Any fraction with a whole number as its numerator represents a whole number quantity, as there is no remainder left in addition to this fraction’s decimal. However, there are some characteristics that will help you identify whether or not a fraction has a whole number or a mixed number in its numerator:
1. A whole number fraction will always be a whole number, because the numerator equals the denominator (numerator = denominator =1), which makes the value of the fraction equal 1.
2. If the numerator is an integer and a multiple of the denominator, then dividing the two will give you an integer result. This means that when you “fill in” the other whole number of a fraction, you will not have any “leftover” fractions.
To tell if a fraction has a whole number or not, simply take the numerator and divide by the denominator. If it is a whole number, you know it is a whole-number fraction.
Here are some examples:
1. Take the fraction 4/2:
4 ÷ 2 = 2 (whole number)
2. Take the fraction 9/3:
9 ÷ 3 = 3 (whole number)
3. Take the fraction 5/5:
5 ÷ 5 = 1 (whole number).
Visual Examples
Example 1 – Calculation 22 ÷ 2 = 1, or
Example 1 visualizes this with the idea of a Half-Pizza cut into 2 Equal Parts. So if I eat 2 parts (22 ÷ 2), it would equal 1 whole (the entire) Pizza.
Example 2 – Calculation 24 ÷ 2 = 2, or (half = 1/2 of a whole.)
Therefore, 24 ÷ 2 = 2. As such, there are 4 halves that equal 2 full objects (for instance, there are 4 quarters in a 1.00).
Example 3 – Calculation 26 ÷ 3 = 2, or (one piece of 1 whole that is divided into 3 Equal parts.) So then 26 ÷ 3 = 2 (That is, 6 Pieces = 2 full sets).
Definition of Fractions Equivalent to Whole Numbers (Grade 3 Level):
When the numerator (upper number) is equal to or a multiple of the denominator (lower number), the resulting fraction represents a whole number with NO fractional remains.
Below are examples:
1. 2/2 = 1
– Two equal parts equal to the whole = 1.
2. 4/2 = 2
– Dividing something into 2 equal parts, where you took 4 equal-sized parts, provides you with 2 whole units.
3. 6/3 = 2
– There are 6 equal-sized parts, and you divided them into 3 equal parts, resulting in a total of 2.
4. 5/5 = 1
– By taking 5 equal-sized parts out of 5, you will have the entire object = 1.
5. 9/3 = 3
– When dividing something into 3 equal parts and taking 9 of them, it results in having 3 whole units.
How to Identify Fractions Equivalent to Whole Numbers:
- Identifying equivalent fractions to whole numbers
A fraction will equal a whole number if the numerator is equal to or a multiple of the denominator.
- Example: 63=2\frac{6}{3} = 236=2 because 6 ÷ 3 = 2.
Exercises for Practice:
Exercise 1- Find the whole number equivalent for each of the following fractions:
4/4=_ ; 3/3=_ ; 8/4=_ ; 10/5=_ ; 6/2=
Exercise 2- Are any of the following fractions equal to a whole number list?
5/5=1 ; True/False
8/4=4 ; True/False
3/9=3 ; True/False
2/6=2 ; True/False
6/12=2 ; True/False
Exercise 3- Choose the fractions that are equivalent to whole numbers only.
Choose your selections for the fractions that are equivalent to whole numbers only.
6/6; 5/4; 10/5; 8/8; 7/3