−5/6÷(−3/2)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of -3/2 is -2/3.
So, −5/6 ÷ (−3/2) is equivalent to −5/6 × (−2/3).
When multiplying fractions, we multiply the numerators together and the denominators together.
(-5/6) × (-2/3) = (5 × 2) / (6 × 3)
= 10/18
Simplifying the fraction gives us:
10/18 = 5/9
−4 2/3÷3 1/5
To divide mixed numbers, we convert them to improper fractions and then proceed with the division.
Let's first convert the mixed numbers to improper fractions.
-4 2/3 = -4 + 2/3 = (-4 * 3 + 2) / 3 = (-12 + 2) / 3 = -10/3
3 1/5 = 3 + 1/5 = (3 * 5 + 1) / 5 = (15 + 1) / 5 = 16/5
Now, we can divide -10/3 by 16/5.
(-10/3) ÷ (16/5) = (-10/3) * (5/16)
When multiplying fractions, we multiply the numerators together and the denominators together.
(-10/3) * (5/16) = (-10 * 5) / (3 * 16) = -50/48
Now, we can simplify the fraction.
-50/48 = -25/24
So, -4 2/3 ÷ 3 1/5 is equal to -25/24.
To divide fractions, you can follow these steps:
Step 1: Flip the second fraction (the divisor) upside down. In this case, the second fraction is -3/2, so flipping it gives you -2/3.
Step 2: Multiply the first fraction (the dividend) by the flipped second fraction. In this case, the first fraction is -5/6:
(-5/6) * (-2/3)
Step 3: Multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately:
(-5) * (-2) = 10
(6) * (3) = 18
Step 4: Simplify the fraction if possible. In this case, both the numerator and denominator are even numbers, so we can simplify by dividing both by 2:
10/2 = 5
18/2 = 9
So the simplified fraction is 5/9.
Therefore, -5/6 ÷ (-3/2) = 5/9.