When signs differ, subtract smaller from larger and keep the sign of the larger.

Solve (-7) + 4

The Question

Find the value of (-7) + 4.

This is a case where we have different signs — one number is negative, the other is positive. Let’s work through this carefully.

Real-Life Understanding

Think of a bank account:

You are ₹7 in debt (your balance is -7). A friend gives you ₹4.

You pay off ₹4 of your debt. But you still owe ₹3 — because the debt was bigger than what you received.

So the final balance is -3.

That’s our answer, and the rule below will confirm it.

The Rule for Different Signs

When the two integers have different signs (one positive, one negative):

Find the difference between the values (subtract the smaller value from the larger value, ignoring signs).
Give the answer the sign of the number with the larger value.

Step 1: Subtract smaller |value| from larger |value| Step 2: Keep the sign of the number with the larger absolute value

|value| means “ignore the sign, just take the number”

Step-by-Step Solution

Problem: (-7) + 4

Step 1: Identify the values (ignore signs): 7 and 4.

Step 2: Find the difference:

7 - 4 = 3

Step 3: Which number has the larger value? 7 (from -7). Its sign is negative.

Step 4: Answer gets a negative sign:

(-7) + 4 = -3

Number Line Method

Start at -7 on the number line. We are adding +4, so we move 4 steps to the right.

← -8  -7  -6  -5  -4  -3  -2  -1  0  +1 →
       →→→→→→→→
              land here at -3

Starting at -7, moving 4 steps right: -7, -6, -5, -4, -3.

We land on -3. Answer confirmed!

Another Example to Build Confidence

Let’s try: (-4) + 9

Step 1: Values are 4 and 9. Difference = 9 - 4 = 5. Step 2: Larger value is 9, which is positive. Answer: +5 (or just 5).

And let’s try: 8 + (-11)

Step 1: Values are 8 and 11. Difference = 11 - 8 = 3. Step 2: Larger value is 11, which is negative (from -11). Answer: -3.

The Tug-of-War Picture

Think of positive and negative as two teams in a tug-of-war.

In (-7) + 4:

Negative team has 7 members pulling left.
Positive team has 4 members pulling right.

Negative team wins (7 > 4), so the rope moves LEFT. The difference is 7 - 4 = 3 steps. We end up at -3.

Common mistake: Writing (-7) + 4 = -11.

This happens when students add the values (7 + 4 = 11) without thinking about which team “wins.” When signs are different, we SUBTRACT, not add.

Remember: different signs → subtract the values → take the sign of the bigger one.

Try These Similar Problems

Problem 1: (-9) + 5 = ?

Values: 9 and 5. Difference: 9 - 5 = 4. Larger value is 9, which is negative. Answer: -4

Problem 2: 6 + (-2) = ?

Values: 6 and 2. Difference: 6 - 2 = 4. Larger value is 6, which is positive. Answer: +4

Problem 3: A building has its ground floor at 0. Riya is on floor -3 (basement). She goes up 7 floors. Which floor is she on now?

(-3) + 7 = ? Values: 3 and 7. Difference: 7 - 3 = 4. Larger value is 7, which is positive. Answer: +4

Riya is on the 4th floor.

Exam tip: When adding integers with different signs, always ask: “Which number is bigger (ignoring signs)?” That bigger number’s sign is your answer’s sign. Then just subtract the smaller from the bigger. This approach works every time.

Solve (-7) + 4 — Adding Positive and Negative Integers