What is the quotient when you divide -7/8 by -1/5.
A. 7/40
B. 5 5/7
C. 4 3/8
D. -4 3/8
B. 5 5/7
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of -1/5 is -5/1.
So, -7/8 ÷ -1/5 can be written as -7/8 × -5/1.
Multiply the numerators and denominators:
(-7) × (-5) = 35
(8) × (1) = 8
Therefore, the quotient is 35/8.
However, the answer choices are given in mixed number form, so we need to convert 35/8 into a mixed number.
To do that, we divide the numerator (35) by the denominator (8):
35 ÷ 8 = 4 with a remainder of 3.
So the mixed number form of 35/8 is 4 3/8.
Since the original question is asking for the quotient when dividing -7/8 by -1/5, the correct answer is D. -4 3/8.
To find the quotient when you divide -7/8 by -1/5, you can follow a few steps:
Step 1: Multiply the dividend (-7/8) by the reciprocal of the divisor (-1/5).
- The reciprocal of a fraction is found by flipping the numerator and denominator. So, the reciprocal of -1/5 is -5/1.
- Multiplying -7/8 by -5/1 can be done by multiplying the numerators (-7 * -5) and the denominators (8 * 1) separately.
Step 2: Simplify the resulting fraction from Step 1.
- After multiplying, you will have a fraction. Simplify this fraction to its simplest form.
Let's go through these steps to find the quotient:
Step 1: Multiply -7/8 by -5/1.
- By multiplying the numerators (-7 * -5) and the denominators (8 * 1), we get: 35/8.
Step 2: Simplify the fraction.
- We cannot simplify the fraction 35/8 any further, so the quotient is 35/8.
Now let's match the quotient 35/8 to one of the given options:
A. 7/40: This does not match the quotient 35/8.
B. 5 5/7: This does not match the fraction 35/8.
C. 4 3/8: This does not match the fraction 35/8.
D. -4 3/8: This does not match the fraction 35/8.
Since none of the given options match, we conclude that none of the options (A, B, C, or D) is the correct quotient when dividing -7/8 by -1/5.