(-3) / 3/4 x 2/7 x -5/16 / 5/7
To simplify the expression (-3) / 3/4 x 2/7 x -5/16 / 5/7, we can follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction.
First, let's simplify the fraction part first: -3 / 3/4
To divide by a fraction, we invert the divisor and multiply:
-3 ÷ 3/4 = -3 x 4/3
= -12/3
= -4
Now, let's substitute this value back into the expression and continue simplifying: -4 x 2/7 x -5/16 / 5/7
Next step, multiply: -4 x 2/7 = -8/7
Now, we have: -8/7 x -5/16 / 5/7
Invert the divisor and multiply: -8/7 ÷ 5/7 = -8/7 x 7/5
Cancel out the common factors between the numerators and denominators:
(8/1) x (1/5) = 8/5
Therefore, (-3) / 3/4 x 2/7 x -5/16 / 5/7 simplifies to 8/5.
To simplify the expression (-3) / (3/4) x (2/7) x (-5/16) / (5/7), follow the order of operations (PEMDAS/BODMAS).
Step 1: Solve the division first:
(-3) / (3/4) = (-3) x (4/3) = -12/3 = -4
Step 2: Multiply all the remaining fractions together:
-4 x (2/7) x (-5/16) x (5/7)
Step 3: Group the negative signs together:
-4 x (-5) x (2/7) x (5/16) x (1/7)
Step 4: Simplify the multiplication:
(-4) x (-5) x (2/7) x (5/16) x (1/7) = 200/1568
Step 5: Reduce the fraction, if possible:
200/1568 = 25/196
Therefore, the simplified expression is 25/196.
To simplify the expression (-3) / (3/4) x (2/7) x (-5/16) / (5/7), we follow the order of operations, which is often remembered with the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
First, let's deal with the division:
(-3) / (3/4) = (-3) x (4/3)
To multiply fractions, multiply the numerators (the top numbers) to get the new numerator and multiply the denominators (the bottom numbers) to get the new denominator:
(-3) x (4/3) = -12/3 = -4
Next, let's bring in the other factors:
(-4) x (2/7) x (-5/16) / (5/7)
Multiply the numerators and denominators together:
(-4) x (2/7) x (-5/16) / (5/7) = (-4) x (2) x (-5) / (7) x (16) x (5/7)
Multiply the numbers together:
(-4) x (2) x (-5) = 40
Multiply the denominators together:
(7) x (16) x (5/7) = 560/7 = 80
Finally, divide the numerator by the denominator:
40 / 80 = 1/2
Therefore, the simplified expression is 1/2.