Santishahi280idn
Answered

IDNLearn.com offers expert insights and community wisdom to answer your queries. Ask anything and receive prompt, well-informed answers from our community of experienced experts.

CLASSWORK EXAMPLES

1. [tex]\(\begin{tabular}{l|r|}
+\quad 9 & 63785 \\
\hline 77458 & 63749
\end{tabular}\)[/tex]

Similarly, to locate:

### Example 1
Locate [tex]\(\frac{3}{5}\)[/tex] on the number line.

Solution:
1. Construct a number line.
2. Construct two parallel lines [tex]\(\ell_1\)[/tex] and [tex]\(\ell_2\)[/tex] from 0 and respectively.

### Example 2
Locate point [tex]\(X\)[/tex].

Solution:
1. Insert 6 rational numbers between 2 and 3.
2. One of the rational numbers is the arithmetic average of 2 and 3, which is [tex]\(\frac{1}{2}(2 + 3) = 2.5\)[/tex].
3. Therefore, one rational number is 2.5.
4. The other rational numbers are calculated similarly by taking the arithmetic average of the subsequent intervals.

Construct 5 equal divisions:
1. Using a pencil compass, divide the interval into 5 equal parts.
2. Example: [tex]\(\frac{1}{2}(2 + \frac{1}{2}) + \ldots\)[/tex]

This process will help you locate the desired points and rational numbers on the number line accurately.

Sagot :

GinnyAnsweridn
Sure, let's tackle these various math exercises step-by-step. We'll aim to understand what's required and explain the reasoning clearly.

### Classwork Examples Breakdown

#### Example 1: Locate [tex]\(\frac{3}{5}\)[/tex] on the Number Line
To locate [tex]\(\frac{3}{5}\)[/tex] on the number line:

1. Construct a Number Line: Draw a straight horizontal line and mark the points [tex]\(0\)[/tex] and [tex]\(1\)[/tex].

2. Divide the Interval: Divide the segment between [tex]\(0\)[/tex] and [tex]\(1\)[/tex] into 5 equal parts, because the denominator is 5.

3. Locate the Point: Count 3 parts from 0 towards 1 to locate [tex]\(\frac{3}{5}\)[/tex]. Mark this point on the number line.

So, [tex]\(\frac{3}{5}\)[/tex] is 3 units to the right of 0 if 1 unit is split into 5 equal parts.

#### Example 2: Insert 6 Rational Numbers

To insert 6 rational numbers between two given numbers:

1. Identify the Given Numbers: Assume the two numbers are [tex]\(a\)[/tex] and [tex]\(b\)[/tex].

2. Find the Arithmetic Sequence: To insert numbers between [tex]\(a\)[/tex] and [tex]\(b\)[/tex], find the common difference [tex]\(d\)[/tex].

3. Calculate the Rational Numbers: Use the formula for the [tex]\(n\)[/tex]-th term of an arithmetic sequence:
[tex]\[ a_n = a + (n-1)d \][/tex]
For six rational numbers in between, create the sequence [tex]\(a\)[/tex], [tex]\(a+d\)[/tex], [tex]\(a+2d\)[/tex], ..., [tex]\(a+6d\)[/tex], [tex]\(b\)[/tex].

4. Determine the Correct Placement: Ensure that each number follows the arithmetic sequence logic and place them evenly between [tex]\(a\)[/tex] and [tex]\(b\)[/tex].

#### Additional Number Line Example (Constructing Divisions)

To further understand constructing divisions on a number line equitably:

1. Draw the Interval: Draw a straight line representing numerical value from 0 to another specific number, say 2.

2. Mark Points Equidistantly: If tasked to divide into 5 equal parts, use a compass or ruler to mark them with equal spacing.

3. Verify Equal Divisions: Check that the segments are indeed equal, ensuring accuracy by perhaps using a compass or a ruler.

By placing segments accurately, you ensure that the divisions such as [tex]\(\frac{1}{2}\left[2 \frac{1}{2}\right]\)[/tex] are correctly represented.

### Summary

- Locating Fractions on a Number Line: Split the interval as per the denominator and locate the specified numerator.
- Inserting Rational Numbers: Utilize arithmetic sequences to evenly distribute numbers between two given values.
- Constructing Equal Divisions: Use tools like compasses or rulers to ensure precision when dividing intervals.

This exercise strengthens our understanding of the number line concept, arithmetic sequences, and accurate placement of rational numbers.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.