Integers · Subtract integers · 5.5

Difference problems.

“How much more/warmer/higher?” is a subtraction. The change from −6 °C to 4 °C is 4 − (−6) = 10°. Add the opposite to find a signed difference.

01 / THE IDEA

See it work.

Watch the method

Difference problems

From −6 °C to 4 °C: 4 − (−6) = 10°.

1 / 3
4−−64 - -6
1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of (-6).

4−(−6)=4+64 - (-6) = 4 + 6
2

Same sign — add the sizes

Both are positive, so add their sizes: 4 + 6.

4+6=104 + 6 = 10
3

Keep the sign

Both positive → the answer is positive.

4+6=104 + 6 = 10
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
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— / WHY IT WORKS

The idea underneath.

Find the gap

The difference between two values is the later minus the earlier; subtracting a negative grows the gap.

Why it works

From −6 up to 4 is a 10-degree climb.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Subtract 4 - 9

1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of 9. 4 - 9 = 4 + (-9)

2

Different signs — subtract

Subtract the smaller size from the larger: 9 − 4. 9 - 4 = 5

3

Take the bigger sign

9 is the larger size and it is negative, so the answer is negative. 4 + (-9) = -5

EX 2medium

Subtract -9 - 8

1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of 8. -9 - 8 = -9 + (-8)

2

Same sign — add the sizes

Both are negative, so add their sizes: 9 + 8. 9 + 8 = 17

3

Keep the sign

Both negative → the answer is negative. -9 + (-8) = -17

EX 3hard

Subtract 4 - 8

1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of 8. 4 - 8 = 4 + (-8)

2

Different signs — subtract

Subtract the smaller size from the larger: 8 − 4. 8 - 4 = 4

3

Take the bigger sign

8 is the larger size and it is negative, so the answer is negative. 4 + (-8) = -4

04 / COMMON TRAPS

Where students slip.

Trap

Subtracting the smaller from the larger size and ignoring signs.

Fix

Use later − earlier with their signs.

Trap

Dropping the −(−) step.

Fix

Subtracting a negative adds.

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 4 - 9

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
C2

Subtract 7 - 7

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
C3

Subtract 6 - 2

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
C4

Subtract -11 - 7

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
Apply

Apply (4)

A1

Subtract -9 - 8

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
A2

Subtract 3 - 10

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
A3

Subtract 2 - 12

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
A4

Subtract -5 - 5

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
Extension

Extension (4)

E1

Subtract 4 - 8

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
E2

Subtract 6 - 11

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
E3

Subtract 1 - 9

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.
E4

Subtract 1 - 4

Need a hint?
  • Write later − earlier.
  • Add the opposite to evaluate.