When we want to compare fractions, decimals, and percentages, it's important to change them into the same format. This makes it easier to see which is bigger or smaller. Here are some simple ways to change these numbers and tips on how to compare them.

How to Convert

1. Fractions to Decimals: To turn a fraction into a decimal, just divide the top number (numerator) by the bottom number (denominator). For example, to change $\frac{3}{4}$ into a decimal:

   $$\frac{3}{4} = 3 \div 4 = 0.75$$

2. Fractions to Percentages: To turn a fraction into a percentage, multiply it by 100. For example, for $\frac{3}{4}$:

   $$\frac{3}{4} \times 100 = 75\%$$

3. Decimals to Fractions: To change a decimal into a fraction, think about where the decimal is. For $0.75$, you can write it as:

   $$0.75 = \frac{75}{100} = \frac{3}{4}$$

4. Decimals to Percentages: To turn a decimal into a percentage, multiply it by 100. For instance:

   $$0.75 \times 100 = 75\%$$

5. Percentages to Decimals: To change a percentage into a decimal, divide by 100. For example:

   $$75\% = \frac{75}{100} = 0.75$$

6. Percentages to Fractions: To convert a percentage into a fraction, put it over 100 and simplify if you can. For example:

   $$75\% = \frac{75}{100} = \frac{3}{4}$$

Comparing and Ordering

• Using Common Denominators: For fractions, find a common number to use for comparison. For example, to compare $\frac{1}{3}$ and $\frac{1}{4}$, we can convert them to have the same denominator, like 12:

  $$\frac{1}{3} = \frac{4}{12}, \quad \frac{1}{4} = \frac{3}{12}$$

  So, $\frac{1}{3}$ is greater than $\frac{1}{4}$.

• Using Benchmarks: You can use simple benchmarks, like $0$, $0.5$, and $1$, to help estimate. For percentages, think of $50\%$ as a middle point. This helps you see if numbers are bigger or smaller than this halfway mark.

By using these methods, you can easily convert, compare, and order fractions, decimals, and percentages. Knowing how to make these changes is important. It helps you get better at math and is useful for solving everyday problems.