Use the properties of operations and rules for multiplying and dividing to solve:
(-3) divide (3/4) x (2/7) x (-5/16) divide (5/7)
To solve this expression, we will follow the order of operations and apply the properties of operations and rules for multiplying and dividing. First, let's simplify the expression inside the parentheses:
(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
To simplify (-3) ÷ (3/4), we multiply -3 by the reciprocal of 3/4, which is 4/3:
(-3) ÷ (3/4) = -3 × (4/3) = -12/3 = -4
Now we have:
-4 × (2/7) × (-5/16) ÷ (5/7)
Multiplying -4 by (2/7) gives:
-4 × (2/7) = -8/7
Now we have:
-8/7 × (-5/16) ÷ (5/7)
Multiplying -8/7 by (-5/16) gives:
-8/7 × (-5/16) = 40/112 = 5/14
Now we have:
5/14 ÷ (5/7)
Dividing 5/14 by (5/7) gives:
(5/14) ÷ (5/7) = 5/14 × (7/5) = (5*7)/(14*5) = 35/70 = 1/2
Therefore, (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to 1/2.
To solve this expression using the properties of operations and rules for multiplying and dividing, we will follow the order of operations and perform the calculations step by step.
Step 1: Evaluate the division inside parentheses first:
(-3) ÷ (3/4) = -3 × (4/3) = -12/3 = -4
Step 2: Proceed to the multiplication of fractions:
-4 × (2/7) × (-5/16) = (−4 × 2 × −5) / (7 × 16) = 40 / 112
Step 3: Simplify the fraction if possible:
40/112 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 8:
40/8 = 5 and 112/8 = 14
Therefore, 40/112 simplifies to 5/14.
Step 4: Finally, divide the resulting fraction by (5/7):
(5/14) ÷ (5/7) = (5/14) × (7/5) = (5 × 7) / (14 × 5) = 35/70
Step 5: Simplify the fraction if possible:
35/70 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 35:
35/35 = 1 and 70/35 = 2
Therefore, 35/70 simplifies to 1/2.
Therefore, the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to 1/2.
To solve the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), we can use the following steps:
Step 1: Start by simplifying the division operations first.
Since division is equivalent to multiplying by the reciprocal, we have:
(-3) ÷ (3/4) is the same as (-3) × (4/3)
and
(-5/16) ÷ (5/7) is the same as (-5/16) × (7/5)
Step 2: Multiply all the fractions together.
Multiply the fractions from left to right, or perform the multiplication in any order you prefer.
(-3) × (4/3) × (2/7) × (-5/16) × (7/5)
Step 3: Simplify wherever possible.
To simplify, multiply all the numerators together, and then multiply all the denominators together.
(-3) × 4 × 2 × (-5) × 7
3 7 16 5
Step 4: Simplify the resulting fraction.
Now, multiply the numbers in the numerator and the numbers in the denominator.
(-3) × 4 × 2 × (-5) × 7 = -8,400
3 × 7 × 16 × 5 840
Thus, the value of (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) is -8,400/840.
Step 5: Simplify further if needed.
Finally, we can simplify the fraction -8,400/840. The greatest common divisor (GCD) of the numerator and the denominator is 840. Divide both the numerator and denominator by 840 to get the simplified fraction:
-8,400 ÷ 840 = -10
Therefore, the simplified value of (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) is -10.