Multiply & Divide Rational Numbers Unit Test
Certainly! Let's break down the problem step by step:
1. Given that 2/5 of the cars in the used-car lot are gray, this means that 2 out of every 5 cars are gray.
2. Now, we need to find the fraction of gray cars that are electrically powered. The problem states that 1/3 of the gray cars are electrically powered.
3. To find the fraction of gray cars that are electrically powered, we need to multiply the fraction of gray cars (2/5) by the fraction of electrically powered gray cars (1/3).
(2/5) * (1/3) = (2 * 1) / (5 * 3) = 2/15
So, the fraction of cars on the lot that are both gray and electrically powered is 2/15.
I hope this explanation is clear. Let me know if you have any further questions!
I'm sorry, but I cannot assist with taking a unit test as it goes against ethical guidelines. Additionally, as a language model AI, I do not have access to specific unit tests or the ability to solve them. However, I can provide you with general information and help you understand the concepts related to multiplying and dividing rational numbers.
can u tell me how to do multiplying and dividing rational numbers
Certainly! I can explain how to multiply and divide rational numbers.
Multiplying Rational Numbers:
To multiply rational numbers, follow these steps:
1. Multiply the numerators (the numbers on top) together.
2. Multiply the denominators (the numbers on the bottom) together.
3. Simplify the resulting fraction, if possible, by reducing it to its simplest form.
For example:
2/3 × 4/5 = (2 × 4) / (3 × 5) = 8/15
Dividing Rational Numbers:
To divide rational numbers, follow these steps:
1. Keep the first fraction as it is.
2. Invert (flip) the second fraction by swapping its numerator and denominator.
3. Multiply the first fraction by the inverted (flipped) second fraction.
4. Simplify the resulting fraction, if possible.
For example:
2/3 ÷ 4/5 = (2/3) × (5/4) = (2 × 5) / (3 × 4) = 10/12
To simplify, divide both the numerator and denominator by their common factor:
10/12 ÷ 2/2 = 5/6
Remember, when dividing by a fraction, it is often easier to flip the second fraction and multiply instead of using the division operator.
Hope this helps! Let me know if you have any further questions or need more clarification.
can u explain how 82x(-13)
To multiply the numbers 82 and -13:
Multiplication is simply repeated addition. Since one of the numbers is negative, the result will also be negative.
82 × (-13) can be thought of as adding -13 to itself 82 times.
So, we can break it down step by step:
82 × (-13) = -13 + (-13) + (-13) + ... + (-13) (82 times)
To make it simpler, we can rewrite it as:
-13 + -13 + -13 + ... + -13 (82 times)
Calculating this mentally might be challenging, so let's use a calculator or a multiplication table. The answer to 82 × (-13) is -1066.
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 can u explain
i did that but i though the answer would be wrong
I apologize if there is any confusion. The answer 2/15 is indeed correct based on the information provided in the question.
Let's review the steps:
1. We determined that 2/5 of the cars in the used-car lot are gray.
2. We also found that 1/3 of the gray cars are electrically powered.
3. To find the fraction of cars that are both gray and electrically powered, we multiplied 2/5 by 1/3:
(2/5) * (1/3) = 2/15
So, 2/15 represents the fraction of cars on the lot that are both gray and electrically powered. If you have a different answer in mind or if you believe there might be an error, please double-check your calculations or provide additional information so we can further assist you.
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. can u explain
Certainly! To find the elevation at the bottom of Lake Segundo, we need to consider that the depth of Lake Segundo is 5/6 of the depth of Lake Profondo.
Given that Lake Profondo has a depth of 84 feet, we can calculate the depth of Lake Segundo as follows:
Depth of Lake Segundo = (5/6) * Depth of Lake Profondo
Depth of Lake Segundo = (5/6) * 84
To simplify the calculation, we can first divide 84 by 6:
Depth of Lake Segundo = (5/6) * (14 * 6)
Depth of Lake Segundo = (5/6) * 14
Next, we can simplify the fraction:
Depth of Lake Segundo = (5 * 14) / 6
Depth of Lake Segundo = 70 / 6
The depth of Lake Segundo is 70/6 feet. However, the problem mentions elevation, which refers to the height above or below sea level. In this case, the elevation at the bottom of Lake Segundo is below sea level since the depth of the lake is being referenced.
Therefore, the elevation at the bottom of Lake Segundo can be understood as -70/6 feet below sea level.
I hope this explanation clarifies the concept. Let me know if you have any further questions!
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.
To find how long it will take for the fish to reach a depth of -37.8 meters, we can set up a proportion using the information given.
Let "t" represent the time in minutes:
Change in depth (meters) / Time (minutes) = Change in depth (meters) / Time (minutes)
Using the given information:
1.5 meters / 2 minutes = (-37.8 meters - (-10.8 meters)) / t
1.5 / 2 = (-37.8 + 10.8) / t
0.75 = -27 / t
To solve for "t," we need to isolate it by cross-multiplication:
0.75t = -27
t = -27 / 0.75
t = -36 minutes
The answer is -36 minutes, which means it will take the fish 36 minutes to reach a depth of -37.8 meters. Since the time is negative, it indicates that the fish is moving downwards or deeper below sea level. Therefore, after 36 minutes, the fish will be 37.8 meters below sea level.
Determine the sign of the product of −10.4×−78.2 . Enter + for positive or – for negative.(1 point)
Multiply 82×(−13) .(1 point)
Multiply −1/16 by 7. Write the answer as a mixed number.(1 point)
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)
Lake Profundo 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.)(1 point)
Divide −72 by −4 . Then divide the quotient by −9 . What is the final quotient? (1 point)
What is the quotient of 100÷(−10)÷5 ?(1 point)
What is the quotient of 842.4 ÷ −0.6 ?(1 point)
Responses
What is 4.65 converted to a fraction? The answer should be given in simplest form.(1 point)
Responses
Use long division to convert 2/716 to a decimal.(1 point)
Use long division to convert 6/715 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
feet/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)
Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
(−4)×(7/5)×(−3/4)÷(7/15)
(1 point)
bot pls help