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, let's break it down step by step using the properties of operations and rules for multiplying and dividing.
First, let's multiply the fractions:
(-2) × (1/5) = -2/5
Next, let's divide the fractions:
-2/5 ÷ (2/3) = -2/5 × (3/2) = (-2 × 3) / (5 × 2) = -6/10 = -3/5
Now, let's multiply the remaining fractions:
-3/5 × (-5/6) = (3/5) × (5/6) = (3 × 5) / (5 × 6) = 15/30 = 1/2
Finally, let's divide by the last fraction:
1/2 ÷ (3/4) = 1/2 × (4/3) = (1 × 4) / (2 × 3) = 4/6 = 2/3
Therefore, (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) simplifies to 2/3.
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
To solve this expression, let's once again break it down step by step using the properties of operations and rules for multiplying and dividing.
First, let's divide 9 by the fraction (5/4):
9 ÷ (5/4) = 9 × (4/5) = (9 × 4) / 5 = 36/5
Next, let's multiply the resulting fraction by (7/9):
(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45
Now, let's multiply the resulting fraction by -5:
(252/45) × (-5) = (252 × -5) / 45 = -1260/45
Finally, let's divide the resulting fraction by (7/2):
(-1260/45) ÷ (7/2) = (-1260/45) × (2/7) = (-1260 × 2) / (45 × 7) = -2520/315
To simplify this fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 45:
-2520/315 = -56/7
Therefore, (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) simplifies to -56/7, or simply -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?
To solve this problem, we can first calculate the distance the runner completes in 1 minute by dividing 1/4 of a 5-mile race by 8 minutes:
(1/4) * 5 miles / 8 minutes = 5/32 miles per minute
Next, we can multiply the miles per minute by the number of minutes (16) to find the distance the runner can go in 16 minutes:
(5/32) miles per minute * 16 minutes = (5/32) * 16 = 80/32 = 2.5 miles
Therefore, the runner can go 2.5 miles in 16 minutes at the same pace.
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?(1 point)
Responses
18 mile
Start Fraction 1 over 8 End Fraction mile
160 miles
160 miles
212 miles
2 Start Fraction 1 over 2 End Fraction miles
110 mile
To solve this problem, we can first calculate the distance the runner completes in 1 minute by dividing 1/8 of a 5-mile race by 8 minutes:
(1/8) * 5 miles / 8 minutes = 5/64 miles per minute
Next, we can multiply the miles per minute by the number of minutes (16) to find the distance the runner can go in 16 minutes:
(5/64) miles per minute * 16 minutes = (5/64) * 16 = 80/64 = 1.25 miles
Therefore, the runner can go 1.25 miles in 16 minutes at the same pace.
what's 25 divided by 2 then multiplied by 2
To solve the expression "25 divided by 2 then multiplied by 2," we follow the order of operations, which states that we should perform the division first and then the multiplication.
25 ÷ 2 = 12.5
Then, we multiply the result by 2:
12.5 × 2 = 25
So, 25 divided by 2, then multiplied by 2, equals 25.