Plot integers -5 to 5 on number line and compare using inequality

Question

Plot the integers from -5 to 5 on a number line. Using the number line, compare: (a) $-3$ and $2$ , (b) $-4$ and $-1$ , (c) $0$ and $-5$ . Write using inequality symbols.

(NCERT Class 6)

Solution — Step by Step

The number line runs from left to right, with numbers increasing as we move right:

\leftarrow \quad -5 \quad -4 \quad -3 \quad -2 \quad -1 \quad 0 \quad 1 \quad 2 \quad 3 \quad 4 \quad 5 \quad \rightarrow

Mark each integer with a dot at equal spacing. Zero sits in the middle. Negative numbers are on the left, positive numbers on the right.

On the number line, $-3$ is to the left of $2$ . A number to the left is always smaller.

\mathbf{-3 < 2}

$-4$ is to the left of $-1$ on the number line. So $-4$ is smaller.

\mathbf{-4 < -1}

Among negative numbers, the one with the larger absolute value is actually smaller. $|-4| = 4 > |-1| = 1$ , so $-4 < -1$ .

$0$ is to the right of $-5$ . So $0$ is greater.

\mathbf{-5 < 0}

Zero is greater than every negative number and less than every positive number.

Why This Works

The number line gives us a visual way to compare any two numbers. The rule is simple: the number further to the right is always greater. This works for all integers — positive, negative, and zero.

For negative numbers, this might feel counterintuitive at first. $-100$ is less than $-1$ even though 100 is “bigger” than 1. Think of it as temperature: $-100°\text{C}$ is much colder (less) than $-1°\text{C}$ .

Alternative Method — Using Rules Without a Number Line

Any positive number > 0 > any negative number
Between two positive numbers: the bigger one is greater ( $5 > 3$ )
Between two negative numbers: the one closer to zero is greater ( $-1 > -4$ )

For exams, the inequality symbols can be confusing. Think of the symbol as a mouth that always opens towards the bigger number: $2 > -3$ (mouth opens towards 2) or $-3 < 2$ (mouth opens towards 2). Both say the same thing.

Common Mistake

Students write $-4 > -1$ because “4 is greater than 1.” This ignores the negative sign. On the number line, $-4$ is further left (further from zero on the negative side) and is therefore less than $-1$ . Always think about the number line position, not just the digits.

Question

Solution — Step by Step

Why This Works

Alternative Method — Using Rules Without a Number Line

Common Mistake

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