Use the properties of operations and rules for multiplying and dividing to solve:
(-3) divided by (3/4) x (2/7) x (-5/16) divided by (5/7)
To solve this expression, we need to follow the order of operations, which is often remembered using the acronym PEMDAS (parentheses, exponents, multiplication/division, addition/subtraction).
First, let's simplify the expression within the parentheses:
(-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7)
= (-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7)
= (-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7)
Next, we can simplify the division by multiplying by the reciprocal:
= (-3) x (4/3) x (2/7) x (-5/16) x (7/5)
= (-3) x (4/3) x (2/7) x (-5/16) x (7/5)
Now, we can cancel out factors that are the same in the numerator and denominator:
= (-1) x (4/1) x (1/7) x (-1/16) x (1/1)
= (-1) x (4/1) x (1/7) x (-1/16) x (1/1)
Finally, let's multiply the remaining factors:
= (-1) x (4/1) x (1/7) x (-1/16) x (1/1)
= -4/112
= -1/28
Therefore, (-3) divided by (3/4) x (2/7) x (-5/16) divided by (5/7) equals -1/28.
To solve the given expression step-by-step, we will 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: Simplify the expression within parentheses:
The expression within parentheses is (-3).
(-3) divided by (3/4) x (2/7) x (-5/16) divided by (5/7) = -3 divided by (3/4) x (2/7) x (-5/16) divided by (5/7)
Step 2: Simplify the division:
To divide by a fraction, we multiply by its reciprocal. So, (-3) divided by (3/4) is the same as (-3) multiplied by (4/3).
(-3) multiplied by (4/3) x (2/7) x (-5/16) divided by (5/7) = (-3) x (4/3) x (2/7) x (-5/16) divided by (5/7)
Step 3: Simplify the multiplication:
Multiply the numerators and denominators together.
(-3) x (4/3) x (2/7) x (-5/16) divided by (5/7) = -120/5040
Step 4: Simplify the division:
Divide the numerator by the denominator.
-120/5040 = -1/42
Therefore, (-3) divided by (3/4) x (2/7) x (-5/16) divided by (5/7) simplifies to -1/42.
To solve the expression (-3) divided by (3/4) x (2/7) x (-5/16) divided by (5/7), we can simplify step by step following the properties of operations and rules for multiplying and dividing.
Step 1: Start by simplifying the division operations.
(-3) divided by (3/4) is the same as multiplying by the reciprocal of (3/4), which is 4/3. So, (-3) divided by (3/4) becomes (-3) x (4/3).
Similarly, (-5/16) divided by (5/7) is the same as multiplying by the reciprocal of (5/7), which is 7/5. So, (-5/16) divided by (5/7) becomes (-5/16) x (7/5).
Now, the expression becomes (-3) x (4/3) x (2/7) x (-5/16) x (7/5).
Step 2: Apply the rule for multiplying fractions.
To multiply fractions, you multiply the numerators together and multiply the denominators together. The resulting fraction can then be simplified if possible.
(-3) x 4 x 2 x (-5) x 7
-----------------------
3 x 1 x 7 x 16 x 5
Step 3: Simplify the numerator and denominator separately.
The numerator simplifies to:
-3 x 4 x 2 x (-5) x 7 = -8 x 7 x (-5) = -280
The denominator simplifies to:
3 x 1 x 7 x 16 x 5 = 2520
Step 4: Simplify the fraction if possible.
Since both the numerator and denominator have a common factor of 10, we can divide both by 10 to simplify the fraction further.
-280 ÷ 10 = -28
2520 ÷ 10 = 252
The simplified fraction is:
-28/252
Step 5: Simplify the fraction to its lowest terms, if possible.
The fraction -28/252 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 28 and 252 is 28.
-28 ÷ 28 = -1
252 ÷ 28 = 9
So, the final simplified result is:
-1/9