Lesson 6: Using Models to Compare Fractions

Think about pizza! Since both fractions have a denominator of 8, we can think about cutting a pizza into 8 slices. Now we can compare the numerator (or number of slices we get to eat). Eating 5 slices is eating more than 3 slices.

3/4 is bigger! The numerators are the same so each person would get 3 pieces. But the denominators are different. If we cut one whole into 4 parts and another into 5 parts, the pieces are bigger if there are only 4. So 3 out of 4 pieces is MORE than 3 out of 5 pieces because the pieces are smaller.

A pizza cut into 10 slices versus 5 slices has smaller pieces. If you eat 6 smaller slices you have less than eating 6 bigger slices.

If we cut a pizza into 10 slices, eating 6 slices is more than eating 4 slices.

5/6 is closer to a whole than 3/4

If we have $$\frac{1}{2}$$ and multipy the numerator and denominator by 2, we get $$\frac{2}{4}$$

A rectangle is divided into 10 equal parts and 4 are shaded in. A rectangle of the same size is divided into 5 equal parts and 2 are shaded in. The area of the shaded region is the same! So $$\frac{4}{10}=\frac{2}{5}$$ .

If you divide 4 by 2 and 10 by 2 you will get 2/5

$$\frac{3}{15},\ \frac{1}{5},\ \frac{4}{20}$$ can all be written as $$\frac{1}{5}$$