Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(15)÷(23)×(−56)÷(34) (1 point) Responses −23 negative Start Fraction 2 over 3 End Fraction 23 Start Fraction 2 over 3 End Fraction −16 negative Start Fraction 1 over 6 End Fraction 16
To solve this expression using the properties of operations and rules for multiplying and dividing, we can proceed step by step:
Step 1: Multiply -2 by 15
-2 × 15 = -30
Step 2: Divide -30 by 23
-30 ÷ 23 ≈ -1.304 (rounded to 3 decimal places)
Step 3: Multiply -1.304 by -56
-1.304 × -56 ≈ 73.184 (rounded to 3 decimal places)
Step 4: Divide 73.184 by 34
73.184 ÷ 34 ≈ 2.155 (rounded to 3 decimal places)
So, the given expression −2 × 15 ÷ 23 × −56 ÷ 34 ≈ 2.155.
Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
To solve this expression using the properties of operations and rules for multiplying and dividing, we can proceed step by step:
Step 1: Multiply -2 by 1/5
-2 × 1/5 = -2/5
Step 2: Divide -2/5 by 2/3
To divide fractions, we multiply the numerator by the reciprocal of the denominator.
-2/5 ÷ 2/3 = -2/5 × 3/2 = -6/10
Step 3: Multiply -6/10 by -5/6
When multiplying fractions, we multiply the numerators together and the denominators together.
-6/10 × -5/6 = 30/60
Step 4: Divide 30/60 by 3/4
To divide fractions, we multiply the numerator by the reciprocal of the denominator.
30/60 ÷ 3/4 = 30/60 × 4/3 = 120/180 = 2/3
Therefore, the given expression (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) simplifies to 2/3.
Use the properties of operations and rules for multiplying and dividing to solve: (9)÷(5/4)×(7/9)×(−5)÷(7/2)
To solve this expression using the properties of operations and rules for multiplying and dividing, we can proceed step by step:
Step 1: Divide 9 by 5/4
To divide by a fraction, we multiply by its reciprocal.
9 ÷ (5/4) = 9 × (4/5) = 36/5
Step 2: Multiply 36/5 by 7/9
To multiply fractions, we multiply the numerators together and the denominators together.
(36/5) × (7/9) = (36 × 7)/(5 × 9) = 252/45
Step 3: Multiply 252/45 by -5
To multiply a fraction by a whole number, we multiply the numerator by the whole number.
(252/45) × -5 = - (252 × 5)/45 = -1260/45
Step 4: Divide -1260/45 by 7/2
To divide by a fraction, we multiply by its reciprocal.
(-1260/45) ÷ (7/2) = (-1260/45) × (2/7) = - (1260 × 2)/(45 × 7) = -5040/315
Now we can simplify the result by dividing the numerator and denominator by their greatest common factor, which is 315.
-5040/315 = -5040 ÷ 315 = -16
Therefore, the given expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) simplifies to -16.
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 1/3×150×4 150 times 4 13÷150÷4 Start Fraction 1 over 3 End Fraction divided by 150 divided by 4 13×150÷14
The correct set of calculations to determine the number of calories per serving would be: 1/3 × 150 ÷ 4.
Explanation:
- The recipe calls for 1/3 of a container of yogurt.
- Each container has 150 calories.
- The recipe makes 4 servings.
To find the number of calories per serving, we need to multiply the fraction of a container used (1/3) by the number of calories in a whole container (150), and then divide by the number of servings (4).
Therefore, the correct calculation is 1/3 × 150 ÷ 4.
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 −480 gallons negative 480 gallons 80 gallons
To find the total change in the amount of water in the tank after 6 days, we need to first determine the change in the amount of water per day and then multiply it by the number of days.
Given that the water tank decreases by 10 gallons every 3 hours, we can calculate the change in gallons per day:
24 hours in a day ÷ 3 hours = 8 sets of 3 hours in a day
So, the water tank decreases by 10 gallons 8 times a day, which gives a decrease of:
10 gallons × 8 = 80 gallons per day
To find the total change in the amount of water after 6 days, we multiply the change per day by the number of days:
80 gallons × 6 days = 480 gallons
Therefore, the total change in the amount of water in the tank after 6 days is 480 gallons.
To solve the expression (-2) × (15) ÷ (23) × (-56) ÷ (34), we can follow the order of operations (PEMDAS/BODMAS).
Step 1: Start by performing the multiplication first. Multiply -2 by 15:
(-2) × (15) = -30
Step 2: Now, perform the division operations from left to right. Divide -30 by 23:
(-30) ÷ (23) = -1.304347826
Step 3: Next, continue with the next division operation. Divide the result from step 2 (-1.304347826) by -56:
(-1.304347826) ÷ (-56) = 0.02327989196
Step 4: Finally, divide the result from the previous step (0.02327989196) by 34:
(0.02327989196) ÷ (34) = 0.0006847029991
So, the final answer is approximately 0.0006847029991.