Math Problem Statement

What is the location of the point that is 1/3 of the distance from C to E on a number line?

Solution

To solve the problem, we first need to identify the positions of points CC, DD, and EE on the number line provided.

Based on the image, the points are positioned as follows:

  • CC is at 4-4
  • DD is at 2-2
  • EE is at 00

Now, the problem asks for the location of a point that is 13\frac{1}{3} of the distance from CC to EE.

Step-by-Step Solution:

  1. Calculate the distance from CC to EE: Distance from C to E=EC=0(4)=4\text{Distance from } C \text{ to } E = E - C = 0 - (-4) = 4

  2. Find 13\frac{1}{3} of the distance: 13×4=431.33\frac{1}{3} \times 4 = \frac{4}{3} \approx 1.33

  3. Determine the position: Since we are moving from CC to EE, starting at 4-4 and moving to the right by 43\frac{4}{3}:

    New position=C+43=4+43=123+43=83\text{New position} = C + \frac{4}{3} = -4 + \frac{4}{3} = -\frac{12}{3} + \frac{4}{3} = -\frac{8}{3}

So, the point is located at 83-\frac{8}{3}, which is approximately 2.67-2.67.

Final Answer:

The location of the point that is 13\frac{1}{3} of the distance from CC to EE is 83-\frac{8}{3}.

Would you like more details on this solution, or do you have any specific questions?

Further Exploration Questions:

  1. What would be the location if the point was 23\frac{2}{3} of the distance from CC to EE?
  2. How would the answer change if point CC was at 6-6 instead of 4-4?
  3. Can you find the point that is 14\frac{1}{4} of the distance from DD to EE?
  4. What is the midpoint between points CC and EE?
  5. How would you calculate a point that is 50% further from EE than point CC?

Tip: Always use a number line to visualize problems involving distances and fractions for more clarity.

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Math Problem Analysis

Mathematical Concepts

Number Line
Distance Calculation
Fractions

Formulas

Distance Formula: Distance = Point2 - Point1
Fraction of Distance: Fraction * Distance

Theorems

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Suitable Grade Level

Grades 6-8