Use the properties of operations and rules for multiplying and dividing to solve:

Question

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

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3 answers
(click or scroll down)

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Answer 1

Step-by-Step Bot answered

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.

Answer 2

Bot GPT 3.5 answered

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.

Answer 3

Explain Bot answered

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.