Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 7th grade adding and subtracting integers? Then this Grade 7 lesson on Adding and Subtracting Positive and Negative Numbers explains each idea step by step, with worked examples.
Quick answer: Combine signed numbers by walking a number line: adding a positive goes right, adding a negative goes left, and opposites cancel to 0. Replace any subtraction p − q with p + (−q). The gap between two numbers equals |p − q|. Decimals and fractions follow identical rules.
Standards: 7.NS.A.1a, 7.NS.A.1b, 7.NS.A.1c, 7.NS.A.1d · Level: Grade 7
What happens when you combine positive and negative numbers?
Picture a walk along a number line. The first number is where you stand; a positive second number sends you east (right), a negative one sends you west (left). Numbers like 8 and −8 sit equally far from zero on opposite sides. Mathematicians call such a pair opposites, and together they always total 0.
The opposite of p is −p, and p + (−p) = 0. For example, 3.5 + (−3.5) = 0 and −23 + 23 = 0.
| Signs | What to do | Example |
|---|---|---|
| Same sign | Add the sizes (absolute values) and keep that shared sign | −5 + (−7) = −12 |
| Different signs | Take the bigger size minus the smaller size, then use the sign of the bigger one | −9 + 4 = −5 |
| Opposites | The total is exactly 0 | 6 + (−6) = 0 |
A checking account is overdrawn at −$6. A deposit of $9 is made. Then −6 + 9: start at −6 and move 9 right, which lands on 3. The balance is $3.
How can subtraction become addition?
To subtract q, add −q instead: p − q = p + (−q). That turns 2 − 9 into 2 + (−9) = −7, and 3 − (−4) into 3 + 4 = 7.
- Rewrite every subtraction as adding the opposite.
- Look at the signs: same signs add, different signs subtract absolute values.
- Give the answer the sign of the number farther from 0.
- Check with a number line or an opposite pair.
How far apart are two numbers?
Subtract one from the other and drop any negative sign by taking the absolute value. A gap can never be below 0, and swapping the two numbers changes nothing: |p − q| = |q − p|.
Dropping the sign: treating −9 − 4 as 5. Rewrite it as −9 + (−4) = −13. Both numbers push in the same direction, left.
Read the minus sign as "add the opposite." Then you only ever have to add.
- Opposites add to 0: p + (−p) = 0.
- Same signs: add absolute values and keep the sign. Different signs: subtract and keep the sign of the larger absolute value.
- Subtracting a number is adding its opposite: p − q = p + (−q).
- The distance between p and q is |p − q|.
- The same rules apply to positive and negative decimals and fractions.
Adding and Subtracting Positive and Negative Numbers: frequently asked questions
What is an additive inverse?
The additive inverse of a number is its opposite, the number that adds to it to give 0. The inverse of 7 is −7 and the inverse of −2.5 is 2.5.
Why does subtracting a negative number make the result larger?
Subtracting a negative means adding its opposite, which is positive. So 3 − (−4) = 3 + 4 = 7, a move of 4 to the right.
How do I add a positive and a negative number?
Subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value. For −9 + 4, 9 − 4 = 5, and the sign is negative, so the answer is −5.
How do I find the distance between two numbers?
Subtract them in either order and take the absolute value. The distance between −7 and 4 is |4 − (−7)| = 11.
Do the same rules work for fractions and decimals?
Yes. You can add and subtract positive and negative fractions and decimals by the same sign rules, after writing fractions with a common denominator.
Mis à jour le