(-3)÷(3/4)×(2/7)×(-5/16)÷(5/7)
To solve this expression, we can follow the order of operations, which is parentheses, then multiplication/division (from left to right), and finally addition/subtraction (from left to right).
First, let's evaluate the expression inside the parentheses:
(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
=(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
=(-3) ÷ (3/4) × (2/7) × (-5/16) × (7/5)
Now let's solve the division from left to right:
=-3 ÷ (3/4) × (2/7) × (-5/16) × (7/5)
=(-3) × (4/3) × (2/7) × (-5/16) × (7/5)
Next, let's simplify the multiplication from left to right:
= (-3) × (4/3) × (2/7) × (-5/16) × (7/5)
= -3 × 4 × 2 × (-5) × 7 × (1/3) × (1/16) × (1/5)
= -3 × 4 × 2 × (-5) × 7 × (1/3) × (1/16) × (1/5)
= - 2 × 5 × (this cancels out the 5 and 2)
= -10
Therefore, (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to -10.
To simplify the expression (-3)÷(3/4)×(2/7)×(-5/16)÷(5/7), follow these steps:
Step 1: Divide -3 by (3/4):
(-3) ÷ (3/4) = -3 × (4/3)
= -12/3
= -4
Step 2: Multiply the result from step 1 by (2/7):
-4 × (2/7) = -8/7
Step 3: Multiply the result from step 2 by (-5/16):
-8/7 × (-5/16) = (8/7) × (5/16)
= 40/112
= 5/14
Step 4: Finally, divide the result from step 3 by (5/7):
(5/14) ÷ (5/7) = (5/14) × (7/5)
= (35/70)
= 1/2
Therefore, (-3)÷(3/4)×(2/7)×(-5/16)÷(5/7) simplifies to 1/2.
To simplify the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), let's break it down step by step:
Step 1: Simplify (-3) ÷ (3/4)
To divide a number by a fraction, we can multiply the number by the reciprocal of that fraction.
Reciprocal of 3/4 is 4/3.
((-3) ÷ (3/4)) can be rewritten as (-3) × (4/3).
Now, let's simplify the multiplication: -3 × 4 = -12, 3 × 1 = 3.
So, (-3) ÷ (3/4) = -12/3 = -4.
Step 2: Simplify -4 × (2/7)
Multiply the numerators: -4 × 2 = -8.
Multiply the denominators: 1 × 7 = 7.
So, -4 × (2/7) = -8/7.
Step 3: Simplify -8/7 × (-5/16)
Multiply the numerators: -8 × -5 = 40.
Multiply the denominators: 7 × 16 = 112.
So, -8/7 × (-5/16) = 40/112.
Step 4: Simplify 40/112 ÷ (5/7)
To divide one fraction by another, we can multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of 5/7 is 7/5.
(40/112) ÷ (5/7) can be rewritten as (40/112) × (7/5).
Now, let's multiply the numerators: 40 × 7 = 280.
And multiply the denominators: 112 × 5 = 560.
So, (40/112) ÷ (5/7) = 280/560.
Step 5: Simplify 280/560
Both the numerator and the denominator have a common factor of 280, so we can simplify:
280 ÷ 280 = 1.
560 ÷ 280 = 2.
So, 280/560 simplifies to 1/2.
Therefore, the final result is 1/2.