Use the properties of operations and rules for multiplying and dividing to solve:
(-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7)
To solve this expression, we need to apply the rules for multiplying and dividing fractions.
First, we can simplify the division by multiplying by the reciprocal of the fraction in the denominator:
(-3) ÷ (3/4) = (-3) x (4/3) = -12/3 = -4
Next, we multiply all the fractions together:
-4 x (2/7) x (-5/16) = (-4) x (2/7) x (-5/16) = 40/112
Finally, we simplify the resulting fraction:
40/112 = 10/28 = 5/14
Therefore, (-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7) simplifies to 5/14.
To solve the expression (-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7), we will follow the order of operations and simplify step by step.
Step 1: Simplify the division (-3) ÷ (3/4):
To divide a number by a fraction, we can multiply the number by the reciprocal of the fraction. The reciprocal of 3/4 is 4/3.
(-3) ÷ (3/4) = (-3) x (4/3)
Multiplying across the numerator and denominator gives us:
(-3) x (4/3) = (-12/3) = -4
So, (-3) ÷ (3/4) simplifies to -4.
Now, the expression becomes -4 x (2/7) x (-5/16) ÷ (5/7).
Step 2: Simplify the multiplication -4 x (2/7):
To multiply fractions, we multiply the numerators together and the denominators together.
-4 x (2/7) = (-4) x (2/7) = (-8/7)
The expression now becomes (-8/7) x (-5/16) ÷ (5/7).
Step 3: Simplify the multiplication (-8/7) x (-5/16):
Multiplying the numerators together and the denominators together, we get:
(-8/7) x (-5/16) = (8/7) x (5/16) = (8 x 5)/(7 x 16) = 40/112
Since both 40 and 112 can be divided by 8, we simplify further:
40/112 = (40 ÷ 8)/(112 ÷ 8) = 5/14
The expression now becomes 5/14 ÷ (5/7).
Step 4: Simplify the division 5/14 ÷ (5/7):
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
5/14 ÷ (5/7) = (5/14) x (7/5)
Multiplying across the numerator and denominator:
(5/14) x (7/5) = (5 x 7)/(14 x 5) = 35/70
Since both 35 and 70 can be divided by 5, we simplify further:
35/70 = (35 ÷ 5)/(70 ÷ 5) = 7/14
Lastly, we can simplify 7/14 by dividing both the numerator and denominator by 7:
7/14 = (7 ÷ 7)/(14 ÷ 7) = 1/2
Therefore, the solution to the expression (-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7) is 1/2.
To solve the expression (-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7), we can use the properties of operations and rules for multiplying and dividing.
Let's break down the expressions step by step:
Step 1: Simplify the division (-3) ÷ (3/4).
To divide by a fraction, we can multiply by its reciprocal.
So, (-3) ÷ (3/4) = (-3) x (4/3)
Now, multiply the numerators and denominators:
(-3) x (4/3) = -12/3
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3:
-12/3 = -4
Step 2: Simplify the multiplication (-4) x (2/7) x (-5/16).
Multiply the numerators together and the denominators together:
(-4) x (2/7) x (-5/16) = (-4 x 2 x -5) / (7 x 16)
Simplify the numerator and denominator:
(-4 x 2 x -5) / (7 x 16) = 40 / (7 x 16)
Step 3: Simplify the division (40) ÷ (5/7).
To divide by a fraction, we can multiply by its reciprocal.
So, (40) ÷ (5/7) = (40) x (7/5)
Multiply the numerators and denominators:
(40) x (7/5) = 280/5
Step 4: Simplify the multiplication (280/5) x (1/1).
Multiply the numerators and denominators together:
(280/5) x (1/1) = 280/5
Step 5: Simplify the fraction 280/5.
To simplify the fraction, divide the numerator by the denominator:
280/5 = 56
Therefore, the result of the expression (-3) ÷ (3/4) x (2/7) x (-5/16) ÷ (5/7) is 56.