Use the properties of operations and rules for multiplying and dividing to solve (-2)x(1/5) Divided by(2/3)x(-5/6) divided by(3/4)
To solve the expression (-2)x(1/5) ÷ (2/3)x(-5/6) ÷ (3/4), we will simplify the expression step by step using the properties of operations and the rules for multiplying and dividing.
First, let's simplify the numerator and denominator separately:
Numerator: (-2) x (1/5) = -2/5
Denominator: (2/3) x (-5/6) = -10/18
Now, let's divide the numerator (-2/5) by the denominator (-10/18):
(-2/5) ÷ (-10/18)
When dividing fractions, we invert the divisor (the second fraction) and multiply:
(-2/5) x (18/-10)
Next, we simplify the fraction:
-2/5 x 18/-10 = -36/(-50)
To reduce this fraction, we can simplify both the numerator and denominator by dividing by their greatest common divisor, which is 2:
-36/(-50) = (-36÷2)/(-50÷2) = -18/(-25)
Finally, the expression becomes -18/(-25) ÷ (3/4):
When dividing fractions, we invert the divisor (the second fraction) and multiply:
-18/(-25) x (4/3)
Next, we simplify the fraction:
-18/(-25) x 4/3 = 72/(-75)
To reduce this fraction, we can simplify both the numerator and denominator by dividing by their greatest common divisor, which is 3:
72/(-75) = (72÷3)/(-75÷3) = 24/(-25) = -24/25
Therefore, (-2)x(1/5) ÷ (2/3)x(-5/6) ÷ (3/4) simplifies to -24/25.
To solve (-2)x(1/5) ÷ (2/3)x(-5/6) ÷ (3/4), we can follow the order of operations and use the properties and rules for multiplying and dividing fractions.
Step 1: Simplify the multiplication of fractions inside parentheses:
(-2) x (1/5) ÷ (2/3) x (-5/6) ÷ (3/4)
= -2/5 ÷ (-10/18) ÷ (3/4)
Step 2: Simplify each division separately:
=-2/5 ÷ (-10/18) ÷ (3/4)
Step 3: To divide fractions, multiply by the reciprocal of the second fraction:
=(-2/5) x (18/(-10)) x (4/3)
Step 4: Simplify the multiplication of fractions:
=(-2/5) x (-9/5) x (4/3)
Step 5: Multiply the numerators and denominators together:
=(-2 x -9 x 4) / (5 x 5 x 3)
Step 6: Simplify the resulting fraction:
=(72) / (75)
Step 7: Reduce the fraction to its simplest form, if possible. In this case, they share a common factor of 3:
= 72 / 75
= 24 / 25
Therefore, the solution to (-2)x(1/5) ÷ (2/3)x(-5/6) ÷ (3/4) is 24/25.
To solve the given expression, (-2)×(1/5) ÷ (2/3)×(-5/6) ÷ (3/4), we'll use the properties of operations and rules for multiplying and dividing fractions.
Step 1: Simplify each part of the expression where possible.
In the numerator, we have (-2) × (1/5). First, multiply the whole number (-2) with the numerator (1), which gives you -2. Then, multiply the denominators (5) to get a final numerator of -2. So, (-2) × (1/5) becomes -2/5.
In the denominator, we have (2/3) × (-5/6) and (3/4). First, multiply the numerators together: (2 × -5) = -10. Then, multiply the denominators: (3 × 6) = 18. So, (2/3) × (-5/6) becomes -10/18.
Step 2: Simplify the expression further.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we calculate (-2/5) ÷ (-10/18) ÷ (3/4).
(-2/5) ÷ (-10/18) is equal to (-2/5) × (18/(-10)). Multiply the numerators: (-2 × 18) = -36. Multiply the denominators: (5 × -10) = -50. Therefore, (-2/5) ÷ (-10/18) becomes -36/-50.
To divide a negative number by a negative number, the result is positive. So, -36/-50 simplifies to 36/50.
Now we need to divide 36/50 by (3/4). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. (36/50) ÷ (3/4) becomes (36/50) × (4/3).
Multiply the numerators: (36 × 4) = 144. Multiply the denominators: (50 × 3) = 150. Hence, (36/50) ÷ (3/4) becomes 144/150.
Step 3: Simplify the final fraction.
To simplify 144/150, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 6. Dividing both numbers by 6, we get 24/25.
So, the final answer to (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) is 24/25.