Division - GED Math

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Question

Divide:

$1,265 \div 5$

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Answer

Use the long division process:

$\left.\begin{matrix} 5 \end{matrix}\right| $\overline{1,265 }$$

$\underline{1; 0}$ 5 goes into 12 2 times; $5 \times 2 = 10$

$\begin{matrix} 26\ $\underline{25}$ \end{matrix}$ 5 goes into 26 5 times; $5 \times 5 = 25$

$\begin{matrix} 15\ $\underline{15}$ \end{matrix}$ 5 goes into 15 3 times; $5 \times 3 = 15$

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Question

Which of the following is an undefined expression?

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Answer

Both differences are defined, as there is no restriction on what two numbers can be subtracted. Zero divided by any nonzero number yields a quotient of zero, so $0 \div 100$ is defined and equal to zero. But zero cannot be a divisor. This makes $100 \div 0$ the undefined quantity.

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Question

If 10,000 is divided by 23, what is the remainder?

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Answer

Use the long division process.

The remainder is 18.

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Question

Forty friends are renting a party bus to the school prom. Rental of the party bus will cost $280 up front plus $20 per hour. The friends have the bus from 5:00 PM to 2:00 AM.

The friends have agreed to split the cost evenly. How much will each pay?

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Answer

From 5:00 PM to 2:00 AM will be

hours.

The bus will cost the students

$$280 + $20 \times 9 = $280 + $180 = \$460$ ,

which, divided evenly among 40 students, means that each will pay

$\$460 \div 40 = \$11.50$ .

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Question

Divide and rewrite as a mixed fraction: $\frac{198}{46}$

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Answer

Rewrite both the numerator and denominator using factors of two.

$\frac{198}{46}$ = $\frac{99\times 2}{23\times 2}$

Reduce this fraction.

$\frac{99}{23}$

The number 99 goes into 23 four times, since $23\times 4 = 92$ , and will have a remainder of seven.

The answer is: $4$\frac{7}{23}$$

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Question

Divide the following:

$\frac{2}{3}$ \div $\frac{1}{2}$

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Answer

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction. To find the reciprocal of a fraction, the numerator becomes the denominator, and the denominator becomes the numerator. In other words, we will flip the fraction. So, we get

$\frac{2}{3}$ \div $\frac{1}{2}$

$\frac{2}{3}$ \cdot $\frac{2}{1}$

$\frac{2 \cdot 2}{3 \cdot 1}$

$\frac{4}{3}$

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Question

Which number is not a factor of 66?

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Answer

Divide 66 by each of the four choices. The division that yields a nonzero remainder reveals the number that is not a factor.

$66 \div 6 = 11$

$66 \cdot 11 = 6$

$66 \div 12 = 5 \textrm{ R }6$

$66 \div 22 = 3$

66 divided by 6, 11, or 22 yields a zero remainder; 66 divided by 12 yields a nonzero remainder. Therefore, 12 is the nonfactor.

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Question

Solve for $\small n$ : $\small nm=p+r$

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Answer

In order to solve for $\small n$ , we'll need to move all the other variables to the other side of the equation. Currently $\small n$ is stuck to $\small m$ , so we need to move the $\small m$ to the other side.

In order to move $\small m$ , we'll have to divide it to the other side of the equation.

$\small nm=p+r$

$\small n=\frac{p+r}{m}$$

Since all the variables are different, we cannot do anything else to simplify this equation.

Our answer is $\small n=\frac{p+r}{m}$$

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Question

Solve for $\small x$ : $\small 2x=6y+4z$

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Answer

In order to solve for $\small x$ , we need to move all the numbers and variables to the other side of the equation.

We can see that $\small x$ is currently being multiplied by $\small 2$ . In order to move the $\small 2$ , we need to divide it on the other side of the equation.

$\small 2x=6y+4z$

$\small x=\frac{6y+4z}{2}$$

Both $\small 6$ and $\small 4$ can be divided by $\small 2$ , which in turn gets rid of the $\small 2$ in the denominator.

$\small x=3y+2z$

We cannot proceed any farther since there is nothing left to do in the equation.

Our answer is $\small x=3y+2z$

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Question

Solve for $\small x$ : $\small $\frac{2}{x}$=y$

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Answer

In order to solve for $\small x$ , we'll need to move all of the variables on its side to the other side of the equation.

We can see that $\small x$ is currently the denominator to $\small 2$ , so we need to move the $\small 2$ in order to solve for $\small x$ .

To move the $\small 2$ , we'll have to divide it on the other side. Keep in mind though that the $\small 2$ is in the numerator, so it will stay in the numerator when it divides over.

$\small $\frac{2}{x}$=y$

$\small x=\frac{2}{y}$$

We cannot proceed with the question as there is nothing left to do. Our variables are different and the $\small 2$ can stay where it is.

Our answer is $\small x=\frac{2}{y}$$

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Question

Solve the equation: $\frac{8}{2}$

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Answer

Division is another way of seeing how many of the number we are dividing with is in the number we are dividing.

Let's take a look at . This is the number we are dividing, and is the number we are dividing with as told by their placement. We want to see how many 's there are in .

To figure this out, we'll add a each time until we get to .

We have now reached , so how many 's did it take us to get there? It took us 's to get to , and if you check with a calculator you will see that this is the answer as well.

Our answer is .

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Question

If 10,000 is divided by 23, what is the remainder?

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Answer

Use the long division process.

The remainder is 18.

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Question

Divide:

$1,265 \div 5$

Tap to reveal answer

Answer

Use the long division process:

$\left.\begin{matrix} 5 \end{matrix}\right| $\overline{1,265 }$$

$\underline{1; 0}$ 5 goes into 12 2 times; $5 \times 2 = 10$

$\begin{matrix} 26\ $\underline{25}$ \end{matrix}$ 5 goes into 26 5 times; $5 \times 5 = 25$

$\begin{matrix} 15\ $\underline{15}$ \end{matrix}$ 5 goes into 15 3 times; $5 \times 3 = 15$

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Question

Which of the following is an undefined expression?

Do not use a calculator.

Tap to reveal answer

Answer

Both differences are defined, as there is no restriction on what two numbers can be subtracted. Zero divided by any nonzero number yields a quotient of zero, so $0 \div 100$ is defined and equal to zero. But zero cannot be a divisor. This makes $100 \div 0$ the undefined quantity.

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Question

Forty friends are renting a party bus to the school prom. Rental of the party bus will cost $280 up front plus $20 per hour. The friends have the bus from 5:00 PM to 2:00 AM.

The friends have agreed to split the cost evenly. How much will each pay?

Tap to reveal answer

Answer

From 5:00 PM to 2:00 AM will be

hours.

The bus will cost the students

$$280 + $20 \times 9 = $280 + $180 = \$460$ ,

which, divided evenly among 40 students, means that each will pay

$\$460 \div 40 = \$11.50$ .

← Didn't Know|Knew It →

Question

Divide and rewrite as a mixed fraction: $\frac{198}{46}$

Tap to reveal answer

Answer

Rewrite both the numerator and denominator using factors of two.

$\frac{198}{46}$ = $\frac{99\times 2}{23\times 2}$

Reduce this fraction.

$\frac{99}{23}$

The number 99 goes into 23 four times, since $23\times 4 = 92$ , and will have a remainder of seven.

The answer is: $4$\frac{7}{23}$$

← Didn't Know|Knew It →

Question

Divide the following:

$\frac{2}{3}$ \div $\frac{1}{2}$

Tap to reveal answer

Answer

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction. To find the reciprocal of a fraction, the numerator becomes the denominator, and the denominator becomes the numerator. In other words, we will flip the fraction. So, we get

$\frac{2}{3}$ \div $\frac{1}{2}$

$\frac{2}{3}$ \cdot $\frac{2}{1}$

$\frac{2 \cdot 2}{3 \cdot 1}$

$\frac{4}{3}$

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Question

Which number is not a factor of 66?

Tap to reveal answer

Answer

Divide 66 by each of the four choices. The division that yields a nonzero remainder reveals the number that is not a factor.

$66 \div 6 = 11$

$66 \cdot 11 = 6$

$66 \div 12 = 5 \textrm{ R }6$

$66 \div 22 = 3$

66 divided by 6, 11, or 22 yields a zero remainder; 66 divided by 12 yields a nonzero remainder. Therefore, 12 is the nonfactor.

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Question

Solve for $\small n$ : $\small nm=p+r$

Tap to reveal answer

Answer

In order to solve for $\small n$ , we'll need to move all the other variables to the other side of the equation. Currently $\small n$ is stuck to $\small m$ , so we need to move the $\small m$ to the other side.

In order to move $\small m$ , we'll have to divide it to the other side of the equation.

$\small nm=p+r$

$\small n=\frac{p+r}{m}$$

Since all the variables are different, we cannot do anything else to simplify this equation.

Our answer is $\small n=\frac{p+r}{m}$$

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Question

Solve for $\small x$ : $\small 2x=6y+4z$

Tap to reveal answer

Answer

In order to solve for $\small x$ , we need to move all the numbers and variables to the other side of the equation.

We can see that $\small x$ is currently being multiplied by $\small 2$ . In order to move the $\small 2$ , we need to divide it on the other side of the equation.

$\small 2x=6y+4z$

$\small x=\frac{6y+4z}{2}$$

Both $\small 6$ and $\small 4$ can be divided by $\small 2$ , which in turn gets rid of the $\small 2$ in the denominator.

$\small x=3y+2z$

We cannot proceed any farther since there is nothing left to do in the equation.

Our answer is $\small x=3y+2z$

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