Scenario: Garden Planning - Plan and calculate garden areas using fractions!
You have a garden plot that is ¾ hectare. You want to plant:
How many hectares will be covered with grass? If each hectare of grass needs 2½ liters of water, how much water is needed for the grass area?
Problem: Multi-step area and resource calculation
Step 1: Calculate areas for roses and tulips
Roses: ¾ × ⅓ = 3/12 = ¼ hectare
Tulips: ¾ × ¼ = 3/16 hectare
Step 2: Calculate grass area
Grass = Total - Roses - Tulips
Grass = ¾ - ¼ - 3/16
Step 3: Find common denominator and subtract
LCD = 16
¾ = 12/16, ¼ = 4/16
Grass = 12/16 - 4/16 - 3/16 = 5/16 hectare
Step 4: Calculate water needed
Water = 5/16 × 2½ = 5/16 × 5/2 = 25/32 liters
Answer: Grass covers 5/16 hectare and needs 25/32 liters of water.
Step 1: Find grass as fraction of total
Grass fraction = 1 - ⅓ - ¼ = 1 - 4/12 - 3/12 = 5/12
Step 2: Calculate grass area
Grass area = ¾ × 5/12 = 15/48 = 5/16 hectare
Step 3: Calculate water needed
Water = 5/16 × 5/2 = 25/32 liters
Verification: Both methods give the same result: 5/16 hectare and 25/32 liters.
If you have 3 liters of water available, is it enough for the grass area? If not, how much more water do you need?
Step 1: Convert 3 liters to fraction
3 liters = 3/1 = 96/32 liters
Step 2: Compare with needed water
Needed: 25/32 liters
Available: 96/32 liters
Since 96/32 > 25/32, you have enough water!
Step 3: Calculate excess water
Excess = 96/32 - 25/32 = 71/32 = 2 7/32 liters
Answer: Yes, 3 liters is enough. You'll have 2 7/32 liters left over.
A rectangular field is 2½ km long and 1⅓ km wide. What is the area of the field? If you need ¾ kg of seeds per square kilometer, how many kg of seeds do you need?
Your solution:
A recipe calls for 1⅔ cups of flour. You want to make 2½ times the recipe. How much flour do you need? If flour costs $2.40 per cup, what's the total cost?
Your solution: