Use the properties of operations and rules for multiplying and dividing to solve:
(−3/5)×(5 1/6)×(7 1/2)÷(−3 1/6)×(−5/7)
To simplify this expression, we will follow the order of operations, which is parentheses, multiplication, and then division.
First, let's simplify the fraction multiplication:
(−3/5) × (5 1/6) = (−3/5) × (31/6)
To multiply fractions, we multiply their numerators and denominators separately:
(−3/5) × (31/6) = (−3 × 31) / (5 × 6) = −93/30
Next, let's simplify the remaining multiplication:
(−93/30) × (7 1/2) × (−3 1/6) × (−5/7)
To multiply mixed numbers, we first need to convert them into improper fractions:
7 1/2 = (14/2) + (1/2) = 15/2
−3 1/6 = (−18/6) + (1/6) = −17/6
Now we multiply all the numbers together:
(−93/30) × (15/2) × (−17/6) × (−5/7)
To multiply fractions, we multiply their numerators and their denominators separately:
(−93 × 15 × −17 × −5) / (30 × 2 × 6 × 7)
= 62205 / 2520
Lastly, let's divide by the remaining fraction:
62205 / 2520 ÷ (−5/7)
To divide fractions, we multiply by the reciprocal of the divisor:
62205 / 2520 × (7/−5)
= (62205 × 7) / (2520 × −5)
= 435435 / −12600
Therefore, the simplified expression is 435435 / −12600.
are you sure
Apologies for the mistake in the previous response. Let's solve the expression correctly:
(−3/5) × (5 1/6) × (7 1/2) ÷ (−3 1/6) × (−5/7)
First, let's simplify the mixed numbers:
5 1/6 = (6 * 5 + 1)/6 = 31/6
7 1/2 = (2 * 7 + 1)/2 = 15/2
−3 1/6 = (6 * -3 + 1)/6 = -17/6
Now we can substitute these values into the expression:
(−3/5) × (31/6) × (15/2) ÷ (−17/6) × (−5/7)
Next, let's simplify the fraction multiplication:
(−3/5) × (31/6) = (−3 × 31)/(5 × 6) = -93/30
Now we can substitute this value into the expression:
(-93/30) × (15/2) ÷ (-17/6) × (-5/7)
Next, let's simplify the remaining multiplication:
(15/2) ÷ (-17/6) = (15/2) × (-6/17) = (-90/34)
Now we can substitute this value back into the expression:
(-93/30) × (-90/34) × (-5/7)
Next, let's simplify the fraction multiplication:
(-93/30) × (-90/34) = (93 × 90)/(30 × 34) = 8370/1020 = 1395/170
Now we can substitute this value back into the expression:
(1395/170) × (-5/7)
Finally, let's simplify the last fraction multiplication:
(1395/170) × (-5/7) = (1395 × -5)/(170 × 7) = -6975/1190
Therefore, the simplified expression is -6975/1190.
To solve the given expression, we need to perform the multiplication and division operations correctly. Let's follow these steps:
Step 1: Convert mixed numbers to improper fractions
- To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Write the sum as the numerator over the denominator.
For example:
5 1/6 = (5 × 6 + 1) / 6 = 31/6
7 1/2 = (7 × 2 + 1) / 2 = 15/2
-3 1/6 = (-3 × 6 + 1) / 6 = -19/6
Now, the expression becomes: (-3/5) × (31/6) × (15/2) ÷ (-19/6) × (-5/7)
Step 2: Perform multiplication
- To multiply fractions, multiply the numerators and multiply the denominators.
For example:
(-3/5) × (31/6) × (15/2) ÷ (-19/6) × (-5/7) =
(-3 × 31 × 15 × (-5)) / (5 × 6 × 2 × 19 × 6 × 7)
So far, our expression is: (-3 × 31 × 15 × (-5)) / (5 × 6 × 2 × 19 × 6 × 7)
Step 3: Simplify the expression
- Perform the multiplication within the numerator and denominator.
For example:
(-3 × 31 × 15 × (-5)) / (5 × 6 × 2 × 19 × 6 × 7) =
(-3 × 31 × 15 × (-5)) / (5 × 6 × 2 × 19 × 6 × 7) =
(-1395 × (-5)) / (5 × 6 × 2 × 19 × 6 × 7)
= 6975 / (5 × 6 × 2 × 19 × 6 × 7)
Now, our expression is: 6975 / (5 × 6 × 2 × 19 × 6 × 7)
Step 4: Perform division
- To divide fractions, multiply the numerator by the reciprocal of the denominator.
For example:
6975 / (5 × 6 × 2 × 19 × 6 × 7) =
6975 / (5 × 6 × 2 × 19 × 6 × 7) =
6975 × (30 × 6 × 7 × 19 × 6 × 5) / (5 × 6 × 2 × 19 × 6 × 7 × 30)
Now, our expression is: 6975 × (30 × 6 × 7 × 19 × 6 × 5) / (5 × 6 × 2 × 19 × 6 × 7 × 30)
Step 5: Simplify and cancel common factors
- Simplify any common factors that can be canceled within the numerator and denominator.
For example:
6975 × (30 × 6 × 7 × 19 × 6 × 5) / (5 × 6 × 2 × 19 × 6 × 7 × 30) =
6975 × (30 × 6 × 7 × 19 × 6 × 5) / (5 × 6 × 2 × 19 × 6 × 7 × 30) =
6975 × 1 / (1 × 2 × 30) =
6975 / (2 × 30) =
6975 / 60
So, the simplified expression is: 6975 / 60
Step 6: Perform the division
- To divide two numbers, divide the numerator by the denominator.
For example:
6975 / 60 = 116.25
Therefore, the solution to the expression is 116.25.