What is the quotient when you divide −10/11 by −2/5?
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of a fraction is obtained by swapping the numerator and denominator.
The reciprocal of -2/5 is -5/2.
So, the quotient of -10/11 divided by -2/5 is:
(-10/11) * (-5/2)
The negative signs cancel each other out (a negative divided by a negative is positive), so we have:
(10/11) * (5/2)
Multiplying the numerators gives us:
(10 * 5) / (11 * 2)
Which simplifies to:
50/22
The quotient is 50/22.
To simplify the fraction 50/22, we need to find the greatest common divisor (GCD) of the numerator (50) and the denominator (22) and divide both numbers by it.
The factors of 50 are 1, 2, 5, 10, 25, and 50.
The factors of 22 are 1, 2, 11, and 22.
The largest common factor between 50 and 22 is 2.
Dividing both numbers by 2, we get:
50 ÷ 2 = 25
22 ÷ 2 = 11
Therefore, the simplified form of 50/22 is 25/11.
To convert the fraction 25/11 to a mixed number, we divide the numerator (25) by the denominator (11).
25 ÷ 11 = 2 with a remainder of 3.
Therefore, the mixed number representation of 25/11 is 2 and 3/11.
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 3/8 is 8/3.
So, the quotient of -3/4 divided by 3/8 is:
(-3/4) * (8/3)
Multiplying the numerators gives us:
-3 * 8 = -24
And multiplying the denominators gives us:
4 * 3 = 12
Therefore, the quotient is -24/12.
To simplify this fraction, we find the greatest common divisor (GCD) of the numerator (-24) and the denominator (12), which is 12.
Dividing both numbers by 12, we get:
-24 ÷ 12 = -2
12 ÷ 12 = 1
Therefore, the simplified form of -24/12 is -2/1, which is just -2.
To divide a mixed number by a fraction, we first need to convert the mixed number into an improper fraction.
-2 3/5 can be written as -13/5.
Now, we can divide -13/5 by 4/5.
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 4/5 is 5/4.
So, the quotient of -13/5 divided by 4/5 is:
(-13/5) * (5/4)
Multiplying the numerators gives us:
-13 * 5 = -65
And multiplying the denominators gives us:
5 * 4 = 20
Therefore, the quotient is -65/20.
To simplify this fraction, we find the greatest common divisor (GCD) of the numerator (-65) and the denominator (20), which is 5.
Dividing both numbers by 5, we get:
-65 ÷ 5 = -13
20 ÷ 5 = 4
Therefore, the simplified form of -65/20 is -13/4.
50/11 in its simplest form
To simplify the fraction 50/11, we need to find the greatest common divisor (GCD) of the numerator (50) and the denominator (11) and divide both numbers by it.
The factors of 50 are 1, 2, 5, 10, 25, and 50.
The factors of 11 are 1 and 11.
The only common factor between 50 and 11 is 1, so the GCD is 1.
Dividing both numbers by 1, we get:
50 ÷ 1 = 50
11 ÷ 1 = 11
Therefore, the simplified form of 50/11 is 50/11.