To solve the given expression (-2) x (1/5) ÷ (2/3) x (- 5/6) ÷ (3/4), we follow the order of operations: parentheses, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, we simplify the multiplication inside the parentheses:
(-2) x (1/5) = -2/5
Then, we divide the fractions:
(-2/5) ÷ (2/3) = (-2/5) x (3/2) = (-6/10) = -3/5
Next, we continue with the remaining multiplication:
(-3/5) x (-5/6) = (3/5) x (5/6) = (15/30) = 1/2 = 0.5
Finally, we divide by the fraction (3/4):
0.5 ÷ (3/4) = 0.5 x (4/3) = 2/6 = 1/3 = 0.3333 (rounded to four decimal places)
Therefore, the solution to the expression (-2) x (1/5) ÷ (2/3) x (- 5/6) ÷ (3/4) is approximately 0.3333.
Use the properties of operations and rules for multiplying and dividing to solve:
(-2) x (1/5) ÷ (2/3) x (- 5/6) ÷ (3/4)
17 answers
As a fraction
The solution to the expression (-2) x (1/5) ÷ (2/3) x (- 5/6) ÷ (3/4) as a fraction is 1/3.
Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
A. −1,225/8
B. −8
C. 1,225/8
D. 8
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
A. −1,225/8
B. −8
C. 1,225/8
D. 8
To solve the given expression (9)÷(5/4)×(7/9)×(−5)÷(7/2), we follow the order of operations: parentheses, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, we divide 9 by 5/4:
9 ÷ (5/4) = 9 x (4/5) = (36/5)
Next, we multiply by 7/9:
(36/5) x (7/9) = (36 x 7) / (5 x 9) = (252/45)
Then, we multiply by -5:
(252/45) x (-5) = - (252/45) x 5 = - (1260/45)
Finally, we divide by 7/2:
- (1260/45) ÷ (7/2) = - (1260/45) x (2/7) = - (2520/315) = -8/1
Therefore, the solution to the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2) is -8.
The correct choice among the given options is B. -8.
First, we divide 9 by 5/4:
9 ÷ (5/4) = 9 x (4/5) = (36/5)
Next, we multiply by 7/9:
(36/5) x (7/9) = (36 x 7) / (5 x 9) = (252/45)
Then, we multiply by -5:
(252/45) x (-5) = - (252/45) x 5 = - (1260/45)
Finally, we divide by 7/2:
- (1260/45) ÷ (7/2) = - (1260/45) x (2/7) = - (2520/315) = -8/1
Therefore, the solution to the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2) is -8.
The correct choice among the given options is B. -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?
A. 1/10 mile
B. 1/8 mile
C. 160 miles
D. 2 1/2 miles
A. 1/10 mile
B. 1/8 mile
C. 160 miles
D. 2 1/2 miles
To solve this problem, we can set up a proportion.
Since the runner completes 1/4 of the race in 8 minutes, we can say that the runner completes 1 mile in 8 minutes.
Let x represent the distance the runner can go in 16 minutes.
The proportion can be set up as:
1 mile / 8 minutes = x miles / 16 minutes
To solve for x, we can cross multiply:
8 minutes * x miles = 1 mile * 16 minutes
8x = 16
Dividing both sides of the equation by 8, we get:
x = 2
Therefore, the runner can complete 2 miles in 16 minutes.
The correct choice among the given options is not listed, as the runner can go 2 miles in 16 minutes.
Since the runner completes 1/4 of the race in 8 minutes, we can say that the runner completes 1 mile in 8 minutes.
Let x represent the distance the runner can go in 16 minutes.
The proportion can be set up as:
1 mile / 8 minutes = x miles / 16 minutes
To solve for x, we can cross multiply:
8 minutes * x miles = 1 mile * 16 minutes
8x = 16
Dividing both sides of the equation by 8, we get:
x = 2
Therefore, the runner can complete 2 miles in 16 minutes.
The correct choice among the given options is not listed, as the runner can go 2 miles in 16 minutes.
Answer as a fraction
Apologies for the oversight.
To answer the question as a fraction, the runner can go 2 miles in 16 minutes, which can be expressed as 2/1.
To answer the question as a fraction, the runner can go 2 miles in 16 minutes, which can be expressed as 2/1.
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?
A. 80 gallons
B. −480 gallons
C.480 gallons
D. −80 gallons
A. 80 gallons
B. −480 gallons
C.480 gallons
D. −80 gallons
To find the total change in the amount of water in the tank after 6 days, we first need to calculate the total change in the amount of water in the tank for one day.
Every day, the water tank decreases by 10 gallons every 3 hours. Since there are 24 hours in a day, the tank decreases by 10/3 gallons per hour (10 gallons divided by 3 hours).
To find the total change in the amount of water in the tank for one day, we multiply the rate of decrease per hour by the number of hours in a day:
(10/3 gallons/hour) x (24 hours/day) = 80 gallons/day
Therefore, the total change in the amount of water in the tank after 6 days is:
(80 gallons/day) x (6 days) = 480 gallons
The correct choice among the given options is C. 480 gallons.
Every day, the water tank decreases by 10 gallons every 3 hours. Since there are 24 hours in a day, the tank decreases by 10/3 gallons per hour (10 gallons divided by 3 hours).
To find the total change in the amount of water in the tank for one day, we multiply the rate of decrease per hour by the number of hours in a day:
(10/3 gallons/hour) x (24 hours/day) = 80 gallons/day
Therefore, the total change in the amount of water in the tank after 6 days is:
(80 gallons/day) x (6 days) = 480 gallons
The correct choice among the given options is C. 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?
A. 1/3×150÷4
B. 1/3×150×4
C. 1/3÷150÷4
D. 1/3×150÷14
A. 1/3×150÷4
B. 1/3×150×4
C. 1/3÷150÷4
D. 1/3×150÷14
To calculate the number of calories per serving, we need to multiply the fraction of a container of yogurt used in the recipe by the number of calories in a full container of yogurt, and then divide it by the number of servings the recipe makes.
The correct set of calculations would be:
A. 1/3×150÷4
This calculation can be broken down step by step as follows:
1/3 × 150 = 50
50 ÷ 4 = 12.5
Therefore, the correct set of calculations to find the number of calories per serving is A. 1/3×150÷4, which gives us 12.5 calories per serving.
The correct set of calculations would be:
A. 1/3×150÷4
This calculation can be broken down step by step as follows:
1/3 × 150 = 50
50 ÷ 4 = 12.5
Therefore, the correct set of calculations to find the number of calories per serving is A. 1/3×150÷4, which gives us 12.5 calories per serving.
Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(34)×(27)×(−516)÷(57)
(−3)÷(34)×(27)×(−516)÷(57)
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?
A. 80 gallons
B. −480 gallons
C.480 gallons
D. −80 gallons
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The Correct answer is -480
A. 80 gallons
B. −480 gallons
C.480 gallons
D. −80 gallons
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The Correct answer is -480
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. 1/10 mile
B. 1/8 mile
C. 160 miles
D. 2 1/2 miles
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The Correct Answer is 2 1/2
A. 1/10 mile
B. 1/8 mile
C. 160 miles
D. 2 1/2 miles
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The Correct Answer is 2 1/2
Use the properties of operations and rules for multiplying and dividing to solve: (8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5)