Master problems involving both fractions and decimals with unit conversions and real-world applications.
• 1/4 = 1 ÷ 4 = 0.25
• 3/8 = 3 ÷ 8 = 0.375
• 5/6 = 5 ÷ 6 = 0.833...
• 1/2 = 5/10 = 0.5
• 3/4 = 75/100 = 0.75
• 1/5 = 2/10 = 0.2
Step 1: Write the decimal as a fraction with 1 as denominator
Step 2: Multiply by 10, 100, 1000, etc. to eliminate decimal
Step 3: Simplify the fraction
• 0.3 = 3/10
• 0.25 = 25/100 = 1/4
• 0.75 = 75/100 = 3/4
• 0.125 = 125/1000 = 1/8
Problem: A recipe calls for 2.5 cups of flour and 3/4 cup of sugar. You want to make 1.5 times the recipe. How much flour and sugar do you need?
Step 1 - Study: Need to multiply both ingredients by 1.5
Step 2 - Think: Convert 1.5 to fraction or work with decimals
Step 3 - Execute:
• Flour: 2.5 × 1.5 = 3.75 cups
• Sugar: 3/4 × 1.5 = 3/4 × 3/2 = 9/8 = 1 1/8 cups
Step 4 - Prove: 3.75 = 3 3/4 cups, 1 1/8 = 1.125 cups
Problem: Store A sells apples for $2.40 per 3/4 pound. Store B sells apples for $3.20 per 1.2 pounds. Which store has the better price per pound?
Step 1 - Study: Find price per pound for each store
Step 2 - Think: Divide price by weight for each store
Step 3 - Execute:
• Store A: $2.40 ÷ 3/4 = $2.40 ÷ 0.75 = $3.20 per pound
• Store B: $3.20 ÷ 1.2 = $2.67 per pound
• Store B is cheaper ($2.67 < $3.20)
Step 4 - Prove: Check calculations and logic
Problem: A piece of wood is 2.5 meters long. You cut off 3/8 of it. How much wood is left? Express your answer as both a decimal and a fraction.
Your solution:
Problem: A race is 5.5 kilometers long. How many miles is this? (1 kilometer = 0.625 miles) Express your answer as both a decimal and a fraction.
Step 1 - Study: Convert 5.5 km to miles
Step 2 - Think: Multiply by conversion factor
Step 3 - Execute:
• 5.5 × 0.625 = 3.4375 miles
• 3.4375 = 3 7/16 miles (since 0.4375 = 7/16)
Step 4 - Prove: 3.4375 × 1.6 ≈ 5.5 km ✓
Problem: A car travels 2.25 hours at 60 miles per hour. Then it travels 1 3/4 hours at 45 miles per hour. What's the total distance?
Step 1 - Study: Calculate distance for each part, then add
Step 2 - Think: Distance = Speed × Time
Step 3 - Execute:
• First part: 60 × 2.25 = 135 miles
• Second part: 45 × 1.75 = 78.75 miles
• Total: 135 + 78.75 = 213.75 miles
Step 4 - Prove: 213.75 = 213 3/4 miles
Problem: A recipe calls for 1.5 cups of milk and 2/3 cup of cream. You want to make 2.5 times the recipe. How much milk and cream do you need? Express your answers as mixed numbers.
Your solution:
Method 1: Convert all to decimals
Method 2: Convert all to fractions
Method 3: Use number line or estimation
Order: 2.3, 2 1/4, 2.75, 2 1/3
Convert to decimals:
• 2.3 = 2.3
• 2 1/4 = 2.25
• 2.75 = 2.75
• 2 1/3 = 2.333...
Ordered: 2.25, 2.3, 2.333..., 2.75
Answer: 2 1/4, 2.3, 2 1/3, 2.75
Problem: Which is larger: 3.6 or 3 5/8? Show your work.
Your comparison:
A construction project needs 3.5 yards of concrete and 2 1/4 yards of gravel. The concrete costs $45 per yard and gravel costs $20 per yard. What's the total cost?
Your solution:
A marathon is 26.2 miles long. How many kilometers is this? (1 mile = 1.6 kilometers) Express your answer as both a decimal and a fraction.
Your solution:
Order these numbers from least to greatest: 4.2, 4 1/5, 4.25, 4 1/3
Your answer:
A recipe serves 6 people and calls for 1.5 cups of flour and 3/4 cup of sugar. You want to serve 10 people. How much flour and sugar do you need? Express your answers as mixed numbers.
Your solution: