Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
−1,2258
negative Start Fraction 1,225 over 8 End Fraction
1,2258
Start Fraction 1,225 over 8 End Fraction
8
8
−8
To solve the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2), we will follow the order of operations (also known as PEMDAS).
First, we will simplify the division operation (9) ÷ (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) can be rewritten as 9 × (4/5).
Now, let's simplify the multiplication operation: 9 × (4/5). We can multiply the numerator with the numerator and the denominator with the denominator.
9 × (4/5) = (9×4)/(1×5) = 36/5
Next, we will multiply this fraction by (7/9):
(36/5) × (7/9) = (36×7)/(5×9) = 252/45
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor. The greatest common divisor of 252 and 45 is 9.
252/45 = (252 ÷ 9) / (45 ÷ 9) = 28/5
Now, we multiply this fraction by (-5):
(28/5) × (-5) = (28×(-5))/5 = -140/5
Finally, we divide this fraction by (7/2):
(-140/5) ÷ (7/2) = (-140/5) × (2/7) = (-140×2)/(5×7) = -280/35
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 35:
-280/35 = (-280 ÷ 35) / (35 ÷ 35) = -8/1
So, the final simplified answer is -8.
Solve this multi-step problem. A runner completes 1/4 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)
Responses
212 miles
2 Start Fraction 1 over 2 End Fraction miles
18 mile
Start Fraction 1 over 8 End Fraction mile
110 mile
Start Fraction 1 over 10 End Fraction mile
160 miles
To solve the given expression (9)÷(5/4)×(7/9)×(−5)÷(7/2), we can use the properties of operations and rules for multiplying and dividing.
Step 1: Simplify the expression inside the parentheses first.
9 ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
Step 2: To divide a number by a fraction, we multiply by its reciprocal. Therefore, divide 9 by (5/4) is the same as multiplying 9 by (4/5).
9 × (4/5) × (7/9) × (-5) ÷ (7/2)
Step 3: Simplify the numbers in the expression.
(9 × 4) / 5 × (7/9) × (-5) ÷ (7/2)
36/5 × (7/9) × (-5) ÷ (7/2)
Step 4: Multiply the fractions and simplify.
[36 × 7 × (-5)] / [5 × 9 × 7/2]
[(-1,260)] / [45/2]
(-1,260) × (2/45)
(-1,260) / (45/2)
Step 5: To divide by a fraction, multiply by its reciprocal. Therefore, divide (-1,260) by (45/2) is the same as multiplying (-1,260) by (2/45).
(-1,260) × (2/45)
-2,520 / 45
Step 6: Simplify the resulting fraction.
-2,520 ÷ 45
-56
So, the expression (9)÷(5/4)×(7/9)×(−5)÷(7/2) simplifies to -56.
To solve the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2), we can use the properties of operations and rules for multiplying and dividing.
First, let's simplify the numerator and denominator separately:
Numerator:
9 × (-5) = -45
Denominator:
(5/4) × (7/9) × (7/2) = (5 × 7 × 7) ÷ (4 × 9 × 2) = 245 ÷ 72
Now, we can divide the numerator by the denominator:
-45 ÷ (245/72)
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
-45 × (72/245)
Now, we can multiply the numerators and the denominators:
(-45 × 72) / 245 = -3240 / 245
To simplify the resulting fraction, we can find the greatest common divisor (GCD) of the numerator and the denominator and divide both of them by the GCD:
GCD of 3240 and 245 = 5
-3240 ÷ 5 / 245 ÷ 5 = -648 / 49
So, the final answer to the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) is -648/49.
If we convert this fraction to a decimal form, it is approximately -13.2245.