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Chapter 6: Problem 51

For Exercises \(49-54,\) divide. $$\frac{-0.96 m^{3} n}{0.15 m}$$

Short Answer

Expert verified
Question: Simplify the fraction \(\frac{-0.96 m^{3} n}{0.15 m}\). Answer: -6.4m^2n

Step by step solution

01

Divide the coefficients

First, we need to divide the coefficients, which are -0.96 and 0.15. To do this, simply divide -0.96 by 0.15: $$\frac{-0.96}{0.15} = -6.4$$ Our simplified term will have a coefficient of -6.4.
02

Divide the variables with the same base

Now, we need to divide the variables. We only have one pair of variables with the same base, which is \(m^3\) and \(m\). To divide them, subtract the exponent in the denominator (1) from the exponent in the numerator (3): $$\frac{m^3}{m} = m^{(3-1)} = m^2$$
03

Combine the terms

Now that we have divided both the coefficients and the variables, we can combine the results to form our simplified fraction: $$\frac{-0.96 m^{3} n}{0.15 m} = -6.4m^2n$$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Coefficient Division
When dividing algebraic expressions, the first step is to tackle the coefficients. Here, the coefficients are the numerical values of the terms, which in this case are
  • -0.96 (from the numerator), and
  • 0.15 (from the denominator).
To divide these, simply perform a straightforward division: \( \frac{-0.96}{0.15} = -6.4 \). This result will be the new coefficient for your simplified expression.
Understanding how to divide coefficients helps lay a firm foundation for simplifying more complex algebraic expressions. Remember:
  • Pay attention to the signs. A negative divided by a positive results in a negative.
  • Accuracy in arithmetic operations is key.
Breaking Down Variable Division
Once the coefficients are divided, turn your attention to the variables. Here we have:
  • \(m^3\) in the numerator, and
  • \(m\) in the denominator.
To divide variables of the same base, subtract the exponent of the denominator from the exponent of the numerator. Hence, \( \frac{m^3}{m} = m^{3-1} = m^2 \).
This method applies when the bases match. You are basically reducing the power of the variable by the number in the denominator. Always:
  • Ensure the bases are the same before proceeding with division.
  • Subtract exponents correctly. Miscalculations can lead to mistakes in the final expression.
Simplifying Expressions for Clarity
The final step is all about simplifying the results from the coefficient and variable divisions to form a neat expression. In our example, after handling the coefficients and variables, combine them together for the final expression: \(-6.4m^2n\).
Simplifying expressions makes them easier to read and further use in math problems. To simplify:
  • Make sure all possible reductions of terms have been assessed.
  • Double-check to confirm that you combined the expressions accurately.
An expression simplified correctly is your ticket to solving more intricate algebraic tasks.

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Most popular questions from this chapter

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