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
8
−1,225/8
To solve the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2), we can simplify step by step:
Step 1: Perform the division (9) ÷ (5/4) by multiplying the numerator (9) by the reciprocal of the denominator (5/4). The reciprocal of 5/4 is 4/5.
(9) ÷ (5/4) = (9) × (4/5) = 36/5
Step 2: Multiply the result from Step 1, 36/5, by (7/9).
(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252/45
Step 3: Multiply the result from Step 2, 252/45, by (-5).
(252/45) × (-5) = -1260/45
Step 4: Perform the division -1260/45 by multiplying the numerator (-1260) by the reciprocal of the denominator (45/1). The reciprocal of 45/1 is 1/45.
(-1260/45) ÷ (45/1) = (-1260/45) × (1/45) = -1260/2025
Simplifying the fraction -1260/2025 gives the final answer:
-1260/2025 = -14/25
Therefore, the value of the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) is -14/25.
To solve the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2), let's use the order of operations:
Step 1: Divide 9 by 5/4.
To divide a number by a fraction, you can multiply the number by the reciprocal of the fraction. The reciprocal of 5/4 is 4/5.
9 ÷ (5/4) = 9 × (4/5)
Step 2: Simplify the fraction 4/5.
There are no common factors between 4 and 5, so we can't simplify the fraction any further.
9 × (4/5) = 36/5
Step 3: Multiply by 7/9.
To multiply fractions, multiply the numerators together and the denominators together.
36/5 × 7/9 = (36 × 7) / (5 × 9)
Step 4: Simplify the fraction (36 × 7) / (5 × 9).
Calculate the numerator and denominator separately.
Numerator: 36 × 7 = 252
Denominator: 5 × 9 = 45
So, (36 × 7) / (5 × 9) = 252/45
Step 5: Divide by -5.
To divide a fraction by a number, multiply the fraction by the reciprocal of the number. The reciprocal of -5 is -1/5.
252/45 ÷ -5 = 252/45 × (-1/5)
Step 6: Simplify the fraction (-1/5) multiplied by (252/45).
Multiply the numerators together and the denominators together.
(-1/5) × (252/45) = (-1 × 252) / (5 × 45)
Step 7: Simplify the fraction (-1 × 252) / (5 × 45).
Calculate the numerator and denominator separately.
Numerator: -1 × 252 = -252
Denominator: 5 × 45 = 225
So, (-1 × 252) / (5 × 45) = -252/225
Therefore, the solution to the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2) is -252/225.
To solve the expression (9)÷(5/4)×(7/9)×(-5)÷(7/2), we can follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
Step 1: Evaluate the expression within the parentheses:
(5/4) is a fraction, so dividing 9 by (5/4) is equivalent to multiplying 9 by its reciprocal, which is (4/5):
(9)÷(5/4) = 9 × (4/5) = 36/5
Step 2: Perform the multiplication and division from left to right:
Multiply 36/5 by 7/9:
(36/5) × (7/9) = (36 × 7) / (5 × 9) = 252 / 45
Divide 252/45 by -5:
(252/45) × (-5) = (252 × -5) / 45 = -1,260 / 45
Divide -1,260/45 by 7/2:
(-1,260/45) ÷ (7/2) = (-1,260/45) × (2/7) = (-1,260 × 2) / (45 × 7) = -2,520 / 315
Step 3: Simplify the final fraction:
To simplify -2,520/315, we can find the greatest common divisor (gcd) of the numerator and denominator:
gcd(2,520, 315) = 45
Divide both the numerator and denominator by the gcd:
(-2,520 ÷ 45) / (315 ÷ 45) = -56 / 7
Simplifying further:
-56 ÷ 7 = -8
Therefore, the solution to the expression (9)÷(5/4)×(7/9)×(-5)÷(7/2) is -8.