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Chapter 4: Problem 22

Simplify if possible. $$\frac{8}{8}$$

Short Answer

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Step by step solution

01

Understand the Problem

Identify the given fraction: \(\frac{8}{8}\). Both the numerator and the denominator are 8.
02

Determine Common Factors

Recognize that the numerator (8) and the denominator (8) are the same number.
03

Simplify the Fraction

Since any number divided by itself equals 1, simplify \(\frac{8}{8}\) to 1.

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Key Concepts

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

Numerator
In a fraction, the top number is called the numerator. It shows how many parts of a whole you have. For example, in the fraction \(\frac{8}{8}\), the number 8 is the numerator.
This number indicates that we are dealing with 8 parts out of a possible 8. Think of it as if you had a pizza cut into 8 equal slices and you have all 8 slices.
Denominator
The bottom part of a fraction is called the denominator. It tells you into how many equal parts the whole is divided. In our example, \(\frac{8}{8}\), the denominator is also 8.
This means the whole pizza (or whatever the whole is) is divided into 8 equal slices. When the numerator and the denominator are the same, you're essentially dealing with the 鈥榳hole鈥� or 1 full item.
To remember what a denominator is, think of it as the 'denominator' that 鈥榙enotes鈥� the total parts of anything you鈥檙e working with.
Common Factors
To simplify a fraction, look for common factors of the numerator and the denominator. A common factor is a number that can divide both the numerator and the denominator without leaving a remainder.
In the example \(\frac{8}{8}\), the greatest common factor between 8 and 8 is 8. This means you can divide both the numerator and denominator by this number.
By identifying common factors, you can reduce fractions to their simplest form.
Simplification
Simplifying a fraction means reducing it to its simplest form. This is done by dividing both the numerator and the denominator by their greatest common factor.
For \(\frac{8}{8}\), since 8 is both the numerator and the denominator, and the greatest common factor is 8, you divide both by 8: \(\frac{8 \div 8}{8 \div 8} = \frac{1}{1}\).
Since \(\frac{1}{1}\) is equal to 1, the simplified form of \(\frac{8}{8}\) is 1. Remember, whatever number divided by itself is always equal to 1.

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Most popular questions from this chapter

Simplify. $$\left|\frac{1}{10}\right|$$

For Exercises 65鈥�76, convert the improper fraction to a mixed number. $$\frac{37}{8}$$

For Exercises 85鈥�94, plot the fraction on the number line. $$\frac{3}{4}$$

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Convert the mixed number to an improper fraction. $$12 \frac{1}{6}$$
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