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Chapter 1: Problem 4

For the following problems, reduce, if possible, each fraction lowest terms. \(\frac{4}{14}\)

Short Answer

Expert verified
Answer: The reduced form of the fraction \(\frac{4}{14}\) is \(\frac{2}{7}\).

Step by step solution

01

Determine the GCD of the numerator and denominator

In this case, the greatest common divisor (GCD) of 4 and 14 is 2, which is the largest number that divides both 4 and 14.
02

Divide the numerator and denominator by the GCD

Divide the numerator (4) and the denominator (14) by the GCD (2): Numerator: \(4 \div 2 = 2\) Denominator: \(14 \div 2 = 7\)
03

Write the reduced fraction

The reduced fraction is \(\frac{2}{7}\), as the numerator and denominator are now both in their lowest terms.

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Key Concepts

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

Greatest Common Divisor
The greatest common divisor (GCD) is a crucial part of simplifying fractions. It's the biggest number that can evenly divide both numbers in a pair. To find the GCD, you can list all the divisors (factors) of each number, then pick the largest number that appears in both lists.
\[\text{For example, if you have the numbers 4 and 14, their divisors are:}\]
  • 4: 1, 2, 4
  • 14: 1, 2, 7, 14
In this case, 2 is the greatest number that divides both 4 and 14. We use '2' to reduce the fraction \(\frac{4}{14}\) to its simplest form.
Numerator and Denominator
Fractions are made up of two main parts: the numerator and the denominator. The **numerator** is the number above the line, representing how many parts we have. The **denominator** is the number below the line, showing how many equal parts the whole is divided into.
For the fraction \(\frac{4}{14}\):
  • 4 is the numerator
  • 14 is the denominator
Understanding these parts is essential for working with fractions. When simplifying, you need to adjust both parts by dividing them by the greatest common divisor (GCD) to get the simplest form.
Fraction Simplification
Simplifying a fraction means reducing it to its lowest terms. This involves finding the greatest common divisor (GCD) of the numerator and denominator and then dividing both by this number. The result is a simpler version of the fraction that represents the same value.
Here is how simplification works for \(\frac{4}{14}\):
1. Find the GCD of 4 and 14, which is 2.
2. Divide both the numerator and denominator by the GCD:
  • Numerator: \(4 \div 2 = 2\)
  • Denominator: \(14 \div 2 = 7\)
The fraction now becomes \(\frac{2}{7}\). This is the simplified version, as 2 and 7 have no common divisors other than 1, meaning you cannot simplify it any further.

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Most popular questions from this chapter

For the following problems, convert each fraction to a percent. $$ \frac{5}{16} $$

For the following problems, perform each indicated operation. \(\frac{2}{5} \cdot \frac{5}{6}\)

For the following problems, reduce, if possible, each fraction lowest terms. \(\frac{121}{132}\)

For the following problems, reduce, if possible, each fraction lowest terms. \(\frac{18}{24}\)

For the following problems, determine the missing numerator or denomin ator. \(\frac{1}{5}=\frac{?}{30}\)
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