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

Billy's analysis of the two numbers, \(-\frac{3}{4}\) and \(-\frac{1}{4}\), is not correct. Let’s clarify why that is.

To compare the two fractions:

1. Represent the fractions as decimals:

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

2. Understanding number line placement:

   • On a number line, numbers become smaller as you move to the left.
   • Thus, \(-0.75\) (or \(-\frac{3}{4}\)) is to the left of \(-0.25\) (or \(-\frac{1}{4}\)).

3. Comparison of values:

   • Since \(-0.75 < -0.25\), it follows that \(-\frac{3}{4} < -\frac{1}{4}\).
   • Therefore, \(-\frac{3}{4}\) is actually smaller than \(-\frac{1}{4}\), confirming Billy's finding about the sizes.

So, to summarize: Billy correctly identified that \(-\frac{3}{4}\) is smaller than \(-\frac{1}{4}\), and his placement on the number line supports this conclusion. The decision was correct based on the locations of the indicated points and their numerical values.