Mixed Operations: Fractions & Decimals - New Numbers

Name:

Date:

$Mathematical symbols and fraction illustrations$

🎯 WALT: We Are Learning To

Perform mixed operations with fractions and decimals

Success Criteria:

✓ I can add and subtract fractions with different denominators
✓ I can multiply and divide fractions and decimals
✓ I can show clear working steps in my calculations
✓ I can convert between fractions and decimals when needed

📝 Worked Example:

Calculate: 3/4 + 0.5

Step 1: Convert 0.5 to a fraction = 1/2
Step 2: Find common denominator: 3/4 + 2/4
Step 3: Add numerators: 5/4 = 1 1/4 or 1.25

📚 Foundation Problems

1. Calculate: 2/3 + 1/6

Step 1: Find a common denominator (6).
Step 2: Convert 2/3 to 4/6.
Step 3: Add: 4/6 + 1/6 = 5/6.
Answer: _________

2. Calculate: 0.8 - 1/4

Step 1: Convert 0.8 to a fraction = 4/5.
Step 2: Convert 1/4 to a fraction with a common denominator (20): 1/4 = 5/20.
Step 3: Convert 4/5 to 16/20.
Step 4: Subtract: 16/20 - 5/20 = 11/20.
Answer: _________

3. Calculate: 3/5 × 0.4

Step 1: Convert 0.4 to a fraction = 2/5.
Step 2: Multiply: 3/5 × 2/5 = 6/25.
Answer: _________

4. Calculate: 1.2 ÷ 3/4

Step 1: Convert 1.2 to a fraction = 6/5.
Step 2: Dividing by a fraction is the same as multiplying by its reciprocal: 6/5 × 4/3.
Step 3: Multiply: (6 × 4) / (5 × 3) = 24/15 = 8/5 or 1.6.
Answer: _________

5. Sarah ate 2/5 of a pizza and bought 0.75 more pizzas. How much pizza does she have in total?

Step 1: Convert 0.75 to a fraction = 3/4.
Step 2: Find a common denominator (20): 2/5 = 8/20 and 3/4 = 15/20.
Step 3: Add: 8/20 + 15/20 = 23/20 = 1 3/20 or 1.15.
Answer: _________ pizzas

🚀 Advanced Problems & Extension

6. Calculate: (3/4 + 0.25) × 2/3

Step 1: Convert 0.25 to a fraction = 1/4.
Step 2: Find a common denominator: 3/4 + 1/4 = 4/4 = 1.
Step 3: Multiply: 1 × 2/3 = 2/3.
Answer: _________

7. A recipe calls for 1.5 cups of flour. If Tom uses 3/4 of this amount, how much flour does he use? Express your answer as both a fraction and a decimal.

Step 1: Convert 1.5 to a fraction = 3/2.
Step 2: Multiply: 3/2 × 3/4 = 9/8 = 1 1/8 or 1.125.
Fraction: _________ Decimal: _________

8. Extension Challenge: A rectangular garden is 2.4 metres long and 5/6 metres wide. What is the area of the garden? If fencing costs $12.50 per metre, how much will it cost to fence the perimeter?

Step 1: Calculate area: 2.4 × 5/6 = 2.4 × 0.8333 = 2.0 m².
Step 2: Calculate perimeter: 2(2.4 + 5/6) = 2(2.4 + 0.8333) = 2(3.2333) = 6.4666 m.
Step 3: Calculate cost: 6.4666 × 12.50 = $80.83.
Area: _________ m² | Fencing cost: $ _________

9. Dyslexia-Friendly Reflection: Draw or use symbols to show how you would explain adding fractions to a friend. You can use pictures, diagrams, or symbols instead of words.