Duration: 45 minutes
By the end of this lesson, you will be able to:
B = Brackets O = Of (powers/orders) D = Division M = Multiplication A = Addition S = Subtraction
This is the ORDER we do operations!
Wrong way: 6 + 3 × 2 = (6 + 3) × 2 = 18
Right way: 6 + 3 × 2 = 6 + (3 × 2) = 6 + 6 = 12
The order changes the answer!
Example: 10 - 2 × 3 = ?
Step 1: Multiply first (2 × 3 = 6) Step 2: Then subtract (10 - 6 = 4)
Answer: 4
Remember: Multiplication before subtraction!
Problem: 1/2 + 1/4 × 2 = ?
Step 1: Multiply first: 1/4 × 2 = 2/4 = 1/2
Step 2: Then add: 1/2 + 1/2 = 2/2 = 1
Answer: 1
Problem: (1/3 + 1/6) × 2 = ?
Step 1: Brackets first! 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2
Step 2: Then multiply: 1/2 × 2 = 1
Problem: 1/2 × 3/4 + 1/8 = ?
Step 1: Multiply: 1/2 × 3/4 = 3/8 Step 2: Add: 3/8 + 1/8 = 4/8 = 1/2
Answer: 1/2
Easy case: Same bottom number
Examples:
Just add or subtract the numerators!
New challenge: Different bottom numbers
Strategy: Find a common denominator first!
Example: 1/2 + 1/3 We need to make both fractions have the same denominator before we can add them.
Problem: 1/2 + 1/3 = ?
Step 1: Find LCD (Least Common Denominator) Multiples of 2: 2, 4, 6, 8... Multiples of 3: 3, 6, 9, 12... LCD = 6
Step 2: Convert both fractions 1/2 = 3/6 and 1/3 = 2/6
Step 3: Now add! 3/6 + 2/6 = 5/6
Answer: 5/6
Remember: Common denominator first, then add!
Problem: 3/4 - 1/6 = ?
Step 1: LCD = 12 Step 2: Convert: 3/4 = 9/12 and 1/6 = 2/12 Step 3: Subtract: 9/12 - 2/12 = 7/12
Answer: 7/12
Solve in your exercise book:
a) 2/5 + 1/10 b) 5/6 - 1/3 c) 1/4 + 1/3 × 2 (Remember BODMAS!)
Show all steps clearly!
What are decimals? Another way to write fractions!
The decimal point separates whole numbers from parts.
Rule: Line up the decimal points!
Example: 3.45 + 2.7 = ?
3.45 + 2.70 (add zero as placeholder) ------ 6.15
Example: 5.8 - 2.35 = ?
5.80 - 2.35 ------ 3.45
Rule: Multiply normally, then count decimal places
Example: 2.5 × 3 = ?
Step 1: Multiply: 25 × 3 = 75 Step 2: One decimal place in 2.5 Answer: 7.5
Example: 1.2 × 0.4 = ?
Step 1: Multiply: 12 × 4 = 48 Step 2: Count decimals: 1 + 1 = 2 places Answer: 0.48
Rule: Make the divisor a whole number first!
Example 1: 6.4 ÷ 2 = 3.2 (Divide normally, keep decimal)
Example 2: 3.6 ÷ 0.4 = ? Multiply both by 10: 36 ÷ 4 = 9
a) 4.5 + 3.25 b) 7.2 - 3.8 c) 2.4 × 5 d) 8.4 ÷ 2
Work carefully with decimal points!
Problem: A shopkeeper has 2.5 kg of sugar. She sells 0.75 kg. How much is left?
Solution: 2.5 - 0.75 = 1.75 kg
She has 1.75 kg of sugar left.
Problem: Okello has 1/4 of a plot of land. He buys another 1/3 of a plot. What fraction does he have now?
Solution: 1/4 + 1/3 = 3/12 + 4/12 = 7/12
He has 7/12 of a plot.
Order of operations:
Important: Multiplication and division are equal; addition and subtraction are equal!
Addition/Subtraction: Line up decimal points
Multiplication: Count total decimal places
Division: Make divisor a whole number
Always: Check your decimal point placement!
Answer in your exercise book:
Akello bought 2.5 kg of beans and 1.75 kg of maize. What is the total weight?
Then: If she uses 1/4 of the total for cooking, how much does she use?
Part A: BODMAS with Fractions
Part B: Adding/Subtracting Fractions 4. 1/3 + 1/4 5. 2/5 + 1/2 6. 5/6 - 1/4 7. 7/8 - 1/2
Part C: Decimal Operations 8. 4.6 + 2.8 9. 8.5 - 3.7 10. 3.4 × 2 11. 9.6 ÷ 3 12. 5.25 + 3.8 13. 7.2 - 4.65
Part D: Word Problems 14. Total weight problem (beans and maize) 15. Cake problem with fractions
Next Lesson: We will learn about ratio and proportion
Connection: Ratios are written like fractions, and understanding fractions helps you master ratios!
Keep practicing!
BODMAS: Always follow the correct order
Common Denominators: Necessary for adding/subtracting different fractions
Decimals: Line up points for +/-, count places for ×, make whole for ÷
Practice regularly and you'll master these skills!