What is the quotient when you divide −2 3/5 by 4/5?
To divide a mixed number by a fraction, the mixed number needs to be converted to an improper fraction.
We convert -2 3/5 to an improper fraction by multiplying the whole number (-2) by the denominator (5) and adding the numerator (3) to get the new numerator. The denominator remains the same. So, -2 3/5 can be written as:
-2 3/5 = (-2 * 5 + 3) / 5 = -13/5
Now we divide -13/5 by 4/5. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(-13/5) ÷ (4/5) = (-13/5) * (5/4)
The denominator cancels out, and we are left with:
(-13 * 1) / (1 * 4) = -13/4
So, the quotient when you divide -2 3/5 by 4/5 is -13/4.
as a mixed number
To express the quotient as a mixed number, we need to divide the numerator (-13) by the denominator (4).
-13 ÷ 4 = -3 remainder 1
The quotient is -3 with a remainder of 1. Since the original fraction had a denominator of 4, we use 4 as the denominator for the mixed number.
Therefore, the quotient when you divide -2 3/5 by 4/5 is -3 1/4.
To divide −2 3/5 by 4/5, follow these steps:
Step 1: Convert the mixed number −2 3/5 to an improper fraction.
To convert a mixed number to an improper fraction, multiply the denominator (5) by the whole number part (-2), and then add the numerator (3). Place the result over the original denominator.
The result is (-2*5 + 3) / 5 = (-10 + 3) / 5 = -7/5.
Step 2: Divide -7/5 by 4/5.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
So, -7/5 ÷ 4/5 can be rewritten as (-7/5) * (5/4).
Step 3: Simplify the result.
Multiply the numerators (-7 * 5) and the denominators (5 * 4).
The result is -35/20.
Step 4: Simplify the fraction (if needed).
Both the numerator and the denominator are divisible by 5.
Dividing both by 5, we get -35/20 = -7/4.
Therefore, the quotient when you divide −2 3/5 by 4/5 is -7/4.