Simplify (2.7(m^2*s))/(m*s^2)
This problem is asking for the simplification of a given algebraic expression that involves variables raised to different powers and multiplied by a decimal coefficient. The expression is a fraction composed of a numerator and a denominator, each containing variables 'm' and 's' with different exponents. The task is to simplify this expression by applying the rules of exponents and division of like terms to reduce it to its simplest form.
$\frac{2.7 \left(\right. m^{2} \cdot s \left.\right)}{m \cdot s^{2}}$
Answer
Solution:
Step 1: Simplify the expression by removing common factors between the numerator and denominator.
Step 1.1: Extract the common variable $m$ from the numerator $2.7(m^2 \cdot s)$.
$$\frac{2.7m(m \cdot s)}{m \cdot s^2}$$
Step 1.2: Eliminate the common variable $m$.
Step 1.2.1: Recognize that $m$ is also a factor in the denominator $m \cdot s^2$.
$$\frac{2.7m(m \cdot s)}{m(s^2)}$$
Step 1.2.2: Cross out the matching $m$ terms.
$$\frac{\cancel{2.7m}(m \cdot s)}{\cancel{m}s^2}$$
Step 1.2.3: Rewrite what's left after cancellation.
$$\frac{2.7(m \cdot s)}{s^2}$$
Step 2: Further simplify by canceling out the common $s$ terms.
Step 2.1: Factor out $s$ from the numerator.
$$\frac{2.7ms}{s^2}$$
Step 2.2: Proceed to cancel the common $s$ terms.
Step 2.2.1: Factor out $s$ from the denominator $s^2$.
$$\frac{2.7ms}{s \cdot s}$$
Step 2.2.2: Cross out the matching $s$ terms.
$$\frac{\cancel{2.7ms}}{\cancel{s} \cdot s}$$
Step 2.2.3: Rewrite the final simplified expression.
$$\frac{2.7m}{s}$$
Knowledge Notes:
Algebraic Simplification: The process of reducing an algebraic expression to its simplest form. This often involves canceling out common factors in the numerator and denominator of a fraction.
Common Factors: A factor that is shared by two or more numbers or terms. In algebra, common factors can include numbers as well as variables (letters that represent numbers).
Cancellation Law: In fractions, if a factor appears both in the numerator and in the denominator, it can be canceled out. This is based on the principle that a number divided by itself equals one.
Factoring: The process of breaking down an expression into its constituent factors. This can make it easier to identify and cancel common factors.
Variables and Exponents: When variables have exponents, they can only be canceled if the exponents are the same or if one is a factor of the other. In this problem, $m^2$ and $m$ share a common factor of $m$, and $s$ is a common factor of $s^2$.
LaTeX Formatting: A typesetting system that is widely used for mathematical and scientific documents. In LaTeX, the backslash (\) indicates a command, curly braces ({}) group elements of a command, and the ampersand (&) is used for alignment in certain environments.
