Use the properties of operations and rules for multiplying and dividing to solve. 9/ divided by (5/4) x (7/9) x (-5) divided by (7/2)
To solve the expression: 9 / (5/4) * (7/9) * (-5) / (7/2), we can simplify it step by step, following the order of operations (parentheses, multiplication/division from left to right, and addition/subtraction from left to right).
First, let's simplify the numerator:
9 * (-5) = -45
Next, let's simplify the denominator:
(5/4) * (7/9) * (7/2) = (5 * 7 * 7) / (4 * 9 * 2) = 245 / 72
Now, we can rewrite the expression as:
-45 / (245 / 72)
To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore:
-45 / (245 / 72) = -45 * (72 / 245) = (-45 * 72) / 245 = -3240 / 245
Now, we can simplify the fraction -3240 / 245 by finding the greatest common divisor (GCD) and dividing both the numerator and denominator by it:
The GCD of 3240 and 245 is 5.
-3240 / 245 = (-3240 / 5) / (245 / 5) = -648 / 49
Therefore, the simplified expression is -648 / 49.
To solve the expression:
9/ (5/4) x (7/9) x (-5) / (7/2)
Step 1: Simplify the expression inside the parentheses from left to right using the division rule.
9/ (5/4) = 9 x (4/5) = 9/1 x 4/5 = 36/5
Step 2: Multiply the remaining fractions from left to right using the multiplication rule.
36/5 x (7/9) = (36 x 7) / (5 x 9) = 252/45
Step 3: Simplify the expression by canceling out common factors between the numerator and the denominator.
252/45 = (7 x 36) / (5 x 9) = 7/5
Step 4: Multiply the remaining fraction by -5 using the multiplication rule.
7/5 x (-5) = (7 x -5) / 5 = -35/5
Step 5: Simplify the expression by canceling out common factors between the numerator and the denominator.
-35/5 = (-7 x 5) / 5 = -7
Therefore, the solution is -7.
To solve the expression 9 / (5/4) x (7/9) x (-5) / (7/2), we need to follow the properties of operations and rules for multiplying and dividing. Let's break it down step by step:
Step 1: Simplify within parentheses:
- In this expression, we have two sets of parentheses, (5/4) and (7/2).
- To simplify, we multiply the fractions within each set of parentheses.
- (5/4) = 5/4
- (7/2) = 7/2
The expression becomes: 9 / (5/4) x (7/9) x (-5) / (7/2)
= 9 / (5/4) x (7/9) x (-5/1) / (7/2)
= 9 / (5/4) x (7/9) x (-5/1) x (2/7)
Step 2: Apply the property of multiplication:
- According to the properties of multiplication, we can multiply the fractions in any order.
- Let's rearrange the expression to group the fractions together.
The expression becomes: 9 x (-5/1) x (5/4) x (7/9) x (2/7)
Step 3: Solve the expression:
- We can now simplify the expression by multiplying all the numbers and fractions together.
9 x (-5/1) x (5/4) x (7/9) x (2/7)
= -45/1 x 5/4 x 7/9 x 2/7
= -45/1 x 5/2 x 1/9
= -45/1 x 5/2 x 1/9
= (-45 x 5)/(1 x 2 x 9)
= -225/18
= -25/2
So, the result of the expression 9 / (5/4) x (7/9) x (-5) / (7/2) is -25/2.