On a number line represent -3 + 5 and explain

Question

Represent $-3 + 5$ on a number line and explain the steps. What is the result?

Solution — Step by Step

Draw a horizontal number line with zero in the middle. Mark integers from $-5$ to $+5$ .

We start at $-3$ . Mark this point clearly on the number line — it is 3 units to the left of zero.

Adding a positive number means moving to the right on the number line.

Adding $+5$ means we will take 5 steps to the right from our starting point of $-3$ .

Starting at $-3$ , count 5 steps to the right:

-3 → -2 → -1 → 0 → 1 → 2

We land at $+2$ .

-3 + 5 = \boxed{+2}

The result is $2$ , which is 2 units to the right of zero (a positive integer).

Why This Works

The number line is a physical model of integer arithmetic. Moving right = adding; moving left = subtracting. The signed number tells you both the direction and distance of movement.

Here, starting at $-3$ (3 steps left of zero) and moving 5 steps right covers the 3 steps back to zero, plus 2 more steps into positive territory. So the 5 “cancels” the 3 and leaves a remainder of 2 on the positive side.

This is the same as saying: the positive part (5) is greater than the negative part (3), so the answer is positive, and its value is $5 - 3 = 2$ .

Alternative Method

Using the rule of signs for addition:

When adding integers with different signs, subtract the smaller absolute value from the larger, and keep the sign of the number with the larger absolute value.

$|+5| = 5$ , $|-3| = 3$
$5 > 3$ , so the answer is positive
$5 - 3 = 2$
Answer: $+2$

This method is faster for calculation without drawing, but the number line method gives you the visual understanding of why the rule works.

Common Mistake

A common error at this level is to add both numbers ignoring signs and write $-3 + 5 = -8$ (treating both as positive and adding) or writing the answer as $-2$ (subtracting but keeping the wrong sign). Remember: when signs differ, we subtract the absolute values and the sign of the larger absolute value wins. Here 5 beats 3, so the answer is positive.

Think of integers as debits and credits. $-3$ means you owe ₹3. $+5$ means you receive ₹5. After receiving ₹5 when you owe ₹3, you have ₹2 left. This is $-3 + 5 = +2$ .

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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