A mixed number is a number that has a whole number part and a fractional part.

Here is a visual representation of a mixed number.

This model shows two rectangles that are shaded completely, which represents whole numbers, and one rectangle that is shaded partially, which represents a fraction.

This fraction model represents the mixed number \(2\frac{3}{8}\).

### Example 1

When adding a mixed number with a whole number, we first add the whole numbers, then include the fraction.

What is the sum of \(11\frac{2}{3}\) and \(19\)?

We will start by adding the whole numbers, which is \(11+19=30\). Then we add the fractional part to the end.

Therefore, the sum of \(11\frac{2}{3}\) and \(19\) is \(30\frac{2}{3}\).

### Example 2

Monica picks two bags of peaches to buy at the Farmer’s Market. She places each bag on the scale and the first bag weighs \(5\) lbs. and the second bag weighs \(6\frac{2}{3}\) lbs. How many pounds of peaches does Monica buy?

When adding a whole number and a fraction we first add the whole numbers, then we include the fraction.

\(5+6=11\), now we include \(\frac{2}{3}\), therefore, Monica buys a total of \(11\frac{2}{3}\) lbs. of peaches.

## Adding Fractions with Whole Numbers Sample Questions

Here are a few sample questions going over adding fractions with whole numbers.

**Question #1:**

Calculate the sum of \(14\frac{5}{6}\) and \(38\).

**Answer:**

When adding fractions and whole numbers, first calculate the whole number plus the whole number, and then include the remaining fraction in the answer. For example, \(14+38=52\), so \(52\frac{5}{6}\) is the answer.

**Question #2:**

Calculate the sum of \(45\) and \(2\frac{1}{3}\).

**Answer:**

Once again, when adding fractions and whole numbers, first calculate the whole number plus the whole number, and then include the remaining fraction in the answer. For example, \(45+2=47\), so \(47\frac{1}{3}\) is the answer.

**Question #3:**

Add \(4\frac{3}{2}+5\).

**Answer:**

The first step is to address the improper fraction within the mixed number \(4\frac{3}{2}\). The fraction \(\frac{3}{2}\) is the same thing as \(1\frac{1}{2}\), so rewrite \(4\frac{3}{2}\) as \(5\frac{1}{2}\). Now, simply combine \(5\frac{1}{2}\) and \(5\) to get \(10\frac{1}{2}\).

**Question #4:**

Add \(3+3\frac{5}{4}\).

**Answer:**

The first step is to address the improper fraction within the mixed number \(3\frac{5}{4}\). The fraction \(\frac{5}{4}\) is the same thing as \(1\frac{1}{4}\), so rewrite \(3\frac{5}{4}\) as \(4\frac{1}{4}\). Now, simply combine \(3\) and \(4\frac{1}{4}\) to get \(7\frac{1}{4}\).

**Question #5:**

Fill in the missing value in order to make the equation true.

\(3\frac{4}{5}+\) ______\(=18\frac{4}{5}\)

**Answer:**

In order to create a balanced equation, the mixed number \(18\frac{4}{5}\) must be on each side. Adding \(3\frac{4}{5}+15=18\frac{4}{5}\), so \(15\) is the missing value.