Use the properties of operations and rules for multiplying and diving to solve:
(9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2)
To solve this expression, you will need to apply the rules for multiplying and dividing. Let's simplify each part step by step.
First, let's simplify the division: (9) ÷ (5/4)
To divide a number by a fraction, we can multiply the number by the reciprocal of the fraction.
Reciprocal of 5/4: 4/5
So, (9) ÷ (5/4) = 9 x (4/5) = 36/5
Next, let's simplify the multiplication: 36/5 x (7/9) x (-5) ÷ (7/2)
To multiply fractions, multiply the numerators together and the denominators together.
(36/5) x (7/9) = (36 x 7) / (5 x 9) = 252/45
Now, the expression is: 252/45 x (-5) ÷ (7/2)
To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number.
252/45 x (-5) = (-5 x 252) / 45 = -1260/45
Finally, let's simplify the division: -1260/45 ÷ (7/2)
Again, to divide by a fraction, we multiply by the reciprocal.
Reciprocal of 7/2: 2/7
(-1260/45) ÷ (7/2) = (-1260/45) x (2/7) = (-1260 x 2) / (45 x 7) = -2520/315
Therefore, the expression (9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2) simplifies to -2520/315, which can also be simplified to -8.
Solve this multi-step problem. A runner completes 1/4 of a 5 mile race every 8 minutes. At the same pace how far can the runner go in 16 minutes?
To solve this problem, we'll need to find out how far the runner can go in 16 minutes.
First, we need to determine how much of the race the runner completes in 1 minute. To do this, we divide 1/4 (the fraction of the race completed in 8 minutes) by 8 (the number of minutes it takes to complete that fraction of the race):
1/4 ÷ 8 = 1/32
This means that the runner completes 1/32 of the race in 1 minute.
Next, we need to determine how many times the runner can complete this fraction of the race in 16 minutes. To do this, we divide 16 (the total time given) by 1 (the fraction of the race completed in 1 minute):
16 ÷ 1/32 = 16 x 32 = 512
Therefore, the runner can complete 512/1 or 512 miles in 16 minutes.
Solve this multi-step problem. A runner completes 1/4 of a 5 mile race every 8 minutes. At the same pace how far can the runner go in 16 minutes?
A. 160 miles
B. 1/8 miles
C. 1/10 miles
D. 2 1/2 miles
To solve this problem, we need to determine the distance the runner can cover in 16 minutes at the same pace as completing 1/4 of a 5 mile race every 8 minutes.
First, we need to determine the distance covered by the runner in 1 minute. To do this, we divide 1/4 (the fraction of the race completed in 8 minutes) by 8 (the number of minutes it takes to complete that fraction of the race):
1/4 ÷ 8 = 1/32
This means that the runner completes 1/32 of a 5 mile race in 1 minute.
Next, we need to determine how many times the runner can complete this fraction of the race in 16 minutes. To do this, we multiply the fraction of the race completed in 1 minute (1/32) by 16 (the total time in minutes):
1/32 x 16 = 1/2
Therefore, the runner can cover 1/2 of a 5 mile race in 16 minutes.
To convert this fraction to a mixed number, we multiply the denominator (2) by the whole number part of the mixed number (1) and add the numerator (1):
2 x 1 + 1 = 2 + 1 = 3
So the runner can cover 2 1/2 miles in 16 minutes.
Therefore, the correct answer is D. 2 1/2 miles.
A water tank decreases by 10 gallons every 3 hours every day. What is the total change in amount of water in the tank after 6 days?
To find the total change in the amount of water in the tank after 6 days, we need to calculate the change in the amount of water for each day and then multiply it by the number of days.
Since the water tank decreases by 10 gallons every 3 hours, we need to calculate the change in gallons per hour and then multiply it by the number of hours in a day.
There are 24 hours in a day, so the total amount of water decreased per day is (10 gallons / 3 hours) * 24 hours = 80 gallons.
Therefore, the total change in the amount of water in the tank after 6 days is 6 days * 80 gallons/day = 480 gallons.
So, the total change in the amount of water in the tank after 6 days is 480 gallons.
A recipe calls for 1/3 of a container of yogurt. Each container of yogurt has 150 calories the recipe makes 4 servings. Which set of calculations would give the correct number of calories per serving?
To find the number of calories per serving, we need to calculate the number of calories in 1 serving of the recipe.
The recipe calls for 1/3 of a container of yogurt, which has 150 calories per container.
To find the number of calories in 1 serving, we need to divide the number of calories in 1/3 of a container of yogurt by the number of servings the recipe makes.
Option A: (1/3) * 150 calories / 4 servings = 50 calories / 4 servings = 12.5 calories per serving
Option B: (1/3) * 150 calories * 4 servings = 50 calories * 4 servings = 200 calories per serving
Option C: 150 calories / (1/3) * 4 servings = 150 calories / (1/12) servings = 150 calories * 12 servings = 1800 calories per serving
Option D: (1/3) * (150 calories / 4 servings) = 50 / 4 = 12.5 calories per serving
From the provided options, the correct set of calculations that would give the correct number of calories per serving is Option A: (1/3) * 150 calories / 4 servings = 12.5 calories per serving.