Use the properties of operations and rules for multiplying and dividing to solve:
(-3) ÷ (3/4) ÷ (2/7) ÷ (-5/16) ÷ (5/7)
Explain your process.
To solve the expression (-3) ÷ (3/4) ÷ (2/7) ÷ (-5/16) ÷ (5/7), we can use the rules for dividing fractions.
First, we need to simplify the division of the fractions. To divide two fractions, we flip the second fraction and multiply them.
(-3) ÷ (3/4) = (-3) * (4/3) = -12/3 = -4
Next, we divide -4 by the next fraction.
-4 ÷ (2/7) = -4 * (7/2) = -28/2 = -14
Then, we divide -14 by the next fraction.
-14 ÷ (-5/16) = -14 * (-16/5) = 224/5
Finally, we divide 224/5 by the last fraction.
224/5 ÷ (5/7) = 224/5 * (7/5) = 1568/25
So, the simplified expression is 1568/25.
To solve this problem using the properties of operations and rules for multiplying and dividing, follow these steps:
Step 1: Rewrite the given expression using the multiplication property of division:
(-3) ÷ (3/4) ÷ (2/7) ÷ (-5/16) ÷ (5/7) = (-3) * (4/3) * (7/2) * (-16/5) * (7/5)
Step 2: Simplify the expression by multiplying the numerators together and multiplying the denominators together:
(-3) * (4/3) * (7/2) * (-16/5) * (7/5) = (-3 * 4 * 7 * -16 * 7) / (3 * 2 * 5 * 5)
Step 3: Multiply the terms in the numerator and denominator:
(-3 * 4 * 7 * -16 * 7) / (3 * 2 * 5 * 5) = (-,672 * -98 * 98) / (150)
Step 4: Simplify the expression by multiplying the numbers together and dividing by 150:
(-,672 * -98 * 98) / (150) = 11,040,576 / 150
Step 5: Divide the numerator by the denominator to get the final answer:
11,040,576 / 150 = 73,603.84
Therefore, the solution to the expression (-3) ÷ (3/4) ÷ (2/7) ÷ (-5/16) ÷ (5/7) is 73,603.84.
To solve this expression, we can use the properties of operations and rules for multiplying and dividing. Let's go step by step:
Step 1: Rewrite the expression using the reciprocal of the divisor:
(-3) * (4/3) * (7/2) * (-16/5) * (7/5)
Step 2: Multiply the numerators of all the fractions together and multiply the denominators together:
(-3 * 4 * 7 * -16 * 7) / (3 * 2 * 5 * 5)
Step 3: Simplify the numerator and denominator:
(-2016 * -49)/(150) = 98624/150
Step 4: Reduce the fraction if possible. In this case, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 2:
98624 ÷ 2 = 49312
150 ÷ 2 = 75
So, the simplified expression is:
49312/75
This cannot be simplified further since 49312 and 75 do not share any common factors other than 1.
Therefore, (-3) ÷ (3/4) ÷ (2/7) ÷ (-5/16) ÷ (5/7) equals 49312/75.