Use the properties of operations and rules for multiplying and dividing to solve:
(9) ÷ (5/4) × (7/9) × (−5) ÷ (7/2)
Possible answers are
8
-8
-1225/8
1225/8
To solve this expression, let's go step by step.
First, we can simplify the expression by multiplying and dividing from left to right:
(9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
First, we can simplify (9) ÷ (5/4):
(9) ÷ (5/4) = 9 × (4/5) = 36/5
Next, we can multiply this result by (7/9):
(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45
Now, we can multiply this result by (-5):
(252/45) × (-5) = (252 × -5) / 45 = -1260/45
Finally, we can divide this result by (7/2):
(-1260/45) ÷ (7/2) = (-1260/45) × (2/7)
=(- 1260 × 2) / (45 × 7) = -2520/315 = -8
Therefore, the answer is -8.
Solve this multi-step problem. A runner completes 14 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)
Responses
possible answers are.
160 miles
1/10 mile
Start Fraction 1 over 10 End Fraction mile.
1/8 mile
Start Fraction 1 over 8 End Fraction mile.
2 1/2 miles
To solve this problem, we can use the runner's rate of completing 14 miles every 8 minutes.
First, we need to find the runner's rate per minute. We can do this by dividing the distance (14 miles) by the time (8 minutes):
Rate per minute = 14 miles / 8 minutes
Rate per minute = 7/4 miles per minute
Now, we just need to calculate how far the runner can go in 16 minutes. We can do this by multiplying the rate per minute by the time in minutes:
Distance in 16 minutes = (7/4 miles per minute) × 16 minutes
Distance in 16 minutes = (7/4) × 16 miles
Distance in 16 minutes = 28 miles
Therefore, the runner can go 28 miles in 16 minutes.
To solve the expression (9) ÷ (5/4) × (7/9) × (−5) ÷ (7/2), we can simplify it step by step using the properties of operations and rules for multiplying and dividing.
Step 1: Simplify the division (9) ÷ (5/4):
To divide by a fraction, you multiply by its reciprocal. Therefore, (9) ÷ (5/4) can be rewritten as (9) × (4/5):
(9) ÷ (5/4) = (9) × (4/5) = 36/5
Step 2: Multiply the result from step 1 by (7/9):
Multiplying fractions is done by multiplying the numerators together and then multiplying the denominators together. Therefore, (36/5) × (7/9) can be calculated as:
(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45
Step 3: Multiply the result from step 2 by (-5):
To multiply a fraction by a whole number, you multiply the numerator of the fraction by the whole number and keep the denominator the same. Therefore, (252/45) × (-5) can be calculated as:
(252/45) × (-5) = - (252 × 5) / 45 = -1260/45
Step 4: Divide the result from step 3 by (7/2):
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, (-1260/45) ÷ (7/2) can be rewritten as:
(-1260/45) ÷ (7/2) = (-1260/45) × (2/7) = -2520/315
Simplifying the fraction -2520/315 by dividing both the numerator and denominator by their greatest common divisor, which is 45, we get:
-2520/315 = (-2520 ÷ 45) / (315 ÷ 45) = -56/7 = -8
Therefore, the answer to the expression (9) ÷ (5/4) × (7/9) × (−5) ÷ (7/2) is -8.