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Chapter 5: Problem 142

Explain how to reduce a rational number to its lowest terms.

Short Answer

Expert verified
Reducing a rational number to its simplest form involves finding common factors of the numerator and denominator, and dividing them by this factor until no common factor remains except 1. The result is the rational number in its reduced form.

Step by step solution

01

Identify the Numerator and Denominator

A rational number is expressed in the form of a fraction \(\frac{a}{b}\), where 'a' is the numerator and 'b' is the denominator.
02

Look for Common Factors

Determine the common factors between the numerator and the denominator. The common factors are numbers that would divide both the numerator and the denominator completely.
03

Divide by the Common Factor

Once a common factor is identified, divide both the numerator and the denominator by this factor.
04

Repeat the Process if Necessary

Check again if there are any other common factors except 1. If you find any, repeat step 3. Continue this process until no common factors remain except 1.
05

Write the Simplified Fraction

With no common factors left except 1, the fraction attained is the rational number in its simplest form.

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Most popular questions from this chapter

What is a geometric sequence? Give an example with your description.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-\frac{1}{8}, r=-2\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication.

If you are given a sequence that is arithmetic or geometric, how can you determine which type of sequence it is?

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{7}\), when \(a_{1}=5, r=-2\).
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