Use the properties of operations and rules for multiplying and dividing to solve:
(9) divide (5/4) x (7/9) x (-5) divide (7/2)
1,225/8
8
-1,225/8
-8
To solve this expression, we can apply the properties of operations and rules for multiplying and dividing.
First, let's simplify the numerator:
(5/4) x (7/9) x (-5) = (5 x 7 x -5)/(4 x 9) = -175/36
Now, let's simplify the denominator:
(7/2) = 7/2
Finally, let's divide the numerator by the denominator:
(-175/36) ÷ (7/2) = (-175/36) x (2/7) = (-175 x 2)/(36 x 7) = -350/252 = -175/126
Therefore, the solution is -175/126.
To solve the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2), we will follow the order of operations, which states we should first perform any operations inside parentheses or brackets, then handle any exponents, followed by multiplication and division (in order from left to right), and finally addition and subtraction (in order from left to right).
Step 1: Simplify the expression inside parentheses.
Since there are no parentheses in the given expression, we will move on to the next step.
Step 2: Evaluate the division and multiplication from left to right.
Starting with the division (9) ÷ (5/4):
To divide by a fraction, we multiply by its reciprocal.
(9) ÷ (5/4) = 9 × (4/5)
Now we multiply:
9 × (4/5) = (9 × 4) / 5 = 36/5
Next, we multiply (36/5) × (7/9):
When multiplying fractions, we multiply the numerators together and the denominators together.
(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45 (which can be simplified to 14/5)
Next, we multiply (14/5) × (-5):
To multiply by a negative number, we simply change the sign of the product.
(14/5) × (-5) = -70/5 (which can be simplified to -14)
Finally, we have the expression -14 ÷ (7/2):
To divide by a fraction, we multiply by its reciprocal.
-14 ÷ (7/2) = -14 × (2/7) = (-14 × 2) / 7 = -28/7
Step 3: Simplify the result.
-28/7 = -4
Therefore, the solution to the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) is -4.
To solve the given expression using the properties of operations and rules for multiplying and dividing, follow these steps:
Step 1: Simplify the expression by performing the division operations first.
(9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2)
Step 2: Divide 9 by 5/4.
9 ÷ (5/4) = 9 × (4/5) = 9/1 × 4/5 = 36/5
So far, the expression simplifies to:
36/5 x (7/9) x (-5) ÷ (7/2)
Step 3: Divide 36/5 by 7/9.
(36/5) ÷ (7/9) = (36/5) × (9/7)
Next, cancel out any common factors if possible:
(36/5) × (9/7) = (36 ÷ 5) × (9 ÷ 7) = 36/5 × 9/7 = 324/35
Now, the expression becomes:
324/35 x (-5) ÷ (7/2)
Step 4: Multiply 324/35 by -5.
324/35 x (-5) = -324/35 x 5 = -324 ÷ 35 × 5/1 = -9720/35
The expression simplifies to:
-9720/35 ÷ (7/2)
Step 5: Divide -9720/35 by 7/2.
(-9720/35) ÷ (7/2) = (-9720/35) × (2/7)
Again, cancel out any common factors:
(-9720/35) × (2/7) = (-9720 ÷ 35) × (2 ÷ 7) = -9720/35 × 2/7 = -139200/245
Therefore, the final solution to the expression is -139200/245.
But to clarify, when simplified, -139200/245 can be further reduced. Dividing the numerator and the denominator by their greatest common divisor (GCD), which is 5, we get:
-139200 ÷ 5 / 245 ÷ 5 = -27,840 / 49
So, the simplified form of the expression is -27,840/49, which is approximately equal to -567.7551.