Number Line & Integers
Watch integers jump along a number line as you add and subtract, compare and order numbers, find absolute values, master the sign rules — then test yourself.
On a number line, adding a positive integer moves you right and adding a negative moves you left, so −3 + 5 means start at −3 and jump 5 to the right, giving 2. Subtracting means adding the opposite: 6 − (−4) = 6 + 4 = 10. For × and ÷, same signs give a positive answer and different signs give a negative one.
Type a sum of integers
Up to 8 numbers. Put a negative number after + or − in brackets, e.g. 4 − (−2).
Step-by-step
Each step is one jump. The highlighted step is playing now.
Compare two integers
On a number line, the number further to the right is always the greater one.
Arrange integers in order
Type up to 12 integers separated by commas or spaces.
Absolute value = distance from 0
Distance is never negative, so |−6| and |6| are both 6.
Try the rules
Pick two integers and an operation — the rule that applies lights up below.
Adding & subtracting
| Case | Rule | Example |
|---|---|---|
| Both positive | Add. Answer is positive. | 4 + 3 = 7 |
| Both negative | Add the absolute values. Answer is negative. | (−4) + (−3) = −7 |
| Different signs | Subtract the smaller absolute value from the larger. Keep the sign of the larger. | (−9) + 4 = −5 |
| Subtraction | Add the opposite (additive inverse) of the second number. | 4 − (−3) = 4 + 3 = 7 |
Multiplying & dividing
Same signs give positive, different signs give negative.
| × or ÷ | positive (+) | negative (−) |
|---|---|---|
| positive (+) | + | − |
| negative (−) | − | + |
Anything × 0 = 0. 0 ÷ any non-zero integer = 0. Division by 0 is not defined.
Why is negative × negative positive?
Follow the pattern: each time the first number goes down by 1, the answer goes up by 4. Keep going past 0 and the answers become positive.
Integer practice — 10 questions
After every answer the number line shows the solution.
| # | Question | Your answer | Correct |
|---|
Make integers make sense
Positive and negative numbers become easy once you can see them move. Every rule here is shown as a jump, a distance or a pattern.
Type a sum
Something like −3 + 5 − (−2). Use the examples or Random for new ones.
Watch the jumps
Green jumps go right, red jumps go left. Play it all or one step at a time.
Learn the rules
Compare, order, absolute value and the sign table for × and ÷ — all on one page.
Practise
10 quick questions at your level, with the number line explaining every answer.
Moving on a number line
Adding a positive number moves you right. Adding a negative number moves you left.
−3 + 5 = 2 → start at −3, jump 5 to the right.
Subtracting = adding the opposite
To subtract an integer, add its additive inverse: a − b = a + (−b).
6 − (−4) = 6 + 4 = 10
Comparing integers
Every positive integer is greater than every negative integer, and 0 sits between them. Among negatives, the one closer to 0 is greater: −2 > −9.
Absolute value & opposites
|a| is the distance of a from 0, so |−8| = |8| = 8. A number and its opposite (8 and −8) add up to 0.
Number Line & Integers — your questions
What are the rules for adding and subtracting integers?
If both signs are the same, add the numbers and keep that sign: (−4) + (−3) = −7. If the signs are different, subtract the smaller absolute value from the larger and keep the sign of the larger: (−9) + 4 = −5. To subtract, add the opposite of the second number, so 4 − (−3) = 4 + 3 = 7.
Why is a negative times a negative a positive?
Follow the pattern. 2 × (−4) = −8, 1 × (−4) = −4, 0 × (−4) = 0 — each time the first number drops by 1, the answer rises by 4. Keep going and (−1) × (−4) = 4 and (−2) × (−4) = 8. Continuing the pattern is the only way the arithmetic stays consistent.
Which integer is greater, −2 or −9?
−2 is greater. On a number line the number further to the right is always the larger one, and −2 sits to the right of −9. Among negative numbers, the one closer to zero is the greater, which feels backwards at first because 9 is bigger than 2. Every positive integer is greater than every negative integer.
What is the absolute value of a number?
The absolute value |a| is the distance of a from zero on the number line, and distance is never negative, so |−6| = 6 and |6| = 6 as well. A number and its opposite, such as 8 and −8, are the same distance from zero and add up to 0. |0| is 0.
What are the sign rules for multiplying and dividing integers?
Same signs give a positive answer and different signs give a negative one: (−6) × (−4) = 24 but (−6) × 4 = −24. The same rule applies to division. Anything multiplied by 0 is 0, and 0 divided by any non-zero integer is 0, but division by 0 is not defined.
Where do we use negative numbers in real life?
Temperatures below 0 °C, basement floors below the ground floor, a bank account that is overdrawn, the depth of a submarine below sea level and a loss in a business are all negative quantities. In each case zero is a chosen starting point and the negative sign shows the opposite direction from it.