You may recall the example below from a previous lesson.

**Example 1**

In example 1, we used circles to help us solve the problem. Now look at the next example.

**Example 2:** At a birthday party, there are 19 cupcakes to be shared equally among 11 guests. What part of the cupcakes will each guest get?

**Analysis: **We need to divide 19 cupcakes by 11 equal parts. It would be time-consuming to use circles or other shapes to help us solve this problem. Therefore, we need an arithmetic method.

**Step 1: **Look at the fraction nineteen-elevenths below. Recall that the fraction bar means to divide the numerator by the denominator. This is shown in step 2.

**Step 2:**

**Step 3:**

**Solution: **

**Example 3:**

**Step 1: **

**Step 2: **

**Answer **

**Analysis: **We need to divide 37 into 10 equal parts.

**Step 1: **

**Step 2: **

**Answer: **

**Example 5: **

**Analysis: **We need to divide 37 into 13 equal parts.

**Step 1: **

**Step 2: **

**Answer: **

In each of the examples above, we converted a fraction to a mixed number through long division of its numerator and denominator. Look at example 6 below. What is wrong with this problem?

**Example 6: **

**Analysis: **In the fraction seven-eighths, the numerator is less than the denominator. Therefore, seven-eighths is a proper fraction less than 1. We know from a previous lesson that a mixed number is *greater* than 1.

**Answer: **Seven-eighths cannot be written as a mixed number because it is a proper fraction.

**Example 7:** Can these fractions be written as mixed numbers? Explain why or why not.

**Analysis: **In each fraction above, the numerator is equal to the denominator. Therefore, each of these fractions is an improper fraction equal to 1. But a mixed number is greater than 1.

**Answer: **These fractions cannot be written as mixed numbers since each is an improper fraction equal to 1.

After reading examples 6 and 7, you may be wondering: **Which types of fractions ****can**** be written as mixed numbers?** To answer this question, let's review an important chart from a previous lesson.

**Comparison of numerator and denominator: **If the numerator < denominator, then the fraction < 1

**Example: **

**Type of Fraction: **proper fraction

**Write As: **proper fraction

**Comparison of numerator and denominator: **If the numerator = denominator, then the fraction = 1.

**Example: **

**Type of Fraction: **improper fraction

**Write As: **whole number

**Comparison of numerator and denominator: **If the numerator > denominator, then the fraction > 1.

**Example: **

**Type of Fraction: **improper fraction

**Write As: **mixed number

The answer to the question is: **Only an improper fraction greater than 1 can be written to a mixed number.**

**Summary: **We can convert an improper fraction greater than one to a mixed number through long division of its numerator and denominator.

**Exercises**

In Exercises 1 through 5, click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR. **Note: To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.**

1. |
Write eleven-fifths as a mixed number. |

2. |
Write eleven-fourths as a mixed number. |

3. |
Write thirteen-ninths as a mixed number. |

4. |
On field day, there are 23 pies to share equally among 7 classes. What part of the pies will each class get? |

5. |
A teacher gives her class a spelling test worth 35 points. If there are 8 words graded equally, then how many points is each word worth? |