Use the properties of operations and rules for multiplying and dividing to solve: (9)÷(5/4)×(7/9)×(−5)÷(7/2)
1. 1,225/8
2. 8
3. -8
4. -1,225/8
To solve this expression, we can use the properties of operations and rules for multiplying and dividing fractions.
First, let's simplify the expression step by step:
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
Step 1: Divide 9 by 5/4
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 5/4 is 4/5.
So, (9) ÷ (5/4) = 9 × (4/5) = 36/5
Step 2: Multiply 36/5 by 7/9
When multiplying fractions, we can multiply the numerators together and the denominators together.
So, (36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45
Step 3: Multiply 252/45 by -5
When multiplying a fraction by a whole number, we can multiply the numerator of the fraction by the whole number.
So, (252/45) × (-5) = (252 × -5) / 45 = -1,260/45
Step 4: Divide -1,260/45 by 7/2
To divide by a fraction, we can multiply by its reciprocal. The reciprocal of 7/2 is 2/7.
So, (-1,260/45) ÷ (7/2) = -1,260/45 × (2/7) = (-1,260 × 2) / (45 × 7) = -2,520/315
Finally, let's simplify -2,520/315:
We can divide both the numerator and the denominator by their greatest common divisor, which is 45.
-2,520 ÷ 45 = -56
315 ÷ 45 = 7
So, -2,520/315 simplifies to -56/7.
Therefore, the final result is -56/7, which can be simplified to -8, so the correct answer is option 3: -8.
To solve the given expression (9)÷(5/4)×(7/9)×(−5)÷(7/2), we will follow the order of operations (also known as PEMDAS) and the properties of operations for multiplication and division.
Step 1: Simplify the division first:
(9) ÷ (5/4) = 9 × (4/5)
= (9 × 4) / 5
= 36 / 5
Step 2: Multiply all the fractions together:
(36/5) × (7/9) × (-5) × (2/7) = (36 × 7 × -5 × 2) / (5 × 9 × 7)
= (-2520) / (315)
= -8
Therefore, the solution to the given expression is -8.
Hence, the answer is option 3. -8.