Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
(1 point)
Responses
−8
1,225/8
−1,225/8
8
To solve (9)÷(5/4)×(7/9)×(−5)÷(7/2), we can follow these steps:
Step 1: Simplify the division:
(9) ÷ (5/4) = (9) × (4/5) = (9 * 4) / 5 = 36/5
Step 2: Simplify the multiplication:
(36/5) × (7/9) × (-5) × (7/2) = (36 * 7 * -5 * 7) / (5 * 9 * 2)
Step 3: Perform the multiplication in the numerator:
36 * 7 * -5 * 7 = -8,820
Step 4: Perform the multiplication in the denominator:
5 * 9 * 2 = 90
Step 5: Final division:
-8,820 / 90 = -98
Therefore, the solution is -98.
To solve this expression, we can simplify it step by step using the properties of operations and rules for multiplying and dividing.
First, let's simplify the division by a fraction:
(9) ÷ (5/4) = 9 × (4/5)
The 5 in the denominator of the fraction becomes a factor of 9 and the denominator becomes 1. So, we have:
= 9 × 4/5
= 36/5
Next, let's simplify the multiplication of fractions:
36/5 × (7/9)
When multiplying fractions, we multiply the numerators and multiply the denominators.
= (36 × 7)/(5 × 9)
= 252/45
Now, let's simplify the division by another fraction:
252/45 ÷ (7/2) = 252/45 × (2/7)
Similarly, we multiply the numerators and multiply the denominators.
= (252 × 2)/(45 × 7)
= 504/315
Finally, let's multiply the result by -5:
504/315 × -5
Multiplying a fraction by a whole number is the same as multiplying the numerator by the whole number.
= (-5) × (504/315)
= -2520/315
We can simplify this fraction by finding a common factor between the numerator and denominator. In this case, we can divide both by 315:
= -2520/315 ÷ 315/315
= -2520/1
= -2520
Therefore, the simplified expression is -2520, which corresponds to the answer -8 from the given options.
To solve the given expression, you need to follow the rules for multiplying and dividing numbers. Let's break down the steps:
Step 1: Simplify the division within parentheses.
(9) ÷ (5/4) = 9 / (5/4)
To divide by a fraction, you can multiply by its reciprocal.
9 / (5/4) = 9 * (4/5)
Step 2: Multiply the fractions.
9 * (4/5) = 36/5
Step 3: Simplify the division within parentheses.
(36/5) × (7/9) = (36/5) * (7/9)
Here, you can multiply numerators and denominators to find the product.
(36/5) * (7/9) = (36 * 7) / (5 * 9)
Step 4: Multiply the numbers.
(36 * 7) / (5 * 9) = 252 / 45
Step 5: Simplify the division.
252 / 45 can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator, which is 9.
252 / 45 = (252 ÷ 9) / (45 ÷ 9) = 28 / 5
Step 6: Simplify the final division.
(28/5) × (−5) ÷ (7/2) = (28/5) * (−5) / (7/2)
To divide by a fraction, multiply by its reciprocal.
(28/5) * (−5) / (7/2) = (28/5) * (−5) * (2/7)
Step 7: Multiply the numbers.
(28/5) * (−5) * (2/7) = (28 * −5 * 2) / (5 * 7)
Step 8: Simplify the multiplication.
(28 * −5 * 2) / (5 * 7) = (−140) / 35
Step 9: Simplify the division.
(−140) / 35 can be simplified by dividing both the numerator and denominator by 35.
(−140) / 35 = (−140 ÷ 35) / (35 ÷ 35) = −4 / 1
Step 10: The final answer.
−4 / 1 can be written simply as −4.
Hence, the answer to the expression is −4.