(-3)÷(3/4)times (2/7) times(-5/16)÷5/7)
Starting from the given expression:
(-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7)
First, simplify the division by multiplying by the reciprocal:
(-3) × (4/3) × (2/7) × (-5/16) × (7/5)
Now, simplify the multiplication:
(-3/1) × (4/3) × (2/7) × (-5/16) × (7/5)
Multiply the numerators together and the denominators together:
(-3 × 4 × 2 × -5 × 7) / (1 × 3 × 7 × 16 × 5)
Simplify:
(-840) / (1680)
Simplify further by dividing both the numerator and denominator by their greatest common factor, which is 840:
-1/2
So, the final answer is -1/2.
To solve the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7), let's break it down step-by-step:
Step 1: Simplify the division and multiplication operations within the expression.
(-3) ÷ (3/4) can be simplified as (-3) × (4/3), which gives -12/3 or -4.
Similarly, (-5/16) ÷ (5/7) can be simplified as (-5/16) × (7/5), which gives -35/80 or -7/16.
So the expression becomes: -4 × (2/7) × (-7/16).
Step 2: Multiply the fractions.
-4 × (2/7) × (-7/16) can be calculated by multiplying the numerators and denominators separately.
(-4 × 2 × -7) / (7 × 16) = 56/112.
Step 3: Simplify the resulting fraction.
56/112 can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which in this case is 8.
56 ÷ 8 = 7, and 112 ÷ 8 = 14.
So the simplified fraction is 7/14, which can be further reduced to 1/2.
Therefore, the final result of the expression (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) is 1/2.
To simplify the expression (-3)÷(3/4) × (2/7) × (-5/16) ÷ (5/7), follow these steps:
Step 1: Simplify the division (-3) ÷ (3/4).
To divide a number by a fraction, you multiply by its reciprocal. The reciprocal of 3/4 is 4/3. So, multiply (-3) by (4/3).
(-3) × (4/3) = -12/3 = -4
Step 2: Multiply the result from step 1 (-4) by (2/7).
To multiply fractions, multiply the numerators together and the denominators together.
(-4) × (2/7) = (-8/7)
Step 3: Multiply the result from step 2 (-8/7) by (-5/16).
Again, multiply the numerators and the denominators.
(-8/7) × (-5/16) = (40/112)
Step 4: Simplify the division (40/112) ÷ (5/7).
When dividing fractions, multiply the first fraction by the reciprocal of the second fraction.
(40/112) ÷ (5/7) = (40/112) × (7/5)
Now, simplify by canceling out common factors.
40 ÷ 8 = 5
112 ÷ 8 = 14
(40/112) × (7/5) = (5/14)
Therefore, the simplified expression is (5/14).