Integers · Subtract integers · 5.3

Subtract on the line.

Subtraction on the line: a − b is how far and which way you go from b to a. Or just add the opposite and hop. 4 − 9 lands 5 left of 0.

01 / THE IDEA

See it work.

On the number line

Start at 4, hop left 9.

4 − 9 = -5

-6-5-4-3-2-1012345-5

Watch the method

Subtract on the line

4 − 9 = 4 + (−9): hop 9 left from 4 → −5.

1 / 3
4−94 - 9
1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of 9.

4−9=4+(−9)4 - 9 = 4 + (-9)
2

Different signs — subtract

Subtract the smaller size from the larger: 9 − 4.

9−4=59 - 4 = 5
3

Take the bigger sign

9 is the larger size and it is negative, so the answer is negative.

4+(−9)=−54 + (-9) = -5
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a whole number — negatives allowed, e.g. -7.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Difference as a hop

Rewrite as adding the opposite, then move left for the negative addend.

Why it works

From 4, walk back 9 steps.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Subtract 3 - 8

1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of 8. 3 - 8 = 3 + (-8)

2

Different signs — subtract

Subtract the smaller size from the larger: 8 − 3. 8 - 3 = 5

3

Take the bigger sign

8 is the larger size and it is negative, so the answer is negative. 3 + (-8) = -5

EX 2medium

Subtract 2 - 8

1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of 8. 2 - 8 = 2 + (-8)

2

Different signs — subtract

Subtract the smaller size from the larger: 8 − 2. 8 - 2 = 6

3

Take the bigger sign

8 is the larger size and it is negative, so the answer is negative. 2 + (-8) = -6

EX 3hard

Subtract 10 - 9

1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of 9. 10 - 9 = 10 + (-9)

2

Different signs — subtract

Subtract the smaller size from the larger: 10 − 9. 10 - 9 = 1

3

Take the bigger sign

10 is the larger size and it is positive, so the answer is positive. 10 + (-9) = 1

04 / COMMON TRAPS

Where students slip.

Trap

Hopping right for a subtraction.

Fix

Subtracting a positive hops left.

Trap

Forgetting to rewrite first.

Fix

Turn it into add-the-opposite.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Subtract 3 - 8

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
C2

Subtract 11 - 4

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
C3

Subtract 1 - 4

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
C4

Subtract 5 - 11

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
Apply

Apply (4)

A1

Subtract 2 - 8

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
A2

Subtract -8 - 7

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
A3

Subtract 5 - 10

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
A4

Subtract -10 - 11

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
Extension

Extension (4)

E1

Subtract 10 - 9

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
E2

Subtract -8 - 3

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
E3

Subtract -5 - 12

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.
E4

Subtract 9 - 3

Need a hint?
  • Rewrite as add the opposite.
  • Then hop on the line.