Question

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

Short answer

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

Step-by-step solution

Identify the Terms

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

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 \(\frac{12}{3} = 4\).

Add the Fractions

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

Simplify if Needed

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

Key concepts

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.