how do you order fractions while estimating with different denominators including mixed numbers and improper fractions quickly?
You could change each to decimals.
To order fractions while estimating with different denominators, including mixed numbers and improper fractions quickly, you can follow these steps:
1. Convert all mixed numbers to improper fractions, if necessary. To do this, multiply the whole number by the denominator, and then add the numerator. The result becomes the new numerator, and the denominator remains the same.
For example, if you have 2 1/2, convert it to 5/2.
2. Find a common denominator for all the fractions. This is the smallest multiple that all the denominators can be evenly divided into.
For example, if you have fractions with denominators of 2, 5, and 3, the common denominator could be 30.
3. To estimate the order of the fractions, you can round all the fractions to a common decimal place, usually two to three decimal places.
For example, if you have 5/2, 1/5, and 2/3, you could round them to 2.50, 0.20, and 0.67.
4. Compare the rounded decimals to determine the order. The fractions with larger rounded decimals would be placed after the fractions with smaller rounded decimals.
Using the example decimals above, the order would be: 1/5, 2/3, 5/2.
5. If you need exact ordering, consider converting all the fractions to the common denominator from step 2. Then compare the numerators. The fractions with smaller numerators would be placed before the fractions with larger numerators.
Using the example fractions above, if you convert them to a common denominator of 30, you would get: 6/30, 10/30, and 75/30. The exact order would be: 6/30, 10/30, 75/30.
Remember, estimation can provide a quick order of fractions, while working with exact fractions ensures precise ordering.