Describe how you can use a number line to order the fractions 3/7, 5/7 and 1/7 from least to greatest.
Arrange the numerators in numerical order.
Read the number line from left to right.
To use a number line to order fractions, follow these steps:
1. Start by drawing a horizontal line and labeling it with the range of fractions you want to order. In this case, label it from 0 to 1 since we are dealing with fractions between 0 and 1.
2. Divide the line into equal parts. Since we are dealing with sevenths (fractions with the denominator 7), divide the line into 7 equal segments.
3. Plot the fractions on the number line. Find the point that represents each fraction by counting from 0. For example:
- The fraction 3/7 is closer to 0 than 1/7, so plot it between 0 and 1/7.
- The fraction 5/7 is closer to 1 than 3/7, so plot it between 3/7 and 1.
- The fraction 1/7 is closer to 0 than 3/7, so plot it between 0 and 3/7.
4. Label the points with their corresponding fractions.
5. Now, you can observe that the fractions are plotted from least to greatest on the number line.
Alternatively, you can also convert the fractions to decimals and compare them numerically:
1. Convert each fraction to a decimal. For example:
- 3/7 ≈ 0.428571 (rounded to six decimal places)
- 5/7 ≈ 0.714286 (rounded to six decimal places)
- 1/7 ≈ 0.142857 (rounded to six decimal places)
2. Compare the decimals. Since 0.142857 < 0.428571 < 0.714286, the fractions can be ordered as 1/7 < 3/7 < 5/7.
Both methods will give you the same result: 1/7 < 3/7 < 5/7.