Should we write or ?

Question

Homi · Accepted Answer

Understand the Question

On a number line, numbers increase as you move to the right and decrease as you move to the left.
To compare $-3$ and $-4$ , look at their relative positions on the number line: the number further to the right is greater, and the number further to the left is smaller.
The symbol $<$ means "less than" (smaller than), and $>$ means "greater than" (bigger than).

Step 1 · Compare Positions on the Number Line

On a number line, numbers get larger as we move to the right and smaller as we move to the left. Diagram 1

Since $-3$ lies to the right of $-4$ , $-3$ is greater than $-4$ , which means $-4$ is smaller than $-3$ .

Step 2 · Write the Comparison

Since $-4$ is smaller than $-3$ , we use the symbol ' $<$ ' (less than): $-4 < -3$

This can also be written using the symbol ' $>$ ' (greater than) as: $-3 > -4$

Answer

We should write $-4 < -3$ .

Common Mistakes

Comparing Magnitudes Directly: Incorrectly assuming $-4 > -3$ because $4 > 3$ . For negative numbers, the number with the larger absolute value is further to the left and hence smaller.
Inequality Symbol Confusion: Confusing $<$ (less than) and $>$ (greater than). Remember that the open/wider end always faces the larger number.

Question 10