Integers · Subtract integers · 5.2

Add the opposite.

The master rule: subtracting is adding the opposite. Keep the first number, change the minus to plus, change the sign of the second — then use the addition rules.

01 / THE IDEA

See it work.

Watch the method

Add the opposite

−3 − 6 = −3 + (−6) = −9.

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−3−6-3 - 6
1

Add the opposite

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

−3−6=−3+(−6)-3 - 6 = -3 + (-6)
2

Same sign — add the sizes

Both are negative, so add their sizes: 3 + 6.

3+6=93 + 6 = 9
3

Keep the sign

Both negative → the answer is negative.

−3+(−6)=−9-3 + (-6) = -9
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.

Subtraction is addition

Every subtraction becomes an addition of the opposite, so you only ever need the addition rules.

Why it works

Removing a gain is the same as adding a loss.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Subtract 10 - 10

1

Add the opposite

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

2

Different signs — subtract

Subtract the smaller size from the larger: 10 − 10. 10 - 10 = 0

3

Take the bigger sign

10 is the larger size and it is negative, so the answer is negative. 10 + (-10) = 0

EX 2medium

Subtract 7 - 2

1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of 2. 7 - 2 = 7 + (-2)

2

Different signs — subtract

Subtract the smaller size from the larger: 7 − 2. 7 - 2 = 5

3

Take the bigger sign

7 is the larger size and it is positive, so the answer is positive. 7 + (-2) = 5

EX 3hard

Subtract -5 - 6

1

Add the opposite

Subtracting is adding the opposite: change − to + and flip the sign of 6. -5 - 6 = -5 + (-6)

2

Same sign — add the sizes

Both are negative, so add their sizes: 5 + 6. 5 + 6 = 11

3

Keep the sign

Both negative → the answer is negative. -5 + (-6) = -11

04 / COMMON TRAPS

Where students slip.

Trap

Changing only one sign.

Fix

Change the operation AND the second number’s sign.

Trap

Flipping the first number too.

Fix

Keep the first number exactly.

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 10 - 10

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
C2

Subtract -3 - 8

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
C3

Subtract 4 - 7

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
C4

Subtract 8 - 10

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
Apply

Apply (4)

A1

Subtract 7 - 2

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
A2

Subtract -9 - 12

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
A3

Subtract -1 - 6

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
A4

Subtract -1 - 4

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
Extension

Extension (4)

E1

Subtract -5 - 6

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
E2

Subtract 11 - 6

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
E3

Subtract 4 - 9

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.
E4

Subtract 8 - 10

Need a hint?
  • Keep the first number.
  • Change − to +, and flip the next sign.