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Chapter 4: Problem 221

In the following exercises, simplify. $$\frac{19-4}{6}$$

Short Answer

Expert verified
\( \frac{5}{2} \)

Step by step solution

01

Simplify the Numerator

First, simplify the expression in the numerator of the fraction. Subtract 4 from 19: \[ 19 - 4 = 15 \]
02

Rewrite the Fraction

Replace the numerator with the simplified value: \[ \frac{15}{6} \]
03

Simplify the Fraction

Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3: \[ \frac{15 \div 3}{6 \div 3} = \frac{5}{2} \]

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Key Concepts

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

Numerator and Denominator
A fraction is a way to express a division of two numbers. The top number is called the numerator, and the bottom number is called the denominator.
In the fraction \(\frac{a}{b}\), \(a\) is the numerator and \(b\) is the denominator. The numerator represents how many parts of the whole we have, and the denominator shows into how many parts the whole is divided.
For example, in the fraction \(\frac{15}{6}\), 15 is the numerator and 6 is the denominator.
Greatest Common Divisor
The greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers without leaving a remainder.
To simplify a fraction, we divide both the numerator and the denominator by their GCD.
In the fraction \(\frac{15}{6}\), the GCD of 15 and 6 is 3. We divide both the numerator and the denominator by 3:
\(\frac{15 \div 3}{6 \div 3} = \frac{5}{2}\). This is the simplified form of the fraction.
Basic Arithmetic
Basic arithmetic involves the operations of addition, subtraction, multiplication, and division. These operations are essential for simplifying fractions.
Let's break down the original problem, \(\frac{19-4}{6}\), step by step:
* First, perform the subtraction within the numerator: \(19 - 4 = 15\).
* Then, rewrite the fraction with the simplified numerator: \(\frac{15}{6}\).
* Finally, simplify the fraction by dividing both the numerator and the denominator by their GCD, 3: \(\frac{15 \div 3}{6 \div 3} = \frac{5}{2}\).
This is how basic arithmetic helps us simplify fractions.

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Most popular questions from this chapter

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(\frac{5}{12}-w\) when (a) \(w=\frac{1}{4} \quad\) (b) \(w=-\frac{1}{4}\)

In the following exercises, perform the indicated operation. $$ 2 \frac{11}{12}-1 \frac{7}{12} $$

In the following exercises, simplify. $$ \frac{7}{11} \div\left(-\frac{7}{11}\right) $$

In the following exercises, simplify. $$ -\frac{3}{13}+\left(-\frac{4}{13}\right) $$

In the following exercises, perform the indicated operation. $$ 6 \frac{2}{5}+7 \frac{3}{5} $$
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