🍪 A Fraction of a Quantity

We have 12 cookies. How many cookies is 3/4 of them? Let’s find out together!

The denominator of 3/4 is 4. The denominator tells us how many equal parts the whole is split into. Let’s share 12 cookies into 4 equal groups: 12 ÷ 4 = 3. Each group has 3 cookies.

One group is 1/4 of the 12 cookies. The numerator is 3, so we take 3 groups: 3 × 3 = 9. Three quarters of 12 cookies is 9 cookies!

We can show the same thing with a strip model. The whole strip is 12. Split into 4 equal parts, each part is 3. We shade 3 parts: 3 + 3 + 3 = 9. The rule: divide by the denominator, then multiply by the numerator.

Which is bigger: 1/4 or 1/8? 8 is bigger than 4, but 1/8 is smaller! If we cut the same pizza into 8 slices, every slice gets smaller. With unit fractions, the bigger the denominator, the smaller the piece.

3/8 + 2/8: the denominators are the same, so the slices are the same size. 3 slices + 2 slices = 5 slices. Add the numerators and keep the denominator: 3/8 + 2/8 = 5/8.

Careful! If we add the denominators too, we get 5/16. But 5/16 is even smaller than 3/8, where we started! Adding never makes the answer smaller. The pizza still has 8 slices, so the denominator stays the same. The right answer: 5/8.

7/4 is an improper fraction: the numerator is bigger than the denominator. 4 of the 7 slices make one whole pizza, and 3 slices are left over. So 7/4 = 1 and 3/4. This is called a mixed number.

Summary: to find a fraction of a quantity, first divide by the denominator, then multiply by the numerator. The bigger the denominator, the smaller a unit fraction. If the denominators are the same, add the numerators and keep the denominator. 7/4 = 1 and 3/4. Now try it in Fraction Pizzeria!