(-3p) x 2 1/6 divide (-1/13p)
To simplify the expression, we can start by multiplying -3p and 2 1/6:
-3p × 2 1/6
First, let's convert the mixed number 2 1/6 to an improper fraction. To do this, we multiply the whole number (2) by the denominator (6) and add the numerator (1):
2 × 6 = 12
12 + 1 = 13
So, 2 1/6 is equivalent to 13/6.
Now we can rewrite the expression:
-3p × 13/6
To divide by -1/13p, we can multiply by its reciprocal:
-3p × 13/6 × -p/1/13
Simplifying, we have:
-3p × 13/6 × -p × 13/(-1)
Multiplying the coefficients and the variable, we get:
(3 × 13 × p × p) / (6 × 13 × 1)
Simplifying further:
(39p²) / (78)
The simplified expression is 39p² / 78.
To solve the expression (-3p) x 2 1/6 ÷ (-1/13p), we'll break down each step one by one.
Step 1: Simplify the mixed number
The mixed number 2 1/6 can be converted to an improper fraction by multiplying the whole number (2) by the denominator (6) and adding the numerator (1). Then we write it over the denominator (6).
2 1/6 = (2 * 6 + 1) / 6 = 13/6
Now the expression becomes (-3p) x (13/6) ÷ (-1/13p).
Step 2: Multiply the numerator of the first fraction with the numerator of the second fraction and the denominator of the first fraction with the denominator of the second fraction.
(-3p) x (13/6) ÷ (-1/13p) simplifies to (-3p * 13/6) ÷ (-1/13p).
Step 3: Simplify the numerator and denominator separately.
The numerator simplifies to (-3p * 13) = -39p.
The denominator simplifies to 6 x (-1) = -6.
Now the expression becomes (-39p/6) ÷ (-1/13p).
Step 4: Invert the second fraction and multiply.
To divide fractions, you flip the denominator and numerator of the second fraction and then multiply.
(-39p/6) ÷ (-1/13p) becomes (-39p/6) x (-13p/1).
Step 5: Multiply the numerators and denominators.
(-39p/6) x (-13p/1) simplifies to (39p * 13p) / (6 * 1).
Step 6: Simplify the numerical part of the expression.
(39p * 13p) / (6 * 1) can be written as 507p^2 / 6.
Step 7: Simplify the expression if possible.
507p^2 / 6 cannot be simplified further because 507 and 6 have no common factors besides 1.
Therefore, the final simplified expression is 507p^2 / 6.