Billy plotted −3

Question

4
and −1
4
on a number line to determine that −3
4
is smaller than −1
4
.

A number line going from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. A point is 1 mark to the right of negative 1, and another point is 1 mark to the left of 0.
Is he correct? Explain why or why not.

Answer 1

To determine if Billy is correct in stating that \(-\frac{3}{4}\) is smaller than \(-\frac{1}{4}\), we can analyze the values and their positions on the number line.

1. Understand the values:

   • \(-\frac{3}{4}\) is equal to -0.75.
   • \(-\frac{1}{4}\) is equal to -0.25.

2. Compare the values:

   • On the number line, values that are further to the left are smaller, and values that are further to the right are larger.
   • Since -0.75 (or \(-\frac{3}{4}\)) is to the left of -0.25 (or \(-\frac{1}{4}\)), \(-\frac{3}{4}\) is indeed smaller than \(-\frac{1}{4}\).

3. Placement on the number line:

   • If you visualize or plot these values on a number line going from negative 2 to positive 2:
     • -1 is one mark away from -0.75 (which would be slightly to the left of -0.5).
     • -0.25 is one mark to the right of -0.5 and lies closer to 0.

Given this mathematical and visual representation, Billy's conclusion is correct. \(-\frac{3}{4}\) is indeed smaller than \(-\frac{1}{4}\).