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Q1 Which of the following is an example of using the Division Property of Equality to rearrange the equation AB = xCD?

c = AB - xD
D = ABxC
x = AB/CD
C = xD/AB

9 answers

To use the Division Property of Equality, we need to isolate one variable by dividing both sides of the equation by a non-zero value.

In the equation \( AB = xCD \), if we want to isolate \( x \), we can do this by dividing both sides by \( CD \):

\[ x = \frac{AB}{CD} \]

So, the correct answer that represents using the Division Property of Equality to rearrange the equation \( AB = xCD \) is:

x = AB/CD

Which of the following is an example of using the Division Property of Equality to rearrange the equation AB = xCD?

c = AB - xD
D = ABxC
x = AB/CD
C = xD/AB

To use the Division Property of Equality with the equation \( AB = xCD \), we would isolate \( x \) by dividing both sides of the equation by \( CD \). This gives us:

\[ x = \frac{AB}{CD} \]

Therefore, the correct option that demonstrates the use of the Division Property of Equality in rearranging the equation \( AB = xCD \) is:

x = AB/CD

Q2 Consider the formula that relates distance, velocity, and time (d = vt). If you are interested in the time it takes for a snail traveling at a speed of 2 centimeters per second to crawl up a 1-meter section of a wall, which unit conversion makes the most sense to use?
A. Converting meters to centimeters by dividing 1 meter by 100 centimeters.
B. Converting meters to centimeters by multiplying 1 meter by 100.
C. Converting meters to centimeters by multiplying 1 meter by (1 meter)/(100 centimeters)
D. Converting meters to centimeters by multiplying 1 meter by (100 centimeters)/(1 meter)

(show your work, original and like a 9th grader wrote it)

To solve the problem and find out how long it takes for a snail traveling at 2 centimeters per second to crawl up a 1-meter section of a wall, we first need to make sure all the units are consistent.

Since the speed of the snail is given in centimeters per second, we need to convert the distance from meters to centimeters because 1 meter equals 100 centimeters.

Conversion Options:

  1. A. Converting meters to centimeters by dividing 1 meter by 100 centimeters.

    • This option doesn’t make sense because dividing by 100 gives a smaller number, which is incorrect for converting meters to centimeters.

  2. B. Converting meters to centimeters by multiplying 1 meter by 100.

    • This is the correct method! Since 1 meter is equal to 100 centimeters, this shows that we are using the correct conversion factor.

  3. C. Converting meters to centimeters by multiplying 1 meter by (1 meter)/(100 centimeters).

    • This option is confusing and incorrect because it effectively divides the meter by 100, which is not how we convert meters to centimeters.

  4. D. Converting meters to centimeters by multiplying 1 meter by (100 centimeters)/(1 meter).

    • Although this option would yield the correct final result of 100 centimeters, it’s unnecessarily complex and not the straightforward multiplication needed for a simple conversion.

The Best Option:

The best option for converting from meters to centimeters is B. Converting meters to centimeters by multiplying 1 meter by 100.

Show the Work:

  1. Convert Distance: \[ 1 \text{ meter} \times 100 \frac{\text{centimeters}}{\text{meter}} = 100 \text{ centimeters} \]

  2. Calculate Time using the formula \( d = vt \):

    • Rearranging the formula to find time \( t = \frac{d}{v} \) \[ t = \frac{100 \text{ cm}}{2 \text{ cm/s}} = 50 \text{ seconds} \]

So it takes the snail 50 seconds to crawl up the 1-meter section of the wall.

Q3 Consider the formula that relates distance, velocity, and time (d = vt). If you are interested in the time it takes for a mouse traveling at a speed of 5 feet per minute to run across a 30-yard field, which unit conversion makes the most sense to use?
a. Converting yards to feet by dividing 30 yards by 3 feet.
b. Converting yards to feet by multiplying 30 yards by 3.
c. Converting yards to feet by multiplying 30 yards by 1 yard/3 feet
d. Converting yards to feet by multiplying 30 yards by 3 feet/1 yard

(show your work, original and like a 9th grader wrote it)

To solve the problem of how long it takes for a mouse running at a speed of 5 feet per minute to run across a 30-yard field, we first need to ensure that the units are consistent. Since the speed of the mouse is given in feet per minute, we need to convert yards to feet because 1 yard equals 3 feet.

Conversion Options:

  1. a. Converting yards to feet by dividing 30 yards by 3 feet.

    • This doesn't make sense for conversion because dividing by 3 would give a smaller value, which is incorrect for converting yards to feet.

  2. b. Converting yards to feet by multiplying 30 yards by 3.

    • This option is correct! Since 1 yard equals 3 feet, multiplying the number of yards by 3 directly converts it to feet.

  3. c. Converting yards to feet by multiplying 30 yards by \( \frac{1 \text{ yard}}{3 \text{ feet}} \).

    • This option is confusing and incorrect for converting yards to feet; it would effectively decrease the number of yards rather than convert it properly.

  4. d. Converting yards to feet by multiplying 30 yards by \( \frac{3 \text{ feet}}{1 \text{ yard}} \).

    • This option will also yield the correct conversion to feet, but the phrasing makes it seem more complicated than necessary for a simple conversion.

The Best Option:

The best option for converting from yards to feet is b. Converting yards to feet by multiplying 30 yards by 3.

Show the Work:

  1. Convert Distance: \[ 30 \text{ yards} \times 3 \frac{\text{feet}}{\text{yard}} = 90 \text{ feet} \]

  2. Calculate Time using the formula \( d = vt \):

    • Rearranging the formula to find time \( t = \frac{d}{v} \) \[ t = \frac{90 \text{ feet}}{5 \text{ feet/min}} = 18 \text{ minutes} \]

So, it takes the mouse 18 minutes to run across the 30-yard field.

Q4 Using the Property of Equality, what first step would you take to rearrange the formula A = P+ Prt using r as the quantity of interest?
a. Subtract P from both sides of the equation.
b. Divide both sides by t.
c. Subtract Pr from both sides.
d. Divide both sides by P.

To rearrange the formula \( A = P + Prt \) and solve for \( r \), we want to isolate \( r \) as the quantity of interest.

The formula can be rewritten as:

\[ A = P(1 + rt) \]

Here’s a breakdown of how we can isolate \( r \):

  1. First, we need to get rid of \( P \) from the right side of the equation.

Looking at the choices:

a. Subtract \( P \) from both sides of the equation.

  • This would give us \( A - P = Prt \), which is correct to isolate the \( Prt \) term but still leaves \( r \) multiplied by \( t \).

b. Divide both sides by \( t \).

  • This would not be applicable in the first step because we haven’t isolated anything involving \( t \) yet.

c. Subtract \( Pr \) from both sides.

  • This does not make sense as we would not isolate \( r \) by doing this.

d. Divide both sides by \( P \).

  • This is a good step, but we would first want to get rid of the \( P(1 + rt) \) term entirely before we can isolate \( r \).

Therefore, the Correct First Step:

The best choice for the first step would be a. Subtract \( P \) from both sides of the equation.

Work:

  1. Starting from \( A = P + Prt \): \[ A - P = Prt \]

  2. The next steps would then involve dividing by \( Pt \) to isolate \( r \).

So, in summary, the first step is: a. Subtract \( P \) from both sides of the equation.