MATHEMATICSNumber & Arithmetic
Four Operations
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● Master Topic Guide Verified 11+ Curriculum
The Four Operations
Master addition, subtraction, multiplication, division, negative number operations, and powers of 10 with core rules, number lines, and step-by-step examples!
★ Core Topic Poster11+ Exam Essential
🔢 The Four Operations
Negative numbers are less than zero. Learn the rules to add, subtract, multiply and divide them.
KEY IDEAS
- ★Zero is neither positive nor negative.
- ★Numbers to the left of 0 on a number line are negative.
- ★Signs (+ or −) are important!
1. ADDITION
Same signs:
Add the numbers and keep the sign.
Different signs:
Subtract the numbers and keep the sign of the larger (in value) number.
Examples:
(−7) + (−3) = −10same signs
5 + (−8) = −3different signs
(−9) + 4 = −5different signs
2. SUBTRACTION
Change subtraction to adding the opposite.
a − b = a + (−b)
Examples:
7 − (−3) = 7 + 3 = 10
(−6) − 4 = (−6) + (−4) = −10
(−2) − (−9) = (−2) + 9 = 7
3. MULTIPLICATION
Same signs: answer is positive.
Different signs: answer is negative.
Signs Rule:
(+) × (+) = +
(−) × (−) = +
(+) × (−) = −
(−) × (+) = −
Examples:
(−4) × (−6) = 24
(−7) × 3 = −21
8 × (−5) = −40
4. DIVISION
Same signs: answer is positive.
Different signs: answer is negative.
Signs Rule:
(+) ÷ (+) = +
(−) ÷ (−) = +
(+) ÷ (−) = −
(−) ÷ (+) = −
Examples:
(−24) ÷ (−4) = 6
(−15) ÷ 3 = −5
18 ÷ (−6) = −3
5. NUMBER LINE REMINDERVisual Guide
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►
-5
-4
-3
-2
-1
0
1
2
3
4
5
Numbers less than 0 are negative.
Numbers greater than 0 are positive.
6. ORDERING NEGATIVE NUMBERSComparison
💡 The closer a number is to zero, the greater it is.
Examples:
−2 > −5
because −2 is closer to 0 than −5.
−8 < −3
because −8 is further from 0 than −3.
7. WORKED EXAMPLESStep-by-Step Solutions
A. Addition
Find (−6) + (−9).
Same signs: add the numbers and keep the sign.
(−6) + (−9) = −15
B. Subtraction
Find 4 − (−7).
Change to adding the opposite.
4 + 7 = 11
C. Multiplication
Find (−5) × 6.
Different signs: answer is negative.
(−5) × 6 = −30
D. Division
Find (−36) ÷ (−9).
Same signs: answer is positive.
(−36) ÷ (−9) = 4
8. PRACTICE QUESTIONS
A. Add
(-5) + (-6) =
15 + (-5) =
(-7) + 9 =
(-2) + (-9) =
B. Subtract
6 − (-3) =
(-9) − 4 =
(-8) − (-3) =
10 − (-3) =
C. Multiply
(-3) × (-9) =
(-4) × 6 =
9 × (-3) =
(-7) × (-8) =
D. Divide
(-6) ÷ (-2) =
(-14) ÷ 2 =
10 ÷ (-2) =
(-42) ÷ (-6) =
9. REAL LIFE EXAMPLESEveryday
Temperature:
−5°C + (−3°C) = −8°C
It gets 3 degrees colder.
Bank Balance:
£15 − £20 = −£5
You are £5 overdrawn.
Lift Floors:
(−2) × (3 floors) = −6 floors
Down 2 floors, 3 times = 6 floors down.
10. TOP TIPSStrategy
Double negatives (− × − or − ÷ −) always make a positive.
Change subtraction to adding the opposite.
Use a number line to help with addition and order.
💡 Practice makes perfect!
11. REMEMBERKey Rules
★ Check the signs!
★ Same signs → positive (+)
★ Different signs → negative (−)
Be careful with subtraction and division!
★ Master Topic Section11+ Essential Skill
⚡ Multiplying & Dividing by 10, 100 and 1000
When you multiply or divide by 10, 100 or 1000, you are moving the digits in a number to the left or to the right.
DECIMAL MOVEMENT
Multiplying moves the decimal point to the RIGHT. Dividing moves the decimal point to the LEFT!
1. MULTIPLYING BY 10, 100 AND 1000Move RIGHT ►
Move the decimal point to the RIGHT. Add zeros if digits run out.
× 10
Move 1 place to the right.
3.45 × 10 = 34.5
0.7 × 10 = 7
25 × 10 = 250
× 100
Move 2 places to the right.
3.45 × 100 = 345
0.7 × 100 = 70
25 × 100 = 2500
× 1000
Move 3 places to the right.
3.45 × 1000 = 3450
0.7 × 1000 = 700
25 × 1000 = 25000
Rule: Multiply by 10ⁿ → move decimal point n places to the RIGHT. (Add zeros if needed.)
2. DIVIDING BY 10, 100 AND 1000◄ Move LEFT
Move the decimal point to the LEFT. Add zeros if digits run out.
÷ 10
Move 1 place to the left.
3.45 ÷ 10 = 0.345
7 ÷ 10 = 0.7
250 ÷ 10 = 25
÷ 100
Move 2 places to the left.
3.45 ÷ 100 = 0.0345
7 ÷ 100 = 0.07
250 ÷ 100 = 2.5
÷ 1000
Move 3 places to the left.
3.45 ÷ 1000 = 0.00345
7 ÷ 1000 = 0.007
250 ÷ 1000 = 0.25
Rule: Divide by 10ⁿ → move decimal point n places to the LEFT. (Add zeros if needed.)
3. PLACE VALUE HELPS YOU SEE THE MOVEMENTVisual Shift
| Thousands 1000 | Hundreds 100 | Tens 10 | Ones 1 | . | Tenths 0.1 | Hundredths 0.01 | Thousandths 0.001 |
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | . | 5 | 6 | 7 |
Multiply by 10, 100, 1000:
Move RIGHT → 1 place (×10), 2 places (×100), 3 places (×1000)
Example: 12.345 × 100 = 1234.5
Divide by 10, 100, 1000:
Move LEFT → 1 place (÷10), 2 places (÷100), 3 places (÷1000)
Example: 12.345 ÷ 100 = 0.12345
4. PRACTICAL EXAMPLESMoney, Length & Weight
💰 Money Example (£12.50):
× 10 = £125.00
× 100 = £1250.00
× 1000 = £12500.00
÷ 10 = £1.25
÷ 100 = £0.125
÷ 1000 = £0.0125
📏 Length Example (2.36 m):
× 10 = 23.6 m
× 100 = 236 m
× 1000 = 2360 m
÷ 10 = 0.236 m
÷ 100 = 0.0236 m
÷ 1000 = 0.00236 m
⚖️ Weight Example (4.8 kg):
× 10 = 48 kg
× 100 = 480 kg
× 1000 = 4800 kg
÷ 10 = 0.48 kg
÷ 100 = 0.048 kg
÷ 1000 = 0.0048 kg
5. QUICK REFERENCECheat Sheet
| Operation | What to do |
|---|---|
| × 10 | Move decimal 1 place RIGHT |
| × 100 | Move decimal 2 places RIGHT |
| × 1000 | Move decimal 3 places RIGHT |
| ÷ 10 | Move decimal 1 place LEFT |
| ÷ 100 | Move decimal 2 places LEFT |
| ÷ 1000 | Move decimal 3 places LEFT |
TOP TIPS FOR POWERS OF 10
Think of 10, 100 and 1000 as moving the decimal point.
Multiplying makes the number bigger, so move RIGHT.
Dividing makes the number smaller, so move LEFT.
Add zeros to the left or right if needed.
Interactive Negative Operations Machine
Adjust the numbers and operator to see live step-by-step calculations!
Live CalculationMachine
(-5) + (3) = -2
Step Explanation:
Different signs: Subtract values (5 and 3) and take sign of larger magnitude.
🚀 Ready to Test Your Knowledge?
Take our graded 11+ The Four Operations assessment now!