Expressing Whole Numbers as Fractions - Third Grade Mathematics
Many students think that fractions and whole numbers belong in separate worlds, but every whole number can be expressed as a fraction! When a fraction has the same numerator and denominator, it equals one whole. When the numerator is a multiple of the denominator, it equals two, three, or more wholes. In this chapter, you will discover how fractions and whole numbers connect seamlessly.
Fractions Equal to 1 Whole
What happens when you have a pizza cut into 4 slices, and you eat all 4 slices? You have eaten 4/4 of the pizza—which is the ENTIRE whole pizza!
Any fraction where the numerator and denominator are the same non-zero number
is equal to 1 whole!
Rule: n/n = 1
Examples:
2/2 = 1 3/3 = 1 4/4 = 1
6/6 = 1 8/8 = 1 100/100 = 1
Visualizing 1 Whole:
+---------------+---------------+
| 1/2 | 1/2 | = 2/2 = 1 whole
+---------------+---------------+
+-------+-------+-------+-------+
| 1/4 | 1/4 | 1/4 | 1/4 | = 4/4 = 1 whole
+-------+-------+-------+-------+
No matter how many slices you cut a cake into, if you have all of the slices, you have 1 whole cake.
Whole Numbers with a Denominator of 1
What does a denominator of 1 mean? A denominator of 1 means that the whole has NOT been split into smaller parts at all—each whole is just 1 complete unit!
Rule: Any whole number n can be written as n/1.
Examples:
1 = 1/1
2 = 2/1 (2 whole units)
3 = 3/1 (3 whole units)
5 = 5/1 (5 whole units)
If you have 4 whole un-cut pies, you have 4 wholes, each partitioned into 1 part: 4/1 pies!
Fractions Equal to Whole Numbers Greater Than 1
What happens when you have more parts than make up a single whole? Suppose you have 6 half-cookies (each piece is 1/2):
Cookie 1: [ 1/2 ] [ 1/2 ] -> 2 halves = 1 whole cookie
Cookie 2: [ 1/2 ] [ 1/2 ] -> 2 halves = 1 whole cookie
Cookie 3: [ 1/2 ] [ 1/2 ] -> 2 halves = 1 whole cookie
Total halves: 6/2
Total whole cookies: 3 whole cookies!
Equation: 6/2 = 3
Notice that the fraction bar means division: 6/2 means 6 ÷ 2 = 3!
+-----------------------+---------------------+-------------------------------+
| Fraction | Division Problem | Whole Number Value |
+-----------------------+---------------------+-------------------------------+
| 4/2 | 4 ÷ 2 | 2 |
| 6/3 | 6 ÷ 3 | 2 |
| 8/4 | 8 ÷ 4 | 2 |
| 12/3 | 12 ÷ 3 | 4 |
| 15/5 | 15 ÷ 5 | 3 |
| 24/6 | 24 ÷ 6 | 4 |
+-----------------------+---------------------+-------------------------------+
Whenever the numerator is a multiple of the denominator, you can divide the numerator by the denominator to find the matching whole number!
Whole Numbers on a Fraction Number Line
Look at a number line where each whole unit is divided into halves:
0 1/2 2/2 3/2 4/2 5/2 6/2
+-------+-------+-------+-------+-------+-------+
0 1 2 3
Notice how:
- 2/2 lands squarely on 1
- 4/2 lands squarely on 2
- 6/2 lands squarely on 3
Chapter Practice Exercises
- Write each fraction as a whole number: a. 3/3 b. 8/8 c. 6/2 d. 8/4 e. 12/4 f. 9/1
- Write each whole number as a fraction with a denominator of 1: a. 5 b. 7 c. 10
- Write the whole number 3 as a fraction with: a. A denominator of 2 b. A denominator of 3 c. A denominator of 4
- Maya has 8 fourths of a waffle. How many whole waffles does Maya have? Write the fraction and the whole number.
- A pizza party ordered pizzas cut into 6 slices each. At the end of the party, 18 slices were eaten. How many whole pizzas were eaten? Write the division sentence and the fraction.
Solutions and Step-by-Step Answers
- Fractions to whole numbers: a. 3/3 = 1 b. 8/8 = 1 c. 6/2 = 6 ÷ 2 = 3 d. 8/4 = 8 ÷ 4 = 2 e. 12/4 = 12 ÷ 4 = 3 f. 9/1 = 9
- As fractions with denominator 1: a. 5 = 5/1 b. 7 = 7/1 c. 10 = 10/1
- Whole number 3 in different forms: a. Denominator 2: 3 x 2 = 6, so 6/2. b. Denominator 3: 3 x 3 = 9, so 9/3. c. Denominator 4: 3 x 4 = 12, so 12/4.
- 8 fourths is written as 8/4. 8 ÷ 4 = 2 whole waffles.
- 18 slices with 6 slices per pizza: 18 ÷ 6 = 3 whole pizzas. Fraction: 18/6 = 3.