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7th Grade Math : Operations

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

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Example Questions

Example Question #1 : Operations

Andrew spends every Saturday at the gym working out. He can complete $\frac{1}{12}$ of his workout in $\frac{1}{6}$ of an hour. If he continues at this rate, how much of his workout does Andrew complete per hour?

Possible Answers:

$\frac{1}{3}\textup{ of his workout}$

$\frac{1}{6}\textup{ of his workout}$

$\frac{1}{4}\textup{ of his workout}$

$\frac{1}{2}\textup{ of his workout}$

Correct answer:

$\frac{1}{2}\textup{ of his workout}$

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of his workout, $\frac{1}{12}$ , divided by hours, $\frac{1}{6}$ :

$\frac{\ \frac{1}{12}\ \textup{of a workout}}{\ \frac{1}{6}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

$\frac{1}{6}\rightarrow \frac{6}{1}$

Therefore:

$\frac{1}{12}\times\frac{6}{1}=\frac{6}{12}=\frac{1}{2}$

Andrew can complete $\frac{1}{2}$ of his workout per hour.

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Example Question #2 : Operations

Solve:

-12+4

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to start at on the number line.

Next, we have which means we need to move places to the right on the number line. When we have an addition sign (+) we move to the right because that is towards the positive side of the number line. When we have a subtraction sign (-) we move to the left because that is towards the negative side of the number line.

The orange arrow moved places to the right, and ended at ; thus,

-12+4=-8

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Example Question #3 : Operations

Solve:

$-35\div-5$

Possible Answers:

Correct answer:

Explanation:

We know the following information:

$35\div5=7$

In this particular case, do the negative numbers change our answer? . There are a couple of rules that we need to remember when multiplying with negative numbers:

A negative number divided by a positive number will always equal a negative number, and a positive number divided by a negative number will always equal a negative number.
A negative number divided by a negative number will always equal a positive number

Thus,

$-35\div-5=7$

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7th Grade Math : Operations

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

All 7th Grade Math Resources

Example Questions

Example Question #1 : Operations

Example Question #2 : Operations

Example Question #3 : Operations

All 7th Grade Math Resources

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