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 need to use the rules for multiplying and dividing fractions.
Step 1: Multiply the denominators and multiply the numerators separately.
(17/6) ÷ (4/17) × (7/34) × (-1) × (6/17)
= (17 * 17 * 7 * -1 * 6) / (6 * 4 * 34 * 17)
= (-14 * 7 * 6) / (4 * 34)
= (-1176) / (136)
Step 2: Simplify the fraction by finding the greatest common divisor of the numerator and denominator.
The greatest common divisor of 1176 and 136 is 8. We can divide both numbers by 8 to simplify the fraction.
= (-147) / (17)
The final answer is -147/17.
To solve the problem (17/6) ÷ (4/17) × (7/34) × (-1) × (6/17), we can follow these steps:
Step 1: Simplify the division:
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore:
(17/6) ÷ (4/17) = (17/6) * (17/4)
Step 2: Multiply the fractions:
To multiply fractions, we multiply the numerators together and multiply the denominators together. Therefore:
(17/6) * (17/4) = (17 * 17) / (6 * 4)
Step 3: Simplify the multiplication:
17 * 17 = 289 and 6 * 4 = 24. Therefore:
(17/6) * (17/4) = 289/24
Step 4: Multiply the remaining fractions and the negative sign:
To multiply fractions, we multiply the numerators together and multiply the denominators together. Therefore:
(289/24) * (7/34) * (-1) * (6/17) = (-289*7*6) / (24*34*17)
Step 5: Simplify the multiplication:
(-289 * 7 * 6) = -12,726 and (24 * 34 * 17) = 13,824. Therefore:
(-289*7*6) / (24*34*17) = -12,726 / 13,824
Therefore, the answer is -12,726/13,824.
To solve the given problem, we can follow the properties of operations and rules for multiplying and dividing fractions.
Step 1: Simplify each fraction individually (if possible) by canceling out any common factors between the numerator and denominator:
(17/6) ÷ (4/17) × (7/34) × (-1) × (6/17)
Step 2: Divide the first fraction by the second fraction:
(17/6) ÷ (4/17) = (17/6) × (17/4)
Step 3: Multiply the resulting fraction by the next fraction:
(17/6) × (17/4) × (7/34)
Step 4: Multiply the resulting fraction by -1:
(17/6) × (17/4) × (7/34) × (-1)
Step 5: Multiply the resulting fraction by the last fraction:
(17/6) × (17/4) × (7/34) × (-1) × (6/17)
Step 6: Now, multiply the numerators together and multiply the denominators together:
(17 × 17 × 7 × -1 × 6) / (6 × 4 × 17 × 34)
Step 7: Simplify the expression:
(-10,654) / (17,424)
Therefore, the answer is -10,654/17,424, which can also be simplified further if needed.