Review Multiplying and Dividing Rational Numbers

Review Multiplying and Dividing Rational Numbers

Open Ended

A whale descends 382.5 feet in 45 seconds. Write a DIVISION equation that can be used to represent the average elevation change of the whale during its descent and solve.

A whale descends 382.5 feet in 45 seconds. Write a DIVISION equation that can be used to represent the average elevation change of the whale during its descent and solve.

• First we have to write a division equation.

• Our division equation would be

   $-382.5\ \div\ 48$  382.5 is negative because the whale is descending

•  $-382.5\ \div\ 48\ =\ -8.5$  

Multiple Choice

The whale's elevation changes at a constant rate. What is the elevation of the whale after 6 seconds?

• -51

• 51

• -8.5

• 8.5

The whale's elevation changes at a constant rate. What is the elevation of the whale after 6 seconds?

• To find the whales elevation you would use the answer in the division equation you wrote in the previous question and multiply is by 6

•  $-8.5\ \cdot\ 6\ =\ -51$  

Multiple Select

The table shows yesterday's change in value of four different stocks. Which of the following statements are true? Choose all that apply.

• The change in value of Stock A is 5 times as much as the change in value of Stock D

• The change in value of Stock B is 4 times as much as the change in value of Stock A

• The change in value of Stock C is 3 times as much as the change in value of Stock B.

• The change in value of Stock D is 2 times as much as the change in value of Stock B.

To solve

To solve this one we would have to use the table to determine which statements are correct.

A is correct because if you do -0.25 x 5 you get -1.25 which is what stock A is.

C is also correct because if you multiply Stock B by 3 you get -1.50 which is the same as stock C

Multiple Choice

Suppose -1 < a < 0. What must be true about the value of b so that ab < a?

• b < -1

• -1 < b < 0

• 0 < b < 1

• b > 1

Suppose -1 < a < 0. What must be true about the value of b so that ab < a?

• the last answer was correct because in order for the product of ab < a then b has to be any number bigger then 1. This is because we know that a is a negative number between -1 and 0. In order for ab to be less then a number between -1 and 0 then b has to be a positive number bigger then 1.

• Remember that when we multiply one negative number and one positive number we get a negative answer

Open Ended

Four submarines start at sea level, which means 0 meters. The table shows the change in position per minute, relative to sea level. After 8 minutes, what is the position of Submarine D, relative to sea level? Write a MULTIPLICATION equation and solve

Four submarines start at sea level, which means 0 meters. The table shows the change in position per minute, relative to sea level. After 8 minutes, what is the position of Submarine D, relative to sea level? Write a MULTIPLICATION equation and solve

• The answer would be -3.75 x 8 = -30

• We would use the rate of change for Submarine D and multiply it by 8 since we want to know the position of that submarine after 8 minutes.

Multiple Choice

True or False? Submarine E also starts at sea level and its position relative to sea level changes at a constant rate per minute. Submarine E is at -32 meters after 10 minutes. Submarine E changes position faster than Submarine D

• True

• False

False

• This is false because Submarine E's rate of change is -3.2 meters which is slower then Submarine D's rate of change (-3.75)

Multiple Choice

True or False? Submarine E also starts at sea level and its position relative to sea level changes at a constant rate per minute. Submarine E is at -32 meters after 10 minutes. The position of Submarine B changes twice as fast as the position of Submarine E.

• True

• False

True

• This is true because Submarine E's rate of change is -3.2 When we do -3.2 x 2 we get -6.4, which is the rate of change for Submarine B

Multiple Choice

True or False? Submarine E also starts at sea level and its position relative to sea level changes at a constant rate per minute. Submarine E is at -32 meters after 10 minutes. The position of Submarine E after 10 minutes is closer to sea level than the position of Submarine A after 10 minutes

• True

• False

True

• This is true because Submarine E is at -32 feet after 10 minutes. Submarine A is at -42 feet after 10 minutes. -32 is closer to zero so this means that is is closer to the surface level.

Multiple Choice

True or False? Submarine E also starts at sea level and its position relative to sea level changes at a constant rate per minute. Submarine E is at -32 meters after 10 minutes. The position of Submarine E will be between the positions of Submarine C and Submarine B after 10 minutes.

• True

• False

False

• This is false because Submarine B will be at -64 meters after 10 minutes. Submarine C will be at -75 meters after 10 minutes. -32 is less then both of those numbers, making this statement false.