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)
A 1,225/8
B 8
C -1,225/8
D -8
To solve this expression, we will follow the order of operations (also known as PEMDAS). First, we evaluate any multiplication or division from left to right, and then we evaluate any addition or subtraction from left to right.
First, let's simplify the expression step by step:
(9) ÷ (5/4) x (7/9) x (-5) ÷ (7/2)
We can rewrite the expression using parentheses:
(9 ÷ (5/4)) x ((7/9) x (-5)) ÷ (7/2)
Now, let's simplify the expression within each set of parentheses:
9 ÷ (5/4) = 9 x (4/5) = 36/5
(7/9) x (-5) = (-5/1) x (7/9) = -35/9
Now let's simplify the expression further:
(36/5) x (-35/9) ÷ (7/2)
To multiply fractions, we multiply the numerators and multiply the denominators:
(36 x -35) / (5 x 9) ÷ (7/2)
-1260 / 45 ÷ (7/2)
To divide fractions, we invert the second fraction and multiply:
-1260 / 45 x (2/7)
Simplifying:
-36 x (2/7)
-72/7
Therefore, the final answer is -72/7, which is approximately -10.29.
Therefore, the correct option is C) -1,225/8.
To solve the expression (9) divided by (5/4) x (7/9) x (-5) divided by (7/2), we follow the order of operations, which states that we should first perform any calculations inside parentheses, then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Let's break down the expression step by step:
Step 1: Simplify the division (9) divided by (5/4):
To divide by a fraction, we multiply by its reciprocal (flip the fraction). So, (9) divided by (5/4) becomes (9) multiplied by (4/5):
(9) multiplied by (4/5) = (9 * 4) / 5 = 36 / 5
Step 2: Simplify the multiplication (36/5) x (7/9):
To multiply fractions, we simply multiply the numerators together and the denominators together:
(36/5) x (7/9) = (36 * 7) / (5 * 9) = 252 / 45
Step 3: Simplify the division (-5) divided by (7/2):
Again, we divide by a fraction by multiplying by its reciprocal:
(-5) divided by (7/2) becomes (-5) multiplied by (2/7):
(-5) multiplied by (2/7) = (-5 * 2) / 7 = -10 / 7
Step 4: Multiply all the remaining fractions:
(252 / 45) x (-10/7)
To multiply fractions, we multiply the numerators together and the denominators together:
(252 x -10) / (45 x 7) = -2520 / 315
Now, we simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5:
-2520 / 315 = -504 / 63
Dividing both the numerator and denominator by 7 gives:
-504 / 63 = -72 / 9
Finally, dividing both the numerator and denominator by 9 gives the simplified fraction:
-72 / 9 = -8
Therefore, the expression (9) divided by (5/4) x (7/9) x (-5) divided by (7/2) simplifies to -8. So, the correct answer is option D.