Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
(1 point)
Responses
−2/3
2/3
−1/6
1/6
To solve the expression, we can apply the division rule and multiply the numbers together.
First, let's simplify the expression step by step:
(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
First, multiply the numerator values for -2 and -5 to get the result: 10.
10×(1/5)÷(2/3)÷(3/4)
Next, multiply the denominator values for 5 and 6 to get the result: 30.
10×(1/5)÷(2/3)÷(3/30)
Simplify the numerator by multiplying 10 and 1 to get the result: 10.
10/5÷(2/3)÷(3/30)
Now, divide the fractions by multiplying the numerator of the first fraction (10) by the denominator of the second fraction (3) and the numerator of the second fraction (2) by the denominator of the first fraction (5):
(10×3)/(5×2)÷(3/30)
Therefore, we get:
= 30/10÷(3/30)
Now, divide 30 by 10 to get the result: 3.
= 3÷(3/30)
To divide fractions, multiply the first fraction (3) by the reciprocal of the second fraction (30/3):
= 3×(30/3)
This simplifies to:
= 10
Therefore, the final answer is 10.
To solve the given expression:
(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4),
we can use the properties of operations and rules for multiplying and dividing.
Step 1: Multiply the numerators of the fractions together and the denominators of the fractions together.
(-2) × 1 × (-5) × 3 / (5) × 2 × 3 × 4
Simplifying further:
-30 / 120
Step 2: Reduce the fraction to its simplest form by dividing both the numerator and denominator by their highest common factor, which in this case is 30.
-30 ÷ 30 / 120 ÷ 30
Simplifying further:
-1 / 4
Therefore, the answer is −1/4.
To solve the expression (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4), we can follow the rules for multiplying and dividing fractions.
Step 1: Multiply the numerators together.
(-2) × 1 × (-5) × (-5) = 50
Step 2: Multiply the denominators together.
5 × 2 × 3 × 4 = 120
Step 3: Divide the numerator by the denominator.
50 ÷ 120 = 5/12
So, the answer to the expression is 5/12.