How do you order fractions from least to greatest?

To order fractions from least to greatest, convert them to a common denominator or compare their decimal equivalents.

When ordering fractions, the first step is to ensure they have a common basis for comparison. One effective method is to convert all the fractions to a common denominator. This involves finding the least common multiple (LCM) of the denominators. Once you have the LCM, adjust each fraction so that they all share this common denominator. For example, to compare 1/4, 2/3, and 5/6, you would find the LCM of 4, 3, and 6, which is 12. Then, convert each fraction: 1/4 becomes 3/12, 2/3 becomes 8/12, and 5/6 becomes 10/12. Now, you can easily see that 3/12 < 8/12 < 10/12, so 1/4 < 2/3 < 5/6.

Another method is to convert each fraction to its decimal equivalent. This can be done by dividing the numerator by the denominator. For instance, 1/4 is 0.25, 2/3 is approximately 0.6667, and 5/6 is approximately 0.8333. Comparing these decimals directly, you can see that 0.25 < 0.6667 < 0.8333, so 1/4 < 2/3 < 5/6.

Both methods are valid, and you can choose the one that you find easier or more intuitive. Using a common denominator is often preferred in exams as it shows a clear understanding of fraction manipulation, but converting to decimals can be quicker and is useful for checking your work.