Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(3/4)×(2/7)×(−5 1/6)÷(5/7)
To solve this expression, we will follow the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
First, let's simplify the division:
(-3) ÷ (3/4) = (-3) × (4/3) = -12/3 = -4
Next, let's simplify the multiplication:
-4 × (2/7) × (-5 1/6) ÷ (5/7)
To multiply fractions, we multiply the numerators together and multiply the denominators together:
(-4) × (2/7) = (-8/7)
To multiply a mixed number, we convert it into an improper fraction:
-5 1/6 = -5 + 1/6 = (-30/6) + (1/6) = (-30+1)/6 = -29/6
Now, we can continue multiplying:
(-8/7) × (-29/6) = (8/7) × (29/6)
To multiply these fractions, we multiply the numerators together and multiply the denominators together:
(8 × 29)/(7 × 6) = 232/42
Finally, let's simplify the division:
232/42 ÷ (5/7)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(232/42) × (7/5) = (232 × 7)/(42 × 5) = 1624/210
The final result is 1624/210.