(9)÷(5/4)×(7/9)×(−5)÷(7/2)
To solve this expression, we follow the order of operations (brackets, exponents, multiplication/division from left to right, and addition/subtraction from left to right).
(9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
First, divide 9 by 5/4:
(9) ÷ (5/4) = 9 * (4/5) = 36/5
Next, multiply by 7/9:
(36/5) × (7/9) = (36 * 7) / (5 * 9) = 252/45
Now, multiply by -5:
(252/45) × -5 = (252 * -5) / 45 = -1260/45
Finally, divide by 7/2:
(-1260/45) ÷ (7/2) = (-1260/45) * (2/7) = (-1260 * 2) / (45 * 7) = -2520/315
The simplified answer is -2520/315.
worng.
Apologies for the confusion. Let's solve the expression correctly:
(9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
First, let's simplify the division:
9 ÷ (5/4) is the same as 9 × (4/5) = (9 * 4) / 5 = 36/5.
Next, let's multiply the fractions:
(36/5) × (7/9) is (36 * 7) / (5 * 9) = 252/45.
Now, let's multiply by -5:
(252/45) × (-5) = (252 * -5) / 45 = -1260/45.
Lastly, let's divide by (7/2):
(-1260/45) ÷ (7/2) is the same as (-1260/45) × (2/7).
Multiplying the fractions gives us (-1260 * 2) / (45 * 7) = -2520/315.
The simplified answer is -2520/315.
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?
To solve this problem, we can set up a proportion to compare the distance covered and the time taken.
The runner completes 14 miles in 8 minutes.
So, the runner's rate is 14 miles / 8 minutes = 7/4 miles per minute.
Now, we need to find out how far the runner can go in 16 minutes using the same pace.
Distance covered = rate * time
Distance covered = (7/4 miles per minute) * 16 minutes
Distance covered = 28 miles / 4
Distance covered = 7 miles
Therefore, the runner can go 7 miles in 16 minutes at the same pace.
To solve the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2), we need to follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Step 1: Simplify the expression inside the parentheses:
(5/4) is the same as 5÷4, which equals 1.25.
Step 2: Replace the division symbol ÷ with multiplication and flip the denominator:
(9)÷(5/4) becomes (9)×(4/5).
Step 3: Simplify the expression:
(9)×(4/5) equals 36/5 or 7.2.
Step 4: Multiply the remaining fractions:
7.2×(7/9)×(−5)÷(7/2)
Step 5: Simplify the expression:
Multiply the numerators together: 7.2 × 7 × -5 = -252.
Multiply the denominators together: 9 × 2 = 18.
So, the expression simplifies to -252/18 or -14.
Therefore, (9)÷(5/4)×(7/9)×(−5)÷(7/2) equals -14.
To solve this expression, we'll follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication & Division, Addition & Subtraction).
Step 1: Evaluate within parentheses (if any)
There are no parentheses in the expression.
Step 2: Perform any divisions or multiplications
Start by calculating the divisions and multiplications from left to right.
(9) ÷ (5/4) = 9 ÷ 1.25 = 7.2
7.2 × (7/9) = 7.2 × 7/9 = 5.6
5.6 × (-5) = -28
-28 ÷ (7/2) = -28 × 2/7 = -8
Therefore, the final result of the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) is -8.