Multiply & Divide Rational Numbers Unit Test
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Question
Of the cars in a used-car lot, 2/5 are the color gray. 1/3 of the gray cars are electrically powered vehicles. What fraction of the cars on the lot are both gray and electrically powered? Leave your answer in simplified fraction form.(1 point)
To find the fraction of cars on the lot that are both gray and electrically powered, you need to multiply the fractions representing the proportion of gray cars and the proportion of electrically powered cars among the gray cars.
The fraction of gray cars is 2/5.
The fraction of electrically powered cars among the gray cars is 1/3.
To find the fraction of cars that are both gray and electrically powered, multiply 2/5 by 1/3:
(2/5) * (1/3) = 2/15
Therefore, 2/15 of the cars on the lot are both gray and electrically powered.
what is 2/15 in simplified form
To simplify the fraction 2/15 further, you need to find the greatest common divisor (GCD) of the numerator (2) and the denominator (15). Both 2 and 15 are divisible by 1, so the GCD is 1.
Dividing both the numerator and denominator by the GCD:
2 ÷ 1 = 2
15 ÷ 1 = 15
Therefore, the simplified form of 2/15 is 2/15.
Lake Profondo has a depth of 84 feet. Lake Segundo is 5/6 as deep. What is the elevation at the bottom of Lake Segundo? (Remember, the elevation is below sea level. Account for this in your answer.)
If Lake Profondo has a depth of 84 feet and Lake Segundo is 5/6 as deep, we can find the depth of Lake Segundo by multiplying its depth by 5/6.
Depth of Lake Segundo = (5/6) * 84
To simplify this multiplication, we can first multiply the numerators and then multiply the denominators:
Depth of Lake Segundo = (5 * 84) / (6)
Multiplying 5 and 84 gives us 420:
Depth of Lake Segundo = 420 / 6
Dividing 420 by 6 gives us 70:
Depth of Lake Segundo = 70
So, the depth of Lake Segundo is 70 feet.
Since the elevation below sea level is negative, the elevation at the bottom of Lake Segundo is -70 feet.
Divide -72 by -4. Then divide the quotient by -9. What is the final quotient? (1 point)
To divide -72 by -4, divide the absolute values of the numbers and then determine the sign of the quotient.
|-72| ÷ |-4| = 72 ÷ 4 = 18
Since both -72 and -4 are negative, the quotient will be positive:
-72 ÷ -4 = 18
Now, divide the quotient 18 by -9:
18 ÷ -9 = -2
Therefore, the final quotient is -2.
What is the quotient of 100 ÷ (-10) ÷ 5? (1 point)
To find the quotient of 100 ÷ (-10) ÷ 5, we perform the divisions in order from left to right.
First, divide 100 by -10:
100 ÷ (-10) = -10
Next, divide the result (-10) by 5:
-10 ÷ 5 = -2
Therefore, the quotient of 100 ÷ (-10) ÷ 5 is -2.
What is the quotient of 842.4 ÷ - 0.6? (1 point)
To find the quotient of 842.4 ÷ -0.6, divide the numerator (842.4) by the denominator (-0.6).
842.4 ÷ (-0.6) = -1404
Therefore, the quotient of 842.4 ÷ -0.6 is -1404.
What is 4.65 converted to a fraction? The answer should be given in simplest form.
To convert 4.65 to a fraction, we can rewrite the decimal as a fraction by placing the decimal part (65) over the appropriate power of ten.
Since there are two decimal places in 4.65, we can write it as:
4.65 = 465/100
To simplify the fraction, we find the greatest common divisor (GCD) of the numerator (465) and the denominator (100). Both 465 and 100 are divisible by 5.
Dividing both the numerator and denominator by 5:
465/5 = 93
100/5 = 20
Therefore, the simplified form of 4.65 as a fraction is 93/20.
Use long division to convert 2 7 to a decimal. (1 point)
I'm sorry, but "2 7" does not form a valid number. It seems like there might be a typo or missing information regarding the number you want to convert to a decimal. Could you please provide the correct number so I can assist you further?
2 7/16
To convert the mixed number 2 7/16 to a decimal, we need to perform long division. We divide the numerator (23) by the denominator (16).
```
23
÷ 16
___________
```
First, we can place the decimal point above the division bar. Then, we begin the long division process:
```
. 1437
÷ 16
___________
23
```
The first step is to divide 23 by 16. The result is 1, which we place on top of the division bar, above the decimal point:
```
. 1 437
÷ 16
___________
23
```
Next, we bring down the next digit, which is 4, and place it next to the partial quotient of 1:
```
. 1 437
÷ 16
___________
23
- 16
___________
7
```
Now, we repeat the process. We divide 7 by 16. Since 7 is less than 16, we add a zero to the right of the decimal point in the quotient:
```
. 1 4375
÷ 16
___________
23
- 16
___________
7 0
```
Bring down the next digit, which is 0, and add it to the remainder 70:
```
. 1 4375
÷ 16
___________
23
- 16
___________
7 0
0
```
Now, divide 70 by 16. The result is 4, so we add 4 to the quotient:
```
. 1 4375
÷ 16
___________
23
- 16
___________
7 0
0 0
- 64
___________
60
```
Finally, we bring down the next digit, which is 0. We add a zero to the quotient:
```
. 1 4375
÷ 16
___________
23
- 16
___________
7 0
0 0
- 64
___________
60
- 48
___________
120
```
We can see that the division process repeats indefinitely without reaching an exact decimal value. Therefore, we can stop here and say that the decimal representation of 2 7/16 is approximately 2.4375.
Use long division to convert 6 7/15 to a decimal. (1 point)
A pilot is flying an airplane. Due to strong winds, the pilot decides to fly 4,000 feet lower to avoid excessive turbulence. It takes the pilot 3.5 minutes to make this adjustment.
Interpret the quotient to describe the rate of change in the plane's altitude. Give your answer to the nearest hundredth, and remember the plane is descending. (1 point)
The quotient that best represents the rate of change in the plane's altitude is___
To interpret the quotient that represents the rate of change in the plane's altitude, we need to divide the change in altitude (4000 feet) by the time taken for the adjustment (3.5 minutes).
Rate of change in altitude = Change in altitude / Time
Rate of change in altitude = 4000 feet / 3.5 minutes
To find the rate of change to the nearest hundredth, we divide 4000 by 3.5:
4000 / 3.5 ≈ 1142.86
Therefore, the rate of change in the plane's altitude to the nearest hundredth is approximately 1142.86 feet per minute.
A fire engine's water tank holds 750 gallons of water. If the pump removes 250 gallons of water in 5 minutes, what is the change in the amount of water in gallons in 1 minute?
(1 point
To find the change in the amount of water in the fire engine's tank in 1 minute, we need to divide the amount of water removed (250 gallons) by the time taken to remove it (5 minutes).
Change in amount of water per minute = Amount of water removed / Time
Change in amount of water per minute = 250 gallons / 5 minutes
To find the change in the amount of water in 1 minute, we divide 250 by 5:
250 / 5 = 50
Therefore, the change in the amount of water in the fire engine's tank in 1 minute is 50 gallons.
Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
(-4)x (7/5)x (-3/4)divided by (7/15)
(1 point)
Solve the following word problem. A fish is swimming at - 10.8 meters, or 10.8 meters below sea level. Every 2 minutes it descends another 1.5 meters. How long will it take for the fish to reach a depth of -37.8 meters? Show your work and write a sentence to explain what your answer means. (4 points)
To solve this word problem, we can calculate the time it takes for the fish to descend from -10.8 meters to -37.8 meters by dividing the change in depth by the rate of descent.
Change in depth = -37.8 meters - (-10.8 meters) = -37.8 meters + 10.8 meters = -27 meters
Rate of descent = -1.5 meters/2 minutes
Time = Change in depth / Rate of descent = -27 meters / (-1.5 meters/2 minutes)
To divide by a fraction, we can multiply by the reciprocal:
Time = (-27 meters) * (2 minutes / -1.5 meters)
Canceling out the meters, we get:
Time = -27 * (2 minutes / -1.5)
Simplifying further, we have:
Time = -27 * (2 / -1.5) = 54 / 1.5 = 36
Therefore, it will take the fish 36 minutes to reach a depth of -37.8 meters.
This means that in 36 minutes, the fish will descend from its initial depth of -10.8 meters to a depth of -37.8 meters.
reword this and shorten it
Solve the following word problem. A fish is swimming at −10.8 meters, or 10.8 meters below sea level. Every 2 minutes it descends another 1.5 meters. How long will it take for the fish to reach a depth of −37.8 meters? Show your work and write a sentence to explain what your answer means.(4 points)
Hello bot
To convert the mixed number 6 7/15 to a decimal, we need to perform long division. We divide the numerator (97) by the denominator (15).
```
97
÷ 15
___________
```
First, we can place the decimal point above the division bar. Then, we begin the long division process:
```
. 6 4
÷ 15
___________
97
```
The first step is to divide 97 by 15. The result is 6, which we place on top of the division bar, above the decimal point:
```
. 6 4
÷ 15
___________
97
- 90
___________
7
```
Now, we bring down the next digit, which is 7, and place it next to the partial quotient of 6:
```
. 6 4
÷ 15
___________
97
- 90
___________
7
7
```
Next, we divide 77 by 15. The result is 5, so we add 5 to the quotient:
```
. 6 4 5
÷ 15
___________
97
- 90
___________
7
7
- 75
___________
25
```
Finally, we bring down the next digit, which is 0. We add a zero to the quotient:
```
. 6 4 5 0
÷ 15
___________
97
- 90
___________
7
7
- 75
___________
25
0
```
Now, we divide 250 by 15. The result is 16, so we add 16 to the quotient:
```
. 6 4 5 0 1
÷ 15
___________
97
- 90
___________
7
7
- 75
___________
25
0
- 15
___________
100
```
We can see that the division process repeats indefinitely without reaching an exact decimal value. Therefore, we can stop here and say that the decimal representation of 6 7/15 is approximately 6.4501.
To solve the expression (-4) x (7/5) x (-3/4) divided by (7/15), we can simplify each part of the expression step by step.
First, we will simplify the multiplication part of the expression:
(-4) x (7/5) x (-3/4) = (4 x 7 x -3) / (5 x 4)
Now, we can simplify the multiplication in the numerator by multiplying the numbers together:
(4 x 7 x -3) = -84
And the multiplication in the denominator:
(5 x 4) = 20
So, now we have:
-84 / 20
Next, we will divide this fraction by (7/15):
(-84/20) / (7/15)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(-84/20) x (15/7)
Now, we can simplify this expression by canceling out common factors:
(-84/4) x (3/7) = -21 x 3
Multiplying -21 by 3, we get:
-21 x 3 = -63
Therefore, the final answer is -63.