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Common Core: 7th Grade Math : Grade 7

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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All Common Core: 7th Grade Math Resources

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Example Questions

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Example Question #9 :How To Find Circumference

Ashley has a square room in her apartment that measures 81 square feet. What is the circumference of the largest circular area rug that she can fit in the space?

Possible Answers:

$18\pi$

$9\pi$

$8\pi$

$10\pi$

$81\pi$

Correct answer:

$9\pi$

Explanation:

我n order to solve this question, first calculate the length of each side of the room.

A=s^2

81=s^2

s=9

The length of each side of the room is also equal to the length of the diameter of the largest circular rug that can fit in the room. Since $C=\pi d$ , the circumference is simply

$C=9\pi$

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Example Question #1 :Finding Theoretical Probability

Kelly spun a spinner, which is pictured below,次了。她在桌上provi记录她的结果ded. What is the theoretical probability of the spinner landing on the orange section?

Screen shot 2016 03 03 at 9.49.24 am

Possible Answers:

$\frac{2}{3}$

$\frac{1}{6}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

The theoretical probability is what should happen. In this case, we havespaces andof those spaces is orange; thus, the theoretical probability of the spinner landing on orange should always be $\frac{2}{6}$ or $\frac{1}{3}$

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Example Question #2 :Finding Theoretical Probability

Kelly spun a spinner, which is pictured below,次了。她在桌上provi记录她的结果ded. What is the theoretical probability of the spinner landing on the yellow section?

Screen shot 2016 03 03 at 10.09.46 am

Possible Answers:

$\frac{1}{6}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

The theoretical probability is what should happen. In this case, we havespaces andof those spaces is yellow; thus, the theoretical probability of the spinner landing on yellow should always be $\frac{3}{6}$ or $\frac{1}{2}$

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Example Question #3 :Finding Theoretical Probability

Kelly spun a spinner, which is pictured below,次了。她在桌上provi记录她的结果ded. What is the theoretical probability of the spinner landing on the green section?

Screen shot 2016 03 03 at 10.09.46 am

Possible Answers:

$\frac{1}{2}$

$\frac{1}{6}$

$\frac{2}{6}$

Correct answer:

$\frac{1}{6}$

Explanation:

The theoretical probability is what should happen. In this case, we havespaces andof those spaces is green; thus, the theoretical probability of the spinner landing on green should always be $\frac{1}{6}$

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Example Question #4 :Finding Theoretical Probability

Kelly spun a spinner, which is pictured below,次了。她在桌上provi记录她的结果ded. Is the experimental probability of landing on pink more likely, less likely, or equally likely in comparison to the theoretical probability?

Screen shot 2016 03 03 at 9.14.25 am

Possible Answers:

Equally likely

Results can't be found based on the data provided

Less likely

More likely

Correct answer:

More likely

Explanation:

The theoretical probability is what should happen. In this case, we havespaces and这些空间是粉色;因此,理论支持bability of the spinner landing on pink should always be $\frac{1}{6}$

The experimental probability is what actually happened in an experiment. In this case, Kelly spun the spinnertimes, and she landed on pink $\frac{13}{50}$ times; thus, our experimental probability is $\frac{13}{50}$

我n order to compare the theoretical probability and the experimental probability let's convert the fractions into decimals so we can put them on a number line:

$\frac{1}{6}=0.17$

$\frac{13}{50}=0.26$

A probability closer tomeans that an event is more likely to occur. In this case, 0.26 is closer to; thus, the experimental probability is more likely than the theoretical probability.

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Example Question #5 :Finding Theoretical Probability

Kelly spun a spinner, which is pictured below,次了。她在桌上provi记录她的结果ded. Is the experimental probability of landing on orange more likely, less likely, or equally likely in comparison to the theoretical probability?

Screen shot 2016 03 03 at 9.49.24 am

Possible Answers:

More likely

Results can't be found based on the data provided

Less likely

Equally likely

Correct answer:

More likely

Explanation:

The experimental probability is what actually happened in an experiment. In this case, Kelly spun the spinnertimes, and she landed on orange $\frac{13}{35}$ times; thus, our experimental probability is $\frac{13}{35}$

我n order to compare the theoretical probability and the experimental probability let's convert the fractions into decimals so we can put them on a number line:

$\frac{1}{3}=0.33$

$\frac{13}{35}=0.37$

A probability closer tomeans that an event is more likely to occur. In this case, 0.37 is closer to; thus, the experimental probability is more likely than the theoretical probability.

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Example Question #6 :Finding Theoretical Probability

Kelly spun a spinner, which is pictured below,次了。The spinner had six equally-sized sections, each of a different color, and she recorded her results in the table provided. What is the theoretical probability of the spinner landing on the pink section?

Screen shot 2016 03 03 at 9.14.25 am

Possible Answers:

$\frac{13}{50}$

$\frac{12}{50}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{6}$

Explanation:

The theoretical probability is what should happen. In this case, we havespaces and这些空间是粉色;因此,理论支持bability of the spinner landing on pink should always be $\frac{1}{6}$

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Example Question #1 :Finding Experimental Probability

Kelly spun a spinner, which is pictured below,次了。她在桌上provi记录她的结果ded. What is the experimental probability of the spinner landing on the pink section?

Screen shot 2016 03 03 at 9.14.25 am

Possible Answers:

$8\frac{1}{3}$

$\frac{12}{50}$

$\frac{1}{6}$

$\frac{13}{50}$

Correct answer:

$\frac{13}{50}$

Explanation:

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Example Question #2 :Finding Experimental Probability

Kelly spun a spinner, which is pictured below,次了。她在桌上provi记录她的结果ded. What is the experimental probability of the spinner landing on the orange section?

Screen shot 2016 03 03 at 9.49.24 am

Possible Answers:

$\frac{2}{6}$

$\frac{13}{35}$

$\frac{1}{3}$

Correct answer:

$\frac{13}{35}$

Explanation:

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Example Question #3 :Finding Experimental Probability

Kelly spun a spinner, which is pictured below,次了。她在桌上provi记录她的结果ded. What is the experimental probability of the spinner landing on the yellow section?

Screen shot 2016 03 03 at 10.09.46 am

Possible Answers:

$\frac{7}{20}$

$\frac{11}{40}$

Correct answer:

$\frac{7}{20}$

Explanation:

The experimental probability is what actually happened in an experiment. In this case, Kelly spun the spinnertimes, and she landed on yellow $\frac{14}{40}$ times; thus, our experimental probability is $\frac{14}{40}=\frac{7}{20}$

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Common Core: 7th Grade Math : Grade 7

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #9 :How To Find Circumference

Example Question #1 :Finding Theoretical Probability

Example Question #2 :Finding Theoretical Probability

Example Question #3 :Finding Theoretical Probability

Example Question #4 :Finding Theoretical Probability

Example Question #5 :Finding Theoretical Probability

Example Question #6 :Finding Theoretical Probability

Example Question #1 :Finding Experimental Probability

Example Question #2 :Finding Experimental Probability

Example Question #3 :Finding Experimental Probability

All Common Core: 7th Grade Math Resources

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