Fraction as Division & Sharing Stories

Every fraction is actually a division problem. When you write 3/4, that is exactly the same as 3 divided by 4.

The rule is: a divided by b equals a/b. The number being divided (the dividend) goes on top as the numerator. The number you divide by (the divisor) goes on the bottom as the denominator.

In sharing stories, the number of items is always the numerator (top number) and the number of people is always the denominator (bottom number).

• 3 pizzas shared by 4 friends: each gets 3/4
• 2 granola bars shared by 3 kids: each gets 2/3
• 1 apple shared by 4 kids: each gets 1/4

Sometimes a fraction can be written in a simpler form. To simplify, find a number that divides evenly into both the top and bottom.

• 2/4 and 1/2 are the same amount (divide top and bottom by 2)
• 3/9 and 1/3 are the same (divide by 3)
• 4/6 and 2/3 are the same (divide by 2)

The simplest form uses the smallest possible numbers.

When there are more items than people, the fraction is greater than 1. This is called an improper fraction.

• 6 cookies for 4 kids: each gets 6/4 = 1 2/4 = 1 1/2 cookies
• 8 apples for 4 people: each gets 8/4 = 2 apples (a whole number!)

Improper fractions can be rewritten as mixed numbers (a whole number plus a fraction).