Integers · Add integers · 4.3

Add different signs.

With different signs, zero pairs cancel: subtract the smaller size from the larger, and take the sign of the number with the bigger size.

01 / THE IDEA

See it work.

Zero pairs

A +1 and a −1 cancel.

-9 + 4

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Watch the method

Add different signs

−9 + 4: 9 − 4 = 5, and 9 is negative, so −5.

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−9+4-9 + 4
1

Different signs — subtract

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

9−4=59 - 4 = 5
2

Take the bigger sign

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

−9+4=−5-9 + 4 = -5
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

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

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— / WHY IT WORKS

The idea underneath.

Net result

Cancelling leaves the difference of the sizes, signed by whichever side had more.

Why it works

Owe 9, earn 4 → still owe 5.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Add 1 + -1

1

Different signs — subtract

Subtract the smaller size from the larger: 1 − 1. 1 - 1 = 0

2

Take the bigger sign

1 is the larger size and it is negative, so the answer is negative. 1 + (-1) = 0

EX 2medium

Add -6 + 7

1

Different signs — subtract

Subtract the smaller size from the larger: 7 − 6. 7 - 6 = 1

2

Take the bigger sign

7 is the larger size and it is positive, so the answer is positive. -6 + 7 = 1

EX 3hard

Add -5 + 11

1

Different signs — subtract

Subtract the smaller size from the larger: 11 − 5. 11 - 5 = 6

2

Take the bigger sign

11 is the larger size and it is positive, so the answer is positive. -5 + 11 = 6

04 / COMMON TRAPS

Where students slip.

Trap

Adding the sizes.

Fix

Opposite signs subtract.

Trap

Taking the wrong sign.

Fix

Use the sign of the larger size.

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

Add 1 + -1

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
C2

Add -10 + 5

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
C3

Add -2 + 1

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
C4

Add -5 + 6

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
Apply

Apply (4)

A1

Add -6 + 7

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
A2

Add 9 + -11

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
A3

Add -7 + 1

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
A4

Add -1 + 8

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
Extension

Extension (4)

E1

Add -5 + 11

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
E2

Add -1 + 3

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
E3

Add 1 + -4

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.
E4

Add -7 + 3

Need a hint?
  • Subtract the smaller size from the larger.
  • Keep the sign of the bigger one.