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.