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Chapter 11: Problem 4

Evaluate. \(\frac{m}{n},\) when \(m=18\) and \(n=3\)

Short Answer

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Step by step solution

01

Substitute the Given Values

Replace the variables with their given values. In this problem, replace \(m\) with 18 and \(n\) with 3 in the expression \(\frac{m}{n}\). This gives us \(\frac{18}{3}\).
02

Perform the Division

Divide 18 by 3 to simplify the fraction. \(\frac{18}{3} = 6\)

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Key Concepts

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

substitution in algebra
In algebra, substitution is a method where you replace variables with their given values. This is a straightforward but vital step in solving many problems. For example, if you are given \(\frac{m}{n}\), and you know that \(m=18\) and \(n=3\), you can substitute 18 for \(m\) and 3 for \(n\).

Substitution looks like this:
\(\frac{m}{n} \rightarrow \frac{18}{3}\).
This process makes your variables disappear, leaving you with numbers that you can handle easily. Always check to ensure you have replaced each variable with the correct number. This method is priceless when handling more complex equations and expressions in algebra.
simplifying fractions
Simplifying fractions means reducing them to their simplest form. A fraction is in its simplest form when the numerator (the top number) and the denominator (the bottom number) have no common factors other than 1. So, in the problem \(\frac{18}{3}\), you can simplify this because both 18 and 3 share the common factor 3.

To simplify \(\frac{18}{3}\), divide both the numerator and the denominator by their greatest common factor, which is 3:
  • 18 梅 3 = 6
  • 3 梅 3 = 1
So, \(\frac{18}{3} = 6 = \frac{6}{1}\), and \(\frac{6}{1}\) is simply 6.
Simplification makes fractions easier to understand and work with, especially in further calculations and comparisons.
basic arithmetic operations
Basic arithmetic operations are fundamental to all areas of mathematics. They include addition, subtraction, multiplication, and division. In the given problem, you mainly use division. Understanding how to perform division is essential.

When you divide 18 by 3, think of it as how many times 3 fits into 18. The division looks like this: 18 梅 3. Performing the division gives us 6.

Each arithmetic operation obeys specific rules and properties. Knowing these can help you solve problems correctly and efficiently:
  • For addition (e.g., 2 + 3), simply combine quantities.
  • For subtraction (e.g., 5 - 2), find the difference between quantities.
  • For multiplication (e.g., 4 脳 3), think of repeated addition.
  • For division (e.g., 20 梅 4), think of how many times the divisor fits into the dividend.
The better you understand these basic operations, the smoother your journey through more advanced math topics will be.

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