Fractions on a Number Line -Worksheets Library - Free Printable

Problem Overview:

The task involves identifying where specific fractions should be placed on number lines. The fractions provided are mixed numbers, and we need to determine their positions accurately on the given number lines.

Key Concepts:

1. Mixed Numbers: A mixed number consists of a whole number and a fraction (e.g., \(7 \frac{2}{3}\)).
2. Number Line Placement: To place a mixed number on a number line:
- Identify the whole number part.
- Determine the fractional part and divide the segment between two whole numbers into equal parts based on the denominator of the fraction.
- Place the point at the appropriate division based on the numerator.

Solution:

#### Step 1: Understand the Number Lines
Each number line is marked with whole numbers (e.g., 5, 6, 7, 8). The task is to place the given mixed numbers on these number lines.

#### Step 2: Solve Each Part

##### Part 1: \(7 \frac{2}{3}\) and \(6 \frac{1}{3}\)
- \(7 \frac{2}{3}\):
- Whole number part: 7
- Fractional part: \(\frac{2}{3}\)
- Divide the segment between 7 and 8 into 3 equal parts. Place the point at the second division from 7.
- \(6 \frac{1}{3}\):
- Whole number part: 6
- Fractional part: \(\frac{1}{3}\)
- Divide the segment between 6 and 7 into 3 equal parts. Place the point at the first division from 6.

##### Part 2: \(5 \frac{1}{3}\) and \(7 \frac{2}{3}\)
- \(5 \frac{1}{3}\):
- Whole number part: 5
- Fractional part: \(\frac{1}{3}\)
- Divide the segment between 5 and 6 into 3 equal parts. Place the point at the first division from 5.
- \(7 \frac{2}{3}\):
- Whole number part: 7
- Fractional part: \(\frac{2}{3}\)
- Divide the segment between 7 and 8 into 3 equal parts. Place the point at the second division from 7.

##### Part 3: \(5 \frac{1}{3}\) and \(6 \frac{1}{3}\)
- \(5 \frac{1}{3}\):
- Whole number part: 5
- Fractional part: \(\frac{1}{3}\)
- Divide the segment between 5 and 6 into 3 equal parts. Place the point at the first division from 5.
- \(6 \frac{1}{3}\):
- Whole number part: 6
- Fractional part: \(\frac{1}{3}\)
- Divide the segment between 6 and 7 into 3 equal parts. Place the point at the first division from 6.

##### Part 4: \(7 \frac{2}{3}\) and \(5 \frac{2}{3}\)
- \(7 \frac{2}{3}\):
- Whole number part: 7
- Fractional part: \(\frac{2}{3}\)
- Divide the segment between 7 and 8 into 3 equal parts. Place the point at the second division from 7.
- \(5 \frac{2}{3}\):
- Whole number part: 5
- Fractional part: \(\frac{2}{3}\)
- Divide the segment between 5 and 6 into 3 equal parts. Place the point at the second division from 5.

##### Part 5: \(6 \frac{2}{3}\) and \(5 \frac{2}{3}\)
- \(6 \frac{2}{3}\):
- Whole number part: 6
- Fractional part: \(\frac{2}{3}\)
- Divide the segment between 6 and 7 into 3 equal parts. Place the point at the second division from 6.
- \(5 \frac{2}{3}\):
- Whole number part: 5
- Fractional part: \(\frac{2}{3}\)
- Divide the segment between 5 and 6 into 3 equal parts. Place the point at the second division from 5.

Final Answer:

The points should be placed as follows:

1. \(7 \frac{2}{3}\) is between 7 and 8, closer to 8.
\(6 \frac{1}{3}\) is between 6 and 7, closer to 6.
2. \(5 \frac{1}{3}\) is between 5 and 6, closer to 5.
\(7 \frac{2}{3}\) is between 7 and 8, closer to 8.
3. \(5 \frac{1}{3}\) is between 5 and 6, closer to 5.
\(6 \frac{1}{3}\) is between 6 and 7, closer to 6.
4. \(7 \frac{2}{3}\) is between 7 and 8, closer to 8.
\(5 \frac{2}{3}\) is between 5 and 6, closer to 6.
5. \(6 \frac{2}{3}\) is between 6 and 7, closer to 7.
\(5 \frac{2}{3}\) is between 5 and 6, closer to 6.

\[
\boxed{
\begin{array}{l}
1. \text{Place } 7 \frac{2}{3} \text{ near 7.67, } 6 \frac{1}{3} \text{ near 6.33} \\
2. \text{Place } 5 \frac{1}{3} \text{ near 5.33, } 7 \frac{2}{3} \text{ near 7.67} \\
3. \text{Place } 5 \frac{1}{3} \text{ near 5.33, } 6 \frac{1}{3} \text{ near 6.33} \\
4. \text{Place } 7 \frac{2}{3} \text{ near 7.67, } 5 \frac{2}{3} \text{ near 5.67} \\
5. \text{Place } 6 \frac{2}{3} \text{ near 6.67, } 5 \frac{2}{3} \text{ near 5.67} \\
\end{array}
}
\]