Use the properties of operations and rules for multiplying and dividing to solve(1 point) Responses 8 8 1,2258 Start Fraction 1,225 over 8 End Fraction −1,225/8 negative Start Fraction 1,225 over 8 End Fraction −8 negative 89) ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
To solve this expression, we can follow the order of operations, which includes multiplication and division from left to right.
First, let's simplify the expression (1,225/8) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) step by step:
1. Divide (1,225/8) by (5/4):
(1,225/8) ÷ (5/4) = (1,225/8) × (4/5)
= (1,225 × 4) / (8 × 5)
= 4,900 / 40
= 122.5
2. Multiply the result from step 1 by (7/9):
122.5 × (7/9) = (122.5 × 7) / 9
= 857.5 / 9
≈ 95.2778 (rounded to 4 decimal places)
3. Multiply the result from step 2 by (-5):
95.2778 × (-5) = -476.3889
4. Divide the result from step 3 by (7/2):
-476.3889 ÷ (7/2) = -476.3889 × (2/7)
= (-476.3889 × 2) / 7
= -952.7778 / 7
≈ -136.1111 (rounded to 4 decimal places)
Therefore, the answer is approximately -136.1111.
To solve the expression (8 + 1,225/8 - (-1,225/8)) ÷ (5/4) × (7/9) × (-5) ÷ (7/2), we can follow these steps:
Step 1: Simplify the expression inside the parentheses.
8 + 1,225/8 - (-1,225/8) equals 8 + (1,225/8) + (1,225/8) since subtracting a negative is equivalent to adding.
This results in:
8 + (1,225/8) + (1,225/8)
Step 2: Find a common denominator for the fraction terms.
The factors of 8 are 1, 2, 4, and 8, and the factors of 9 are 1 and 9. Since the common denominator should be the smallest number that is divisible by both denominators, we choose 8. Therefore, we rewrite the fractions using the common denominator:
1,225/8 = 1,225 * (1/8) = 1,225/8
Step 3: Simplify the expression inside the parentheses.
8 + (1,225/8) + (1,225/8) can be simplified as follows:
8 * 8/8 + 1,225/8 + 1,225/8
This results in:
64/8 + 1,225/8 + 1,225/8
Step 4: Add the terms that have the same denominators.
64/8 + 1,225/8 + 1,225/8 equals:
(64 + 1,225 + 1,225)/8
This results in:
2,514/8
Step 5: Simplify the fraction.
2,514/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. We get:
1,257/4
Now, we have:
(1,257/4) ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
Step 6: Multiply and divide from left to right.
(1,257/4) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) equals:
(1,257 × 4)/(4 × 5) × (7/9) × (-5) ÷ (7/2)
This simplifies to:
5,028/20 × (7/9) × (-5) ÷ (7/2)
Step 7: Simplify the expression.
5,028/20 × (7/9) × (-5) ÷ (7/2) can be simplified as follows:
(5,028 × 7)/(20 × 9) × (-5) ÷ (7/2)
Step 8: Further simplify the expression.
(5,028 × 7)/(20 × 9) × (-5) ÷ (7/2) equals:
35,196/180 × (-5) ÷ (7/2)
Step 9: Multiply and divide from left to right.
35,196/180 × (-5) ÷ (7/2) can be calculated as follows:
(35,196 × -5)/(180 × 7/2)
Simplifying this expression gives:
-175,980/1,260
Finally, we have solved the expression to be -175,980/1,260.
To solve the given expression using the properties and rules for multiplying and dividing, follow these steps:
Step 1: Simplify the division operation:
Start by dividing 1,225 by 8:
1,225 ÷ 8 = 153.125
Step 2: Simplify the multiplication operation:
Next, multiply the simplified division result from Step 1 by -1,225/8:
153.125 × (-1,225/8) = -18,731.25
Step 3: Simplify the remaining multiplication and division operations:
Now, multiply the result from Step 2 by -5:
-18,731.25 × (-5) = 93,656.25
Finally, divide the previous result by (5/4) × (7/9) × (7/2):
93,656.25 ÷ ((5/4) × (7/9) × (7/2))
To simplify this division, we need to multiply the denominator's reciprocal with the numerator:
93,656.25 × (4/5) × (9/7) × (2/7)
Simplify the factors:
93,656.25 × (4/5) × (9/7) × (2/7) = 8,073.75
So, the solution to the given expression is 8,073.75.