Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(15)÷(23)×(−56)÷(34)
(1 point)
Responses
23
Start Fraction 2 over 3 End Fraction
−23
negative Start Fraction 2 over 3 End Fraction
−16
negative Start Fraction 1 over 6 End Fraction
16
To solve the expression, we can follow the order of operations (PEMDAS/BODMAS).
First, we perform the multiplication:
(−2) × (15) = −30
Then, we perform the division from left to right:
−30 ÷ (23) = Start Fraction -30 over 23 End Fraction
Then, we continue with the next division:
Start Fraction -30 over 23 End Fraction × (−56) = Start Fraction -30 over 23 End Fraction × Start Fraction -56 over 1 End Fraction = Start Fraction -30 × -56 over 23 × 1 End Fraction = Start Fraction 1680 over 23 End Fraction
Finally, we perform the last division:
Start Fraction 1680 over 23 End Fraction ÷ (34) = Start Fraction 1680 over 23 End Fraction ÷ Start Fraction 34 over 1 End Fraction = Start Fraction 1680 over 23 End Fraction × Start Fraction 1 over 34 End Fraction = Start Fraction 1680 × 1 over 23 × 34 End Fraction = Start Fraction 1680 over 782 End Fraction
Therefore, the value of the expression is Start Fraction 1680 over 782 End Fraction.
Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
(1 point)
Responses
23
Start Fraction 2 over 3 End Fraction
−23
negative Start Fraction 2 over 3 End Fraction
−16
negative Start Fraction 1 over 6 End Fraction
16
To solve this expression, we can follow the order of operations (PEMDAS/BODMAS).
First, we perform the multiplication:
(−2) × (1/5) = -2/5
Then, we perform the division from left to right:
-2/5 ÷ (2/3) = -2/5 × (3/2) = (-6/10) = -3/5
Then, we continue with the next division:
-3/5 × (−5/6) = (-3/5) × (−5/6) = (15/30) = 1/2
Finally, we perform the last division:
1/2 ÷ (3/4) = (1/2) × (4/3) = 4/6 = 2/3
Therefore, the value of the expression is 2/3.
Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(54)×(79)×(−5)÷(72)
(1 point)
Responses
1,2258
Start Fraction 1,225 over 8 End Fraction
−1,2258
negative Start Fraction 1,225 over 8 End Fraction
−8
negative 8
8
8
To solve this expression, we can follow the order of operations (PEMDAS/BODMAS).
First, we perform the division from left to right:
(9) ÷ (54) = 1/6
Then, we continue with the multiplication:
(1/6) × (79) = 79/6
Next, we multiply by (-5):
(79/6) × (-5) = -395/6
Finally, we perform the last division:
(-395/6) ÷ (72) = -395/6 ÷ 72 = -395/432
Therefore, the value of the expression is -395/432.
Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
(1 point)
Responses
1,2258
Start Fraction 1,225 over 8 End Fraction
−1,2258
negative Start Fraction 1,225 over 8 End Fraction
−8
negative 8
8
8
To solve this expression, we can follow the order of operations (PEMDAS/BODMAS).
First, we perform the division from left to right:
(9) ÷ (5/4) = 9 × (4/5) = 36/5
Then, we continue with the multiplication:
(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45
Next, we multiply by (-5):
(252/45) × (-5) = (-252/45) × (5/1) = -1260/45
Finally, we perform the last division:
(-1260/45) ÷ (7/2) = (-1260/45) × (2/7) = (-1260 × 2) / (45 × 7) = -2520/315
Simplifying the fraction, we get:
-2520/315 = -8
Therefore, the value of the expression is -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
110 mile
Start Fraction 1 over 10 End Fraction mile
212 miles
2 Start Fraction 1 over 2 End Fraction miles
18 mile
Start Fraction 1 over 8 End Fraction mile
160 miles
To find out how far the runner can go in 16 minutes, we can first calculate how far the runner can go in 1 minute.
Since the runner completes 1/4 of a 5-mile race every 8 minutes, they complete (1/4) * 5 = 5/4 mile in 8 minutes.
To find out how far the runner goes in 1 minute, we divide 5/4 mile by 8 minutes: (5/4) mile / 8 minutes = 5/4 * 1/8 = 5/32 mile.
Now, we can find how far the runner can go in 16 minutes by multiplying the distance per minute by 16 minutes: (5/32) mile * 16 minutes = 5/32 * 16 = 80/32 = 2.5 miles.
Therefore, the runner can go 2.5 miles in 16 minutes.