What is the quotient when you divide −10/11 by −2/5? Show your work.
To divide fractions, we multiply by the reciprocal of the second fraction.
First, we rewrite -10/11 and -2/5 as equivalent fractions with a common denominator of 55:
-10/11 = -50/55
-2/5 = -22/55
Now, we multiply -50/55 by the reciprocal of -22/55:
-50/55 * -55/22 = -(-2500)/(55*22) = 2500/1210
Therefore, the quotient is 2500/1210, which simplifies to 125/66 in lowest terms.
To find the quotient when you divide -10/11 by -2/5, you can follow these steps:
Step 1: Invert the divisor (the number you're dividing by). The reciprocal of -2/5 is -5/2.
Step 2: Multiply the dividend (the number being divided) by the inverted divisor. Multiply -10/11 by -5/2.
(-10/11) * (-5/2) = (10/11) * (5/2)
Step 3: Simplify the expression.
(10/11) * (5/2) = (10 * 5) / (11 * 2) = 50/22
Step 4: Make the fraction in simplest form.
50/22 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
50/22 = (50 ÷ 2) / (22 ÷ 2) = 25/11
So, the quotient when you divide -10/11 by -2/5 is 25/11.