Use the properties of operations and rules for multiplying and dividing to solve:
( -3) divided by (3/4) x (2/7) x (-5/16 divided by (5/7)
To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).
First, let's simplify the expression in the parentheses:
(-5/16) ÷ (5/7) = (-5/16) * (7/5) [Since division is the same as multiplying by the reciprocal]
= -35/80
= -7/16
Now, let's simplify the expression further:
(-3) ÷ (3/4) * (2/7) * (-7/16) = (-3) * (4/3) * (2/7) * (-7/16) [Again, division is the same as multiplying by the reciprocal]
= -12/3 * 2/7 * -7/16
= -8 * 2/1 * -1/2
= -16/1 * -1/2
= 16/1 * 1/2
= 16/2
= 8
Therefore, (-3) ÷ (3/4) * (2/7) * (-5/16 divided by (5/7) equals 8.
To solve the expression ( -3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), we can follow the rules for multiplying and dividing fractions step by step.
Step 1: Simplify the Division
To simplify a division of fractions, we multiply the numerator by the reciprocal of the denominator. In this case, we need to divide -3 by (3/4):
(-3) ÷ (3/4)
= (-3) × (4/3) (reciprocal of 3/4 is 4/3)
= -12/3
= -4
So, (-3) ÷ (3/4) simplifies to -4.
Step 2: Multiply
Now, we can multiply all the remaining fractions together:
-4 × (2/7) × (-5/16) ÷ (5/7)
To multiply fractions, we multiply the numerators together and the denominators together. The result is a fraction:
= (-4 × 2 × -5) / (7 × 16) (Multiply numerators and denominators separately)
= 40 / 112
Step 3: Simplify
To simplify the fraction 40/112, we find the greatest common divisor (GCD) of the numerator and the denominator and divide both by it. In this case, the GCD is 8:
= (40/8) / (112/8)
= 5/14
So, the final answer is 5/14.
Therefore, the expression ( -3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to 5/14.
To solve the expression:
(-3) / (3/4) * (2/7) * (-5/16) / (5/7)
Step 1: Simplify the division operations within the expression.
(-3) * (4/3) * (2/7) * (-5/16) * (7/5)
Step 2: Look for any possible cancellations.
In this case, the negative signs can cancel out:
(-3) * (4/3) * (2/7) * (-5/16) * (7/5) = -3 * 4/3 * 2/7 * -5/16 * 7/5
Step 3: Now, let's multiply the numerators and denominators.
(-3 * 4 * 2 * -5 * 7) / (3 * 7 * 16 * 5)
This simplifies to:
(-840) / (1680)
Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 40.
(-840) / (1680) = (-21) / (42)
Step 5: Simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 21.
(-21) / (42) = -1/2
Therefore, (-3) / (3/4) * (2/7) * (-5/16) / (5/7) simplifies to -1/2.