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Chapter 3: Problem 58

Simplify. See Sections \(1.5,1.6,\) and 1.7 $$ \frac{12-3}{10-9} $$

Short Answer

Expert verified
The simplified expression is 9.

Step by step solution

01

Calculate the Numerator

The numerator of the expression is \(12 - 3\). Subtract 3 from 12 to get 9.
02

Calculate the Denominator

The denominator of the expression is \(10 - 9\). Subtract 9 from 10 to get 1.
03

Simplify the Expression

Now that we have the numerator as 9 and the denominator as 1, we can simplify the fraction \(\frac{9}{1}\). Any number divided by 1 is the number itself, so \(\frac{9}{1} = 9\).

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Key Concepts

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

Numerator and Denominator
When dealing with fractions, you'll often hear about numerators and denominators. These terms describe the top and bottom parts of a fraction respectively.
To simplify a fraction like \( \frac{12-3}{10-9} \), first, let's understand what numerators and denominators truly mean.
  • Numerator: The numerator is the top number of a fraction. It tells us how many parts we have.
  • Denominator: The denominator is the bottom number. It indicates the total number of equal parts into which something is divided.
In the fraction \( \frac{12-3}{10-9} \), after performing basic arithmetic operations, we find that the numerator is 9 and the denominator is 1. This understanding is the groundwork before moving forward with any operation regarding fractions.
Basic Arithmetic Operations
Basic arithmetic operations鈥攁ddition, subtraction, multiplication, and division鈥攁re essential in simplifying fractions.
In our exercise, understanding subtraction comes into play.
Let's explore how we carry out these operations within a fraction:
  • Subtraction: To simplify the numerator, compute \(12 - 3\). This leaves us with a result of 9.
  • Subtraction for Denominator: Similarly, for the bottom of the fraction, perform \(10 - 9\), which equals 1.
By mastering these fundamental arithmetic skills, you can confidently simplify any complex-looking fractions.
Fraction Simplification
Fraction simplification is the process of reducing a fraction to its simplest form, where the numerator and denominator have no common factors other than 1.
In the fraction \(\frac{9}{1}\), simplification becomes straightforward:
  • Any fraction where the denominator is 1, simplifies directly to the numerator alone. Therefore, \(\frac{9}{1} = 9\).
This means, our fraction represents the whole number 9.
When simplifying fractions, always ensure that:
  • Both numerator and denominator are reduced by any common factors.
  • If the denominator equals 1, the fraction equals the numerator.
These steps can make simplifying any fraction an easy task, turning what might seem complex into something as simple as working with whole numbers.

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