Use the properties of operations and rules for multiplying and dividing to solve:
(-3(÷(3/4)×(-5/16)÷(5/7)
To solve the expression (-3 ÷ (3/4) × (-5/16) ÷ (5/7), we can follow these steps:
Step 1: Simplify the expression within the parentheses.
(-3 ÷ (3/4)) can be simplified as -3 * (4/3) = -12/3 = -4
Step 2: Simplify the expression outside the parentheses.
(-4 × (-5/16) ÷ (5/7))
To simplify the multiplication (-4 × (-5/16)), we multiply the numerators and denominators:
-4 × (-5) = 20
1 × 16 = 16
So, -4 × (-5/16) is equal to 20/16.
Now, the expression becomes 20/16 ÷ (5/7).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(20/16) ÷ (5/7) = (20/16) × (7/5)
Next, we multiply the numerators and denominators:
20 × 7 = 140
16 × 5 = 80
So, (20/16) ÷ (5/7) is equal to 140/80.
Now, we can simplify the fraction 140/80 by dividing both the numerator and denominator by their greatest common factor, which is 20:
140 ÷ 20 = 7
80 ÷ 20 = 4
Therefore, the simplified fraction is 7/4.
As a final step, the expression becomes:
7/4
To solve the expression (-3 ÷ (3/4) × (-5/16) ÷ (5/7)), we will follow the order of operations (PEMDAS/BODMAS) and use the properties of operations and rules for multiplying and dividing.
Step 1: Simplify the division operation inside the parentheses.
-3 ÷ (3/4) = -3 × (4/3) [Reciprocal property of division]
= -12/3
= -4
Step 2: Substitute the simplified value back into the expression.
(-4 × (-5/16) ÷ (5/7))
Step 3: Simplify the multiplication operation.
-4 × (-5/16) = 20/16
Step 4: Simplify the division operation.
(20/16) ÷ (5/7) = (20/16) × (7/5) [Reciprocal property of division]
= (20 × 7)/(16 × 5)
= 140/80 [Multiply the numerators and denominators]
= 7/4 [Reduce the fraction by dividing both numerator and denominator by the greatest common divisor, which is 20]
Therefore, the final result of the expression (-3 ÷ (3/4) × (-5/16) ÷ (5/7)) is 7/4 or 1 3/4.
To solve the expression (-3 ÷ (3/4) × (-5/16) ÷ (5/7)), we can follow the rules for multiplying and dividing.
Step 1: Simplify the division first:
(-3 ÷ (3/4)) becomes (-3 × (4/3)). To divide by a fraction, you can multiply by its reciprocal. In this case, the reciprocal of (3/4) is (4/3). So, (-3 ÷ (3/4)) = (-3 × (4/3)) = -12/3 = -4.
Step 2: Simplify the remaining multiplication:
Now we have (-4 × (-5/16) ÷ (5/7)). To multiply two fractions, we simply multiply their numerators and denominators. So, (-4 × (-5/16)) = (20/16) = 5/4.
Step 3: Simplify the final division:
Now the expression becomes (5/4 ÷ (5/7)). Again, to divide by a fraction, we multiply by its reciprocal. The reciprocal of (5/7) is (7/5). So, (5/4 ÷ (5/7)) = (5/4 × (7/5)) = (35/20) = 7/4.
Therefore, the solution to the expression (-3 ÷ (3/4) × (-5/16) ÷ (5/7)) is 7/4.