Use the properties of operations and rules for multiplying and dividing to solve the following problem: (17/6)÷(4/17)×(7/34)×(−1)×(6/17). (1 point) Responses −7/578 −14/289 −2,856/58,956 −7/8
To solve the problem, we can multiply and divide the given numbers in any order as long as we follow the rules for multiplying and dividing fractions.
Let's start by multiplying the numbers:
(17/6) ÷ (4/17) × (7/34) × (-1) × (6/17)
= (17/6) × (7/34) × (-1) × (6/17) ÷ (4/17)
Now let's simplify the expression:
= (17 × 7 × 6 × (-1)) ÷ (6 × 34 × 4)
= (-7 × 2 × 2 × (-1)) ÷ (17 × 2 × 2)
= (-7 × (-1)) ÷ 17
= 7/17
Therefore, the answer to the problem is 7/17.
To solve this problem, let's go step-by-step using the properties of operations and rules for multiplying and dividing.
Step 1: Simplify the division of the fractions:
(17/6) ÷ (4/17) = (17/6) × (17/4)
Step 2: Simplify the multiplication of the fractions:
(17/6) × (17/4) × (7/34) × (-1) × (6/17)
Step 3: Cancel out any common factors in the numerator and denominator:
(17/6) × (17/4) × (7/34) × (-1) × (6/17) = (1/6) × (1/4) × (1/2) × (-1) × (1) = -1/48
Therefore, the final answer is -1/48.
To solve the given problem, let's break it down step by step using the properties of operations and rules for multiplying and dividing fractions:
Step 1: Simplify the given expression by canceling out common factors between the numerators and denominators:
(17/6) ÷ (4/17) × (7/34) × (-1) × (6/17)
We can cancel out the common factor of 17 between the first fraction's numerator and the second fraction's denominator:
(1/6) × (7/4) × (7/34) × (-1) × (6/1)
Step 2: Multiply the numerators together and the denominators together:
(1 × 7 × 7 × (-1) × 6) / (6 × 4 × 34 × 1)
Step 3: Simplify the numerator and the denominator separately:
Numerator: 1 × 7 × 7 × (-1) × 6 = -294
Denominator: 6 × 4 × 34 × 1 = 816
Step 4: Simplify the fraction by dividing the numerator by the denominator:
-294/816
Step 5: Further simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
GCD of -294 and 816 = 6
-294/6 ÷ 816/6 = -49/136
Therefore, the answer to the given problem is -49/136.