frac{.01\ meter\times 6\ centimeters}{1\ centimeter}$ $\displaystyle x\ meters=\frac{.01\ meter\times 6\ centimeters}{1\ centimeter}$

The $\displaystyle centimeters$ will cancel and we are left with $.06\ meters$ $\displaystyle .06\ meters$

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Example Question #4 : Measurement & Data

How many $\displaystyle centimeters$ are in $3\ meters?$ $\displaystyle 3\ meters?$

Possible Answers:

3,000 $\displaystyle 3,000$

$\displaystyle 3$

300 $\displaystyle 300$

$\displaystyle 30$

$\displaystyle .03$

Correct answer:

300 $\displaystyle 300$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ $\displaystyle 1\ centimeter= .01\ meters$ and we can use $\displaystyle x$ as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{3\ meters}$ $\displaystyle \frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{3\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 3\ meters=.01\ meter\times x\ centimeters$ $\displaystyle 1\ centimeter\times 3\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 3\ meters}{.01\ meter}= x\ centimeters$ $\displaystyle \frac{1\ centimeter\times 3\ meters}{.01\ meter}= x\ centimeters$

The meters $\displaystyle meters$ will cancel and we are left with $300\ centimeters$ $\displaystyle 300\ centimeters$

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Example Question #4 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

How many $\displaystyle centimeters$ are in $7\ meters?$ $\displaystyle 7\ meters?$

Possible Answers:

$\displaystyle 70$

$\displaystyle .07$

700 $\displaystyle 700$

7,000 $\displaystyle 7,000$

$\displaystyle .007$

Correct answer:

700 $\displaystyle 700$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ $\displaystyle 1\ centimeter= .01\ meters$ and we can use $\displaystyle x$ as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{7\ meters}$ $\displaystyle \frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{7\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 7\ meters=.01\ meter\times x\ centimeters$ $\displaystyle 1\ centimeter\times 7\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 7\ meters}{.01\ meter}= x\ centimeters$ $\displaystyle \frac{1\ centimeter\times 7\ meters}{.01\ meter}= x\ centimeters$

The meters $\displaystyle meters$ will cancel and we are left with $700\ centimeters$ $\displaystyle 700\ centimeters$

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Example Question #5 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

How many $\displaystyle centimeters$ are in $9\ meters?$ $\displaystyle 9\ meters?$

Possible Answers:

$\displaystyle .009$

$\displaystyle .09$

900 $\displaystyle 900$

$\displaystyle 90$

9,000 $\displaystyle 9,000$

Correct answer:

900 $\displaystyle 900$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ $\displaystyle 1\ centimeter= .01\ meters$ and we can use $\displaystyle x$ as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{9\ meters}$ $\displaystyle \frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{9\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 9\ meters=.01\ meter\times x\ centimeters$ $\displaystyle 1\ centimeter\times 9\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 9\ meters}{.01\ meter}= x\ centimeters$ $\displaystyle \frac{1\ centimeter\times 9\ meters}{.01\ meter}= x\ centimeters$

The meters $\displaystyle meters$ will cancel and we are left with $900\ centimeters$ $\displaystyle 900\ centimeters$

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Example Question #6 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

How many $\displaystyle centimeters$ are in $17\ meters?$ $\displaystyle 17\ meters?$

Possible Answers:

1.7 $\displaystyle 1.7$

$\displaystyle .0017$

1,700 $\displaystyle 1,700$

170 $\displaystyle 170$

17,000 $\displaystyle 17,000$

Correct answer:

1,700 $\displaystyle 1,700$

Explanation:

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ $\displaystyle 1\ centimeter= .01\ meters$ and we can use $\displaystyle x$ as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{17\ meters}$ $\displaystyle \frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{17\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 17\ meters=.01\ meter\times x\ centimeters$ $\displaystyle 1\ centimeter\times 17\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 17\ meters}{.01\ meter}= x\ centimeters$ $\displaystyle \frac{1\ centimeter\times 17\ meters}{.01\ meter}= x\ centimeters$

The meters $\displaystyle meters$ will cancel and we are left with $1,700\ centimeters$ $\displaystyle 1,700\ centimeters$

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Example Question #3 : Measurement

How many inches $\displaystyle inches$ are in $6\ yards?$ $\displaystyle 6\ yards?$

Possible Answers:

216 $\displaystyle 216$

246 $\displaystyle 246$

200 $\displaystyle 200$

232 $\displaystyle 232$

304 $\displaystyle 304$

Correct answer:

216 $\displaystyle 216$

Explanation:

To solve this problem we can make proportions.

We know that $1\ yard=36\ inches$ $\displaystyle 1\ yard=36\ inches$, and we can use $\displaystyle x$ as our unknown.

$\frac{1\ yard}{36\ inches}=\frac{6\ yards}{x\ inches}$ $\displaystyle \frac{1\ yard}{36\ inches}=\frac{6\ yards}{x\ inches}$

Next, we want to cross multiply and divide to isolate the $\displaystyle x$ on one side.

$36\ inches\times 6\ yards= 1\ yard \times x\ inches$ $\displaystyle 36\ inches\times 6\ yards= 1\ yard \times x\ inches$

$\frac{36\ inches\times 6\ yards}{1\ yard}= 216\ inches$ $\displaystyle \frac{36\ inches\times 6\ yards}{1\ yard}= 216\ inches$

The $\yards$ $\displaystyle \yards$ $\ yards$ $\displaystyle \ yards$ will cancel and we are left with $216\ inches$ $\displaystyle 216\ inches$

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Example Question #8 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

How many inches $\displaystyle inches$ are in $3\ yards?$ $\displaystyle 3\ yards?$

Possible Answers:

108 $\displaystyle 108$

116 $\displaystyle 116$

$\displaystyle 36$

112 $\displaystyle 112$

$\displaystyle 49$

Correct answer:

108 $\displaystyle 108$

Explanation:

To solve this problem we can make proportions.

We know that $1\ yard=36\ inches$ $\displaystyle 1\ yard=36\ inches$, and we can use $\displaystyle x$ as our unknown.

$\frac{1\ yard}{36\ inches}=\frac{3\ yards}{x\ inches}$ $\displaystyle \frac{1\ yard}{36\ inches}=\frac{3\ yards}{x\ inches}$

Next, we want to cross multiply and divide to isolate the $\displaystyle x$ on one side.

$36\ inches\times 3\ yards= 1\ yard \times x\ inches$ $\displaystyle 36\ inches\times 3\ yards= 1\ yard \times x\ inches$

$\frac{36\ inches\times 3\ yards}{1\ yard}= 108\ inches$ $\displaystyle \frac{36\ inches\times 3\ yards}{1\ yard}= 108\ inches$

The $\yards$ $\displaystyle \yards$ $\ yards$ $\displaystyle \ yards$ will cancel and we are left with $108\ inches$ $\displaystyle 108\ inches$

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Example Question #9 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

How many yards $\displaystyle yards$ are in $396\ inches?$ $\displaystyle 396\ inches?$

Possible Answers:

$\displaystyle 11$

$\displaystyle 10$

$\displaystyle 8$

$\displaystyle 7$

$\displaystyle 9$

Correct answer:

$\displaystyle 11$

Explanation:

To solve this problem we can make proportions.

We know that $1\ yard=36\ inches$ $\displaystyle 1\ yard=36\ inches$, and we can use $\displaystyle x$ as our unknown.

$\frac{1\ yard}{36\ inches}=\frac{x\ yards}{396\ inches}$ $\displaystyle \frac{1\ yard}{36\ inches}=\frac{x\ yards}{396\ inches}$

Next, we want to cross multiply and divide to isolate the $\displaystyle x$ on one side.

$36\ inches\times x\ yards= 1\ yard \times 396\ inches$ $\displaystyle 36\ inches\times x\ yards= 1\ yard \times 396\ inches$

$11\ yards= \frac{1\ yard \times 396\ inches}{36\ inches}$ $\displaystyle 11\ yards= \frac{1\ yard \times 396\ inches}{36\ inches}$

The $\yards$ $\displaystyle \yards$ $\ inches$ $\displaystyle \ inches$ will cancel and we are left with $11\ yards$ $\displaystyle 11\ yards$

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Common Core: 5th Grade Math : Measurement & Data

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

All Common Core: 5th Grade Math Resources

Example Questions

Example Question #1 : Measurement & Data

Example Question #2 : Measurement & Data

Example Question #3 : Measurement & Data

Example Question #4 : Measurement & Data

Example Question #4 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

Example Question #5 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

Example Question #6 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

Example Question #3 : Measurement

Example Question #8 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

Example Question #9 : Convert Among Different Sized Standard Measurement Units: Ccss.Math.Content.5.Md.A.1

All Common Core: 5th Grade Math Resources

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