Question

Help pls. 20 pts

Match each rational number with a point on the number line.
(Be sure to use the numbers 1 through 4 to indicate which rational number goes in each answer box)

Answer 1

The correct option is Option D) A=-0.7,B=-9/16,C=-0.4,D=-5/16

Explanation:

Consider the provided number line.

From the number line we can observed that:

1) A, B, C and D lies between -1 and 0.

2) Point A and B lies between -1 and -0.5

3) Point C and D lies between -0.5 and 0

Therefore, the value of A and B must have a negative value lying between -1 and -0.5

Also, the value of C and D must have a negative value lying between -0.5 and 0.

Now consider the provided options.

Option A) A=-5/16,B=-9/16,C=-0.7,D=-0.4

This is Incorrect representation because the value of C and D should lying between -0.5 and 0.

Option B) A=-0.4,B=-0.7,C=-5/16,D=9/16

This is Incorrect representation because the value of A and B should lying between -1 and -0.5.

Option C) A=9/16,B=-5/16,C=-0.4,D=-0.7

This is Incorrect representation because the value of C and D should lying between -0.5 and 0.

Option D) A=-0.7,B=-9/16,C=-0.4,D=-5/16

Here the value of A and B lying between -1 and -0.5 also the value of C and D lying between -0.5 and 0.

Also they are in ascending order from -1 to 0.

Hence, the correct option is Option D) A=-0.7,B=-9/16,C=-0.4,D=-5/16

Explanation:

Answer 2

The completed matches would be:

1.
`\(-(4)/(5)\) - B`

2.
`\(-1.2\) - A`

3.
`\(0.2\) - C`

4.
`\((3)/(5)\) - D`

Let's solve the problem step by step:

1. Identifying Points on the Number Line

We have a number line with points labeled A through D. It's important to note the intervals and where each point lies in relation to the numbers -2, -1, 0, 1, and 2.

2. Locating Rational Numbers

We will locate each of the given rational numbers on the number line:

• 
  `\(-(4)/(5)\)` is a negative number, so it lies between 0 and -1. It's closer to -1 because -4/5 is just a fifth away from -1. This would likely correspond to point B.
• 
  `\(-1.2\)` is less than -1, so it should be to the left of point B on the number line. Since there's no mark between -1 and -2, we can place it mentally and know it would be between A and B, closer to A.
• 
  `\(0.2\)` is a positive number that's a fifth away from 0 towards 1. This is likely point C.
• 
  `\((3)/(5)\)` is also a positive number, slightly more than halfway between 0 and 1. This could be between C and D, but since we have already allocated C to 0.2, which is less than 3/5, this number must correspond to D.

3. Matching the Rational Numbers with Points

• For
  `\(-(4)/(5)\)`, we look for the point just left of -1, which is point B.
• For
  `\(-1.2\)`, since it is not exactly on a labeled point but is closest to -2, we would associate it with point A.
• For
  `\(0.2\)`, we would associate it with point C because it is just right of 0.
• For
  `\((3)/(5)\)`, we would associate it with point D because it is right of 0.2 and less than 1.

4. Filling in the Answer Box

Now we fill in the answer boxes with the corresponding letters:

• 
  `\(-(4)/(5)\)` matches with point B.
• 
  `\(-1.2\)` matches with point A.
• 
  `\(0.2\)` matches with point C.
• 
  `\((3)/(5)\)` matches with point D.