To solve these problems, we need to compare the fractions. The best way to do this is to make the bottom numbers (denominators) the same. This lets us see which fraction has more "pieces" of the same size.
Here is the step-by-step solution for each pair:
1. Compare $\frac{2}{4}$ and $\frac{6}{8}$
* Look at the first fraction: $\frac{2}{4}$. If we multiply the top and bottom by 2, it becomes $\frac{4}{8}$.
* Now compare $\frac{4}{8}$ and $\frac{6}{8}$.
* Since 4 is less than 6, $\frac{4}{8}$ is smaller.
* Therefore, $\frac{2}{4} < \frac{6}{8}$.
2. Compare $\frac{1}{2}$ and $\frac{5}{8}$
* Look at the first fraction: $\frac{1}{2}$. To get a denominator of 8, multiply the top and bottom by 4. It becomes $\frac{4}{8}$.
* Now compare $\frac{4}{8}$ and $\frac{5}{8}$.
* Since 4 is less than 5, $\frac{4}{8}$ is smaller.
* Therefore, $\frac{1}{2} < \frac{5}{8}$.
3. Compare $\frac{2}{3}$ and $\frac{2}{4}$
* When the top numbers (numerators) are the same, the fraction with the *smaller* bottom number is actually *larger*. This is because cutting a pizza into 3 slices gives you bigger pieces than cutting it into 4 slices.
* Since 3 is smaller than 4, the pieces in thirds are bigger.
* Therefore, $\frac{2}{3} > \frac{2}{4}$.
*(Note: You can also check this with common denominators. $\frac{2}{3} = \frac{8}{12}$ and $\frac{2}{4} = \frac{6}{12}$. Since 8 is greater than 6, the first one is larger.)*
Final Answer:
$\frac{2}{4} < \frac{6}{8}$
$\frac{1}{2} < \frac{5}{8}$
$\frac{2}{3} > \frac{2}{4}$
Parent Tip: Review the logic above to help your child master the concept of equivalent fraction worksheet 3rd grade singapore math.
