Use the properties of operations and rules for multiplying and dividing to solve: (−3)÷(3/4)×(2/7)×(−5/16)÷(5/7) (1 point)
To solve the expression (-3)÷(3/4)×(2/7)×(-5/16)÷(5/7), we can follow the order of operations (parentheses, exponents, multiplication and division from left to right).
First, let's start by simplifying the division:
(-3) ÷ (3/4) = -3 × (4/3)
Now, let's simplify the multiplication:
-3 × (4/3) × (2/7) × (-5/16) ÷ (5/7) = -3 × (4/3) × (2/7) × (-5/16) × (7/5)
Next, we can cancel out some factors:
-3 × (4/3) × (2/7) × (-5/16) × (7/5) = -1 × (4/1) × (1/1) × (-1/4) × (1/1)
Now, we can multiply the numerators and denominators:
-1 × (4/1) × (1/1) × (-1/4) × (1/1) = (-1 × 4 × 1 × -1 × 1) / (1 × 1 × 4 × 1)
Finally, we can calculate the result:
(-1 × 4 × 1 × -1 × 1) / (1 × 1 × 4 × 1) = (-4 × -1) / (4 × 1) = 4 / 4 = 1
Therefore, the solution to the expression (-3)÷(3/4)×(2/7)×(-5/16)÷(5/7) is 1.
To solve the given expression (−3)÷(3/4)×(2/7)×(−5/16)÷(5/7), we can follow the order of operations (PEMDAS/BODMAS) and apply the properties of multiplication and division.
Step 1: Simplify the division
(−3) ÷ (3/4) = (−3) × (4/3)
To divide by a fraction, we can multiply by its reciprocal. Therefore, we can rewrite the division expression as a multiplication expression:
(−3) × (4/3) = (−3) × (4/3) × (1/1)
Step 2: Simplify the multiplication
Now we can multiply all the fractions together. To multiply fractions, we multiply the numerators and multiply the denominators:
(−3) × (4/3) × (2/7) × (−5/16) × (1/1) = (−3 × 4 × 2 × −5) / (3 × 7 × 16)
Step 3: Calculate the numerator and denominator separately
For the numerator:
(−3 × 4 × 2 × −5) = (−120)
For the denominator:
(3 × 7 × 16) = (336)
Step 4: Simplify the fraction
Combine the numerator and denominator to simplify the fraction:
(−120) / (336)
Step 5: Simplify the fraction further, if possible
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD) which is 24:
(−120) / (336) = (−5) / (14)
Therefore, the simplified form of the expression (−3)÷(3/4)×(2/7)×(−5/16)÷(5/7) is (−5/14).
To solve this expression, we can simplify the given expression step by step using the properties of operations and rules for multiplying and dividing.
First, let's simplify the division part:
(-3) ÷ (3/4) = (-3) × (4/3)
Using the rule for dividing by a fraction, we can rewrite the division as a multiplication by the reciprocal:
(-3) × (4/3) = (-3) × (4/3) × (1/1)
Next, let's simplify the multiplication:
(-3) × (4/3) × (2/7) × (-5/16) × (5/7)
Using the property of multiplication, we can rewrite the above expression by multiplying all the numerators and multiplying all the denominators:
((-3) × 4 × 2 × (-5) × 5) / (3 × 7 × 16 × 7)
Now, let's simplify the numerator:
((-3) × 4 × 2 × (-5) × 5) = 600
And simplify the denominator:
(3 × 7 × 16 × 7) = 2,352
Therefore, the simplified expression is:
600 / 2,352
= 25 / 98
Final Answer: 25/98