Introduces the relationship between mixed numbers and improper fractions. Students use visual models (fraction strips, number lines) to convert between the two forms, compare mixed numbers, and place them on a number line, building the foundation for fraction computation with values greater than one.
Upper Elementary • 3-5
You know that fractions like 3/4 represent parts of a whole. But what happens when you have more than one whole? You can write the amount as a mixed number (like 2 3/4) or as an improper fraction (like 11/4). These are just two different ways to write the same amount.
| Term | Definition | Example |
|---|---|---|
| Proper fraction | Numerator is less than the denominator (less than 1 whole) | 3/4 |
| Improper fraction | Numerator is greater than or equal to the denominator (1 whole or more) | 11/4 |
| Mixed number | A whole number plus a proper fraction | 2 3/4 |
Divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator.
Convert 17/5 to a mixed number.
Multiply the whole number by the denominator, add the numerator. Keep the same denominator.
Convert 4 2/3 to an improper fraction.
Imagine circles divided into equal slices. For 2 3/4:
Total slices: 4 + 4 + 3 = 11 slices, each one is a fourth, so 11/4.
Which is greater: 3 1/4 or 3 2/5?
To place 2 3/4 on a number line, find 2 and 3, then divide the space between them into 4 equal parts. Count 3 parts past 2. That is where 2 3/4 goes.
When converting a mixed number to an improper fraction, students sometimes forget to add the numerator. Remember: multiply the whole number by the denominator, then add the numerator on top.
1. Convert 23/6 to a mixed number.
23 / 6 = 3 remainder 5. So 23/6 = 3 5/6.
2. Convert 5 1/8 to an improper fraction.
5 x 8 = 40, plus 1 = 41. So 5 1/8 = 41/8.
3. Is 7/7 a proper fraction, improper fraction, or whole number?
7/7 = 1. It is an improper fraction equal to the whole number 1.
4. Which is greater: 2 5/6 or 2 3/4?
Same whole number (2). Compare fractions: 5/6 = 10/12 and 3/4 = 9/12. Since 10/12 > 9/12, 2 5/6 > 2 3/4.
5. Place 1 2/3 on a number line. Between which two whole numbers does it fall?
Between 1 and 2. Divide the space between 1 and 2 into 3 equal parts and mark the second line.