(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
(1 point)
Responses
−2/3
negative Start Fraction 2 over 3 End Fraction
1/6
Start Fraction 1 over 6 End Fraction
2/3
Start Fraction 2 over 3 End Fraction
−1/6
−1/6
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
(1 point)
Responses
8
8
1,225/8
Start Fraction 1,225 over 8 End Fraction
−8
negative 8
−1,225/8
−1,225/8
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?(1 point)
Responses
2 1/2 miles
2 Start Fraction 1 over 2 End Fraction miles
1/10 mile
Start Fraction 1 over 10 End Fraction mile
1/8 mile
Start Fraction 1 over 8 End Fraction mile
160 miles
The runner completes 1/4 of a 5-mile race every 8 minutes. This means that in 1 minute, the runner completes 1/4 divided by 8, or 1/32 of the race. In 16 minutes, the runner would complete 16 times 1/32, which is 16/32 or 1/2 of the race.
Therefore, the runner can go 1/2 of 5 miles, which is 2 1/2 miles in 16 minutes.
The correct answer is:
2 1/2 miles
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?(1 point)
Responses
480 gallons
480 gallons
−80 gallons
negative 80 gallons
80 gallons
80 gallons
−480 gallons
The water tank decreases by 10 gallons every 3 hours, so it decreases by 10/3 gallons per hour.
In 6 days, there are 6 times 24, or 144 hours.
Therefore, the total change in the amount of water in the tank after 6 days would be 144 times (10/3) gallons.
Calculating this, we get 144 * (10/3) = 480 gallons.
The correct answer 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?(1 point)
Responses
1/3×150×4
Start Fraction 1 over 3 End Fraction times 150 times 4
1/3÷150÷4
Start Fraction 1 over 3 End Fraction divided by 150 divided by 4
1/3×150÷4
Start Fraction 1 over 3 End Fraction times 150 divided by 4
1/3×150÷14
Start Fraction 1 over 3 End Fraction times 150 divided by Start Fraction 1 over 4 End Fraction
The recipe calls for 1/3 of a container of yogurt, which has 150 calories. The recipe makes 4 servings.
To find the number of calories per serving, we need to calculate (1/3) times 150 divided by 4.
Therefore, the correct set of calculations is:
1/3×150÷4
The correct answer is:
Start Fraction 1 over 3 End Fraction times 150 divided by 4
To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction.
First, let's simplify the expression step-by-step:
Step 1: Simplify the multiplication and division from left to right.
(-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4)
-2 × 1/5 = -2/5
Step 2: Continue simplifying the expression.
-2/5÷ (2/3) × (-5/6) ÷ (3/4)
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.
-2/5 ÷ (2/3) = -2/5 × (3/2) = -6/10 = -3/5
Step 3: Simplify the expression further.
-3/5 × (-5/6) ÷ (3/4)
-3/5 × (-5/6) = 15/30 = 1/2
Step 4: Final simplification.
1/2 ÷ (3/4)
To divide fractions, you multiply the first fraction by the reciprocal of the second fraction.
1/2 ÷ (3/4) = 1/2 × (4/3) = 4/6 = 2/3
Therefore, the final answer is 2/3.