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Chapter 0: Problem 57

Evaluate each expression. $$ 4+\frac{1}{3} $$

Short Answer

Expert verified
\(4 + \frac{1}{3} = \frac{13}{3}\)

Step by step solution

01

Identify the Terms

The expression given is \(4 + \frac{1}{3}\). Identify that there are two terms: a whole number 4, and a fraction \(\frac{1}{3}\).
02

Convert to a Common Format

To add a whole number and a fraction, it can be helpful to convert the whole number into a fraction. Rewrite 4 as \(\frac{12}{3}\), since \(\frac{12}{3} = 4\).
03

Add the Fractions

Now add the fractions \(\frac{12}{3}\) and \(\frac{1}{3}\) to get \(\frac{12 + 1}{3} = \frac{13}{3}\).
04

Simplify if Needed

The fraction \(\frac{13}{3}\) cannot be simplified further, so the final answer is \( \frac{13}{3} \).

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Key Concepts

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

fractions
Fractions are a way to express parts of a whole. A fraction has two parts: the numerator and the denominator.
The numerator is the top number and tells you how many parts you have. The denominator is the bottom number and tells you how many equal parts the whole is divided into.
For example, in the fraction \(\frac{1}{3}\), the numerator is 1, and the denominator is 3. This means you have 1 part out of 3 equal parts.
whole numbers
Whole numbers are numbers without fractions or decimals. They include all positive numbers, including zero.
Examples of whole numbers are 0, 1, 2, 3, and so on. When you add a whole number to a fraction, it can sometimes be easier to think of the whole number as a fraction too.
For example, you can rewrite the whole number 4 as \(\frac{12}{3}\) to perform the addition more easily.
common denominators
To add fractions, you need to have common denominators. This means the bottom numbers of both fractions must be the same.
If they are not the same, you can't add them directly. In the example \(\frac{12}{3} + \frac{1}{3}\), both fractions already have the same denominator (3), so you can add them directly.
Always make sure your fractions have common denominators before adding or subtracting them.
simplification
Simplification is the process of reducing a fraction to its simplest form. This means making the numerator and denominator as small as possible while still having the same value.
In some cases, the fraction will already be in its simplest form, and no further action is needed.
For example, \(\frac{13}{3}\) cannot be simplified any further, so it is already in its simplest form. Simplifying fractions makes them easier to understand and work with.

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Most popular questions from this chapter

Simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. $$ \frac{\left(16 x^{2} y^{-1 / 3}\right)^{3 / 4}}{\left(x y^{2}\right)^{1 / 4}} $$

Expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and radicals appear. $$\frac{\sqrt{1+x}-x \cdot \frac{1}{2 \sqrt{1+x}}}{1+x} \quad x>-1$$

Simplify each expression. Assume that all variables are positive when they appear. $$\sqrt[4]{32 x}+\sqrt[4]{2 x^{5}}$$

The period \(T\), in seconds, of a pendulum of length \(l,\) in feet, may be approximated using the formula $$T=2 \pi \sqrt{\frac{l}{32}}$$ Express your answer both as a square root and as a decimal approximation. Find the period \(T\) of a pendulum whose length is 64 feet.

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{1}{\sqrt{2}}$$
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