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Chapter 1: Problem 51

Simplify. \(13+\frac{24}{8}\)

Short Answer

Expert verified
The simplified expression is 16.

Step by step solution

01

Simplify the Fraction

First, simplify the fraction \( \frac{24}{8} \). This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 8. \( \frac{24}{8} = \frac{24 \div 8}{8 \div 8} = \frac{3}{1} = 3 \).
02

Add the Simplified Fraction to the Whole Number

Now that we have simplified \( \frac{24}{8} \) to 3, we add it to the whole number 13. This gives us: \( 13 + 3 = 16 \).
03

Write the Final Answer

Having completed the previous operations, the simplified expression of \( 13 + \frac{24}{8} \) is \( 16 \).

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Key Concepts

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

Understanding Fractions
Fractions are expressions that represent a part of a whole. They consist of two main parts: the numerator and the denominator.
  • The numerator is the number above the slash. It shows how many parts we have.
  • The denominator is the number below the slash. It indicates the total number of equal parts the whole is divided into.
When simplifying fractions, the goal is to reduce them to their simplest form. This means finding an equivalent fraction where the numerator and denominator have no common factors other than 1. For example, in the fraction \( \frac{24}{8} \), both 24 and 8 can be divided by 8. Hence, the simplest form is \( \frac{3}{1} \), which is just 3 as a whole number. Understanding fractions as part of an operation is crucial to solving many mathematical expressions.
The Greatest Common Divisor (GCD)
The greatest common divisor, or GCD, is the largest number that divides two or more numbers without leaving a remainder. It's fundamental in simplifying fractions.
  • To find the GCD of two numbers, list all the factors of each number.
  • Identify the largest factor that both numbers share.
For example, the numbers 24 and 8 share common divisors of 1, 2, 4, and 8. The greatest of these is 8, thus the GCD of 24 and 8 is 8. When simplifying the fraction \( \frac{24}{8} \), dividing both the numerator and denominator by their GCD (8 in this example), results in the simplest form of the fraction.
Whole Numbers in Expressions
Whole numbers are simply the basic counting numbers 0, 1, 2, 3, and so on, without any fractions or decimals. They are fundamental in arithmetic operations and provide a basis for understanding more complex numbers.
  • Adding whole numbers is straightforward. For instance, adding 13 and a simplified fraction that equals a whole number, like the 3 from \( \frac{24}{8} \), results in a new whole number: 16.
  • Whole numbers are useful in operations, as they maintain the simplicity of calculations.
In expressions like \( 13 + \frac{24}{8} \), simplifying the fraction first and then adding it to a whole number makes the calculation neat and straightforward. This method helps to keep arithmetic operations simple and clear, catering to understanding larger mathematical concepts.

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Most popular questions from this chapter

Write down any two numbers whose quotient is 25.

Perform each indicated operation. $$ \begin{array}{r} 134 \\ \times \quad 16 \\ \hline \end{array} $$

Write each whole number in expanded form. $$66,049$$

Check each addition below. If it is incorrect, find the correct answer. $$ \begin{array}{r} 773 \\ 659 \\ +481 \\ \hline 1913 \end{array} $$

Write each phrase as a variable expression. Use \(x\) to represent "a number." 6 divided by a number
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