Math Problem Statement

Which point represents 2 3/4 on the number line below? The second question asks for the surface area of a cube given its net with side length 5 inches.

Solution

I see you uploaded two images! Let’s start by solving the first question about the number line.

For the first image:

We are asked to find which point represents 2342 \frac{3}{4} on the number line.

To solve this:

  1. Notice the numbers 2 and 3 on the number line.
  2. 2342 \frac{3}{4} is between 2 and 3, so it will be closer to 3.
  3. We need to divide the space between 2 and 3 into four equal parts since we are working with 34\frac{3}{4}.
  4. 2342 \frac{3}{4} is three of those four equal parts.

Looking at the points on the number line:

  • Point W is at 2.
  • Point X is at 2.25 (which is 2142 \frac{1}{4}).
  • Point Y is at 2.5 (which is 2122 \frac{1}{2}).
  • Point Z is at 2.75 (which is 2342 \frac{3}{4}).

So, the correct answer is Z.


For the second image:

We are asked to find the surface area of the cube given its net.

  • The net consists of 6 squares, and each square has a side length of 5 inches.
  • To find the surface area, we need to calculate the area of one square and then multiply that by 6 (since there are 6 faces on a cube).

The area of one square is: Area=side2=52=25square inches.\text{Area} = \text{side}^2 = 5^2 = 25 \, \text{square inches}.

Since there are 6 faces: Surface Area=6×25=150square inches.\text{Surface Area} = 6 \times 25 = 150 \, \text{square inches}.


Would you like further details on any of these problems, or do you have additional questions? Here are some related questions you might find helpful:

  1. How would you handle a fraction that’s not an easy common fraction like 34\frac{3}{4}?
  2. What are some other ways to represent fractions on number lines?
  3. How would the surface area calculation change if the cube’s sides were a different length?
  4. What is the importance of understanding net diagrams in geometry?
  5. Could you solve this problem if the figure was a rectangular prism instead of a cube?

Tip: Always try to simplify fractions or decimals to make them easier to work with, especially when placing them on a number line!

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Math Problem Analysis

Mathematical Concepts

Number Line
Fractions
Surface Area
Geometry

Formulas

Surface Area = 6 × side²

Theorems

Surface Area of a Cube

Suitable Grade Level

Grades 5-7