Use the properties of operations and rules for multiplying and dividing to solve:
(-3)➗(3/4) x (-5/16)➗(5/7)
To solve this expression, we can follow the order of operations and apply the properties of operations:
1. First, let's simplify the expression within each set of parentheses:
(-3) ➗ (3/4) = -3 x (4/3) = -12/3 = -4
(-5/16) ➗ (5/7) = (-5/16) x (7/5) = -35/80 = -7/16
2. Now, let's multiply the results together:
-4 x (-7/16) = (-4) x (-7) / (16) = 28/16
3. Finally, we can simplify the fraction:
28/16 = 7/4
Therefore, (-3) ➗ (3/4) x (-5/16) ➗ (5/7) = 7/4.
To solve this expression, we will use the properties of operations and the rules for multiplying and dividing fractions. Let's break it down step by step:
Step 1: Simplify the first division:
(-3) ÷ (3/4) = (-3) x (4/3)
The division is equivalent to multiplying by the reciprocal of the second fraction.
Step 2: Simplify the second division:
(-5/16) ÷ (5/7) = (-5/16) x (7/5)
Similarly, divide by a fraction by multiplying by its reciprocal.
Step 3: Simplify the multiplication:
(-3) x (4/3) x (-5/16) x (7/5)
Step 4: Multiply the numbers:
-3 x 4 x -5 x 7 = 420
Step 5: Multiply the denominators:
3 x 16 x 5 = 240
Step 6: Simplify the fraction:
420/240
Step 7: Reduce the fraction:
Divide both the numerator and denominator by their greatest common factor, which is 60:
420/240 = (7/4) x (1/1) = 7/4
Therefore, the expression (-3) ÷ (3/4) x (-5/16) ÷ (5/7) simplifies to 7/4.