Use the properties of operations and rules for multiplying and dividing to solve: (9)÷(5/4)×(7/9)×(−5)÷(7/2) (1 point)
To solve the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2), we can simplify it step by step using the properties of operations and rules for multiplying and dividing.
Step 1: Simplify the division (9) ÷ (5/4):
To divide by a fraction, we multiply by its reciprocal. The reciprocal of (5/4) is (4/5). So, the expression becomes:
(9) ÷ (5/4) = (9) × (4/5) = (9 * 4) / 5 = 36/5
Step 2: Simplify the multiplication (36/5) × (7/9):
To multiply fractions, we multiply the numerators and denominators. So, the expression becomes:
(36/5) × (7/9) = (36 * 7) / (5 * 9) = 252/45
Step 3: Simplify the division (252/45) ÷ (-5):
To divide by a negative number, we can multiply by its reciprocal (or simply change the sign). So, the expression becomes:
(252/45) ÷ (-5) = (252/45) × (-1/5) = (-252/45) / 5 = -252/225
Step 4: Simplify the division (-252/225) ÷ (7/2):
Similar to Step 1, we multiply by the reciprocal of (7/2), which is (2/7). So, the expression becomes:
(-252/225) ÷ (7/2) = (-252/225) × (2/7) = (-252 * 2) / (225 * 7) = -504/1575
Therefore, the final result of the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) is -504/1575.
To solve the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2), we can follow the order of operations: parentheses, multiplication, and division (working from left to right).
First, let's simplify the expression inside the parentheses: (9) ÷ (5/4).
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 5/4 is 4/5.
Therefore, (9) ÷ (5/4) = 9 × (4/5).
Now, let's multiply: 9 × (4/5) = (9 × 4) ÷ 5 = 36 ÷ 5.
Next, we multiply by the fraction (7/9): (36 ÷ 5) × (7/9).
To multiply fractions, we multiply the numerators and denominators together: (36 × 7) ÷ (5 × 9) = 252 ÷ 45.
Now, we multiply by -5: (-5) × (252 ÷ 45).
Multiplying a number by -1 flips its sign, so the expression becomes: -(5) × (252 ÷ 45) = -5 × (252 ÷ 45).
Finally, we divide by the fraction (7/2): -5 × (252 ÷ 45) ÷ (7/2).
Similar to before, we can multiply by the reciprocal of 7/2, which is 2/7.
Therefore, -5 × (252 ÷ 45) ÷ (7/2) = -5 × (252 ÷ 45) × (2/7).
To simplify: -5 × (252 ÷ 45) = -5 × (252/45).
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 45/252 is 252/45.
So, -5 × (252 ÷ 45) = -5 × (252/45) = -5 × (252/45) × (252/45).
To multiply fractions, we multiply the numerators and denominators together: -5 × (252 × 252) ÷ (45 × 45).
Now we multiply: -5 × 63504 ÷ 2025.
Finally, we divide: -5 × 63504 ÷ 2025 = -317520 ÷ 2025.
Dividing these two numbers will give you the solution.
To solve this expression, we will use the following properties of operations and rules for multiplying and dividing:
1. Division of fractions: To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction.
2. Multiplication with negative numbers: When multiplying two numbers, if one of them is negative, the product will be negative.
Using these properties, we can simplify the expression:
(9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
First, we can divide 9 by 5/4:
(9) ÷ (5/4) = 9 × (4/5) = 36/5
Next, we can multiply by 7/9:
(36/5) × (7/9) = (36 × 7)/(5 × 9) = 252/45
Now, let's multiply by -5:
(252/45) × (-5) = -5 × (252/45) = -1260/45
Finally, let's divide by 7/2:
(-1260/45) ÷ (7/2) = (-1260/45) × (2/7) = (-1260 × 2)/(45 × 7) = -2520/315
The simplified expression is -2520/315.