Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(54)×(79)×(−5)÷(72)
To solve this expression, we will follow the rules for multiplying and dividing.
First, we can multiply the numbers together in any order since multiplication is commutative.
(9) × (79) × (-5) × (54) ÷ (72)
Next, we can multiply the numbers together since multiplication is associative.
(9 × 79 × -5 × 54) ÷ 72
Now, we can perform the multiplication:
(6378 × -5 × 54) ÷ 72
Next, we divide the result by 72:
(6378 × -5 × 54) ÷ 72 = -18090 ÷ 72 = -251.25
So, the solution to the expression (9)÷(54)×(79)×(−5)÷(72) is -251.25.
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?
To solve this problem, we can set up a proportion to find out how far the runner can go in 16 minutes.
We know that the runner completes 14 miles in 8 minutes. Let's call the distance the runner can go in 16 minutes "x".
The proportion can be set up as:
14 miles / 8 minutes = x miles / 16 minutes
To solve for x, we can cross-multiply and then divide:
14 * 16 = 8 * x
224 = 8x
x = 224 / 8
x = 28
So, the runner can go 28 miles in 16 minutes.
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?
18 mile
Start Fraction 1 over 8 End Fraction mile
212 miles
2 Start Fraction 1 over 2 End Fraction miles
160 miles
160 miles
110 mile
To solve this problem, we need to find out how far the runner can go in 16 minutes, using the information given that the runner completes 14 miles of a 5-mile race every 8 minutes.
First, we need to find the runner's pace in miles per minute. To do this, we divide the distance (5 miles) by the time (8 minutes):
5 miles / 8 minutes = 0.625 miles per minute
Next, we can multiply the runner's pace (0.625 miles per minute) by the time (16 minutes) to find out how far the runner can go:
0.625 miles per minute * 16 minutes = 10 miles
Therefore, the runner can go 10 miles in 16 minutes.
A water tank decreases by 10 gallons every 3 hours every day. What is the total change in the 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 determine the change in water per day and then multiply it by the number of days.
We know that the tank decreases by 10 gallons every 3 hours. Since there are 24 hours in a day, we can divide the 24 hours by 3 to find out how many times the tank decreases in a day:
24 hours / 3 hours = 8 decreases
Therefore, the tank decreases by 10 gallons 8 times in a day, resulting in a total decrease of:
10 gallons * 8 decreases = 80 gallons per day
To find the total change in the amount of water in the tank after 6 days, we multiply this daily decrease by the number of days:
80 gallons per day * 6 days = 480 gallons
Therefore, the total change in the amount of water in the tank after 6 days is a decrease of 480 gallons.
A recipe calls for 13 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 correct number of calories per serving, we need to divide the total number of calories in the containers of yogurt by the number of servings.
The recipe calls for 13 of a container of yogurt, and each container has 150 calories. Therefore, the total number of calories in the yogurt is:
13 containers * 150 calories per container = 1950 calories
The recipe makes 4 servings. To find the number of calories per serving, we divide the total number of calories by the number of servings:
1950 calories / 4 servings = 487.5 calories per serving
So, the correct set of calculations is:
13 containers * 150 calories per container = 1950 calories
1950 calories / 4 servings = 487.5 calories per serving
Therefore, the correct number of calories per serving is 487.5.
To solve the expression (9)÷(54)×(79)×(−5)÷(72), let's break it down step by step using the properties of operations and rules for multiplying and dividing.
Step 1: Simplify division
Start by simplifying the division operation (9)÷(54). To do this, divide 9 by 54:
9 ÷ 54 = 0.16666667 (rounded to eight decimal places)
Step 2: Multiply remaining numbers
Next, multiply the remaining numbers: 0.16666667 × (79) × (−5) ÷ (72).
Step 3: Apply the Commutative Property of Multiplication
Since multiplication is commutative, the order of numbers being multiplied does not affect the result. Therefore, we can choose the order of multiplication that makes the calculation easier.
Let's rearrange the calculation:
(0.16666667 × 79 × −5) ÷ 72
Step 4: Perform multiplication
Multiply the numbers: 0.16666667 × 79 × −5 = -6.58333335 (rounded to eight decimal places)
Step 5: Perform division
Divide the result from step 4 by 72:
-6.58333335 ÷ 72 ≈ -0.09143750 (rounded to eight decimal places)
So, the value of the expression (9)÷(54)×(79)×(−5)÷(72) is approximately -0.09143750.