Find the product of:
4 over 7(−20 over 2)
A) -2 over 35
B) 5 and 5 over 7
C) -5 and 5 over 7
D) -9 and 3 over 7
To find the product of 4/7 and (-20/2), we first need to simplify the second fraction. (-20/2) can be simplified to -10.
Now we have:
4/7 * -10
To multiply fractions, we multiply the numerators together and the denominators together.
4 * -10 = -40
7 * 1 = 7
So the product is -40/7.
Looking at the answer choices, we see that none of them match -40/7. Therefore, none of the given options are correct.
To find the product of the two fractions, let's break it down step-by-step.
1. Start by multiplying the numerators together: 4 × (-20) = -80.
2. Next, multiply the denominators together: 7 × 2 = 14.
3. Now, combine the results from steps 1 and 2 to get the final answer: -80 over 14.
4. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: -80 ÷ 2 = -40 and 14 ÷ 2 = 7.
5. Put the simplified fraction in its simplest form: -40 over 7.
Therefore, the product of 4 over 7 and -20 over 2 is -40 over 7.
The correct answer is D) -9 and 3 over 7.
To find the product of fractions, we simply multiply the numerators together and the denominators together.
First, let's multiply the numerators:
4 * -20 = -80
Next, let's multiply the denominators:
7 * 2 = 14
So, the product of the fractions 4/7 and -20/2 is -80/14.
To simplify this fraction, we can find the greatest common divisor (GCD) of the numerator and denominator, and divide both by it. In this case, the GCD of 80 and 14 is 2.
-80/14 divided by 2 gives us -40/7.
Now let's express -40/7 as a mixed number. A mixed number is a whole number combined with a fraction. To do this, we divide the numerator (40) by the denominator (7).
40 divided by 7 gives us 5 with a remainder of 5.
Therefore, the final answer is -5 and 5/7.
Hence, the correct option is C) -5 and 5/7.