Order the following fractions from least to greatest: [tex]$\frac{7}{4}, \frac{3}{4}, 2 \frac{1}{8}, \frac{2}{3}, 2 \frac{2}{4}$[/tex]
Answer (2)
Convert all fractions to a common format, such as decimals.
Compare the decimal values to determine the order.
Order the original fractions based on their decimal values.
The fractions from least to greatest are: 3 2 , 4 3 , 4 7 , 2 8 1 , 2 4 2 .
Explanation
Problem Analysis We need to order the fractions 4 7 , 4 3 , 2 8 1 , 3 2 , 2 4 2 from least to greatest. To do this, we will convert all the mixed numbers to improper fractions and then compare the values.
Converting Mixed Numbers to Improper Fractions First, let's convert the mixed numbers to improper fractions:
2 8 1 = 8 2 × 8 + 1 = 8 16 + 1 = 8 17
2 4 2 = 4 2 × 4 + 2 = 4 8 + 2 = 4 10 = 2 5
Converting Fractions to Decimals Now we have the fractions 4 7 , 4 3 , 8 17 , 3 2 , 2 5 . To easily compare them, we can convert them to decimals:
4 7 = 1.75
4 3 = 0.75
8 17 = 2.125
3 2 ≈ 0.667
2 5 = 2.5
Ordering Decimal Values Now we can order the decimal values from least to greatest:
0.667 , 0.75 , 1.75 , 2.125 , 2.5
Final Answer Finally, we convert these back to the original fractions and write them in order:
3 2 , 4 3 , 4 7 , 2 8 1 , 2 4 2
Examples
Ordering fractions is a fundamental skill in mathematics with various real-life applications. For instance, imagine you are baking and need to add ingredients in specific proportions. If a recipe calls for 3 2 cup of flour, 4 3 cup of sugar, and 4 7 cups of water, being able to order these fractions helps you determine which ingredient you need the most or least of, ensuring your recipe turns out perfectly. Similarly, in financial planning, comparing fractional investments (e.g., 2 1 in stocks, 4 1 in bonds) allows you to understand the distribution of your portfolio and make informed decisions.
To order the fractions 4 7 , 4 3 , 2 8 1 , 3 2 , 2 4 2 , we convert the mixed numbers to improper fractions. After converting to decimals and ordering them, we find that the correct order from least to greatest is 3 2 , 4 3 , 4 7 , 2 8 1 , 2 4 2 .
;
