(9)divided by (5/4)x(7/9)x(-5)divided by (7/2)
To solve this expression, we will follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
First, let's simplify the expression inside the parenthesis:
(5/4) * (7/9) * (-5) = -35/36
Now, let's substitute this value back into the main expression:
(9) / (-35/36) / (7/2)
Now, let's simplify the division operations by multiplying by the reciprocal:
(9) * (36/-35) * (2/7)
Calculating the numerator:
9 * 36 * 2 = 648
Calculating the denominator:
-35 * 7 = -245
Therefore, the simplified form of the expression is 648/(-245).
incorrect
Apologies for the mistake. Let's correct it:
To solve the expression, let's simplify it step by step:
First, let's simplify the multiplication inside the parentheses:
(5/4) * (7/9) * (-5) = -175/36
Now, let's substitute this value back into the main expression:
(9) / (-175/36) / (7/2)
To divide by a fraction, we can multiply by its reciprocal:
(9) * (36/(-175)) * (2/7)
Now, let's simplify the numerator:
9 * 36 * 2 = 648
And simplify the denominator:
-175 * 7 = -1225
Therefore, the simplified form of the expression is 648/(-1225).
options
-1225/8
8
-8
1225/8
Apologies for the error in my previous response. Let's reevaluate the expression and get the correct answer:
To solve the expression (9) / (-175/36) / (7/2), we can simplify it step by step:
First, let's simplify the division inside the parentheses:
(-175/36) / (7/2) = (-175/36) * (2/7)
Next, let's multiply the fractions:
(-175/36) * (2/7) = (-175*2) / (36*7) = -350/252
Now, let's substitute this value back into the main expression:
(9) / (-350/252)
To divide by a fraction, we can multiply by its reciprocal:
(9) * (252/-350)
Now, let's simplify the numerator:
9 * 252 = 2268
And simplify the denominator:
-350
Therefore, the simplified form of the expression is 2268/-350.
However, none of the provided options match this simplified form.
To simplify this expression, follow these steps:
Step 1: Convert the division of fractions to multiplication by taking the reciprocal of the denominator.
(9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
is the same as:
(9) × (4/5) × (7/9) × (-5) × (2/7)
Step 2: Cancel out any common factors between numerators and denominators.
The factors 9 and 9 cancel each other out, and the factors 5 and 5 also cancel each other out.
(9) × (4/5) × (7/9) × (-5) × (2/7)
= (1) × (4/1) × (7/1) × (-1) × (2/1)
Step 3: Multiply the numerators and denominators.
(1) × (4/1) × (7/1) × (-1) × (2/1)
= 4 × 7 × (-1) × 2
Step 4: Simplify the expression.
4 × 7 × (-1) × 2 = -56
Therefore, (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) simplifies to -56.
To compute this expression, you need to apply the order of operations (PEMDAS/BODMAS) which states that you should first perform any calculations inside parentheses/brackets, then handle any exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.
Let's calculate step-by-step:
1. Start with the division: (9) divided by (5/4) divided by (7/9) divided by (-5) divided by (7/2).
2. Convert the division into multiplication by taking the reciprocal (inverting) the denominator: (9) multiplied by (4/5) multiplied by (9/7) multiplied by (-1/5) multiplied by (2/7).
3. Simplify the multiplication:
9 * 4 = 36
5 * 9 = 45
7 * 2 = 14
So the expression simplifies to: 36/45 * 9/7 * (-1/5) * (1/14).
4. Cancel out common factors, if possible:
The numerator 36 and denominator 45 both have a common factor of 9, which simplifies to 4 in the numerator and 5 in the denominator.
The expression becomes: 4/5 * 1/7 * (-1/5) * (1/14)
5. Perform the remaining multiplication:
4 * (-1) = -4
So the expression further simplifies to: -4/5 * 1/7 * 1/5 * 1/14.
6. Multiply the fractions:
-4 * 1 * 1 * 1 = -4
The final simplified expression is -4/5 * 1/7 * 1/5 * 1/14, which can also be written as -4/((5 * 7 * 5 * 14)).
Therefore, the value of (9) divided by (5/4) multiplied by (7/9) divided by (-5) divided by (7/2) is -4/((5 * 7 * 5 * 14)).