Decimal multiplication and division are valuable tools for solving a variety of real-world problems. Here are some contexts in which they can be applied, along with examples:
1. Financial Calculations
Multiplication:
- If you want to calculate the cost of multiple items, you can use decimal multiplication. For example, if an item costs $15.75 and you want to buy 4 of them, the calculation would be: \[ 15.75 \times 4 = 63.00 \] This tells you that 4 items will cost $63.00 total.
Division:
- To find out how much each person should contribute if you share a bill, divide the total bill by the number of people. For instance, if a dinner bill is $120.50 and you're splitting it among 5 people: \[ 120.50 \div 5 = 24.10 \] Each person pays $24.10.
2. Measurement in Cooking
Multiplication:
- When scaling a recipe, you can use decimal multiplication. If a recipe that serves 4 requires 2.5 cups of flour and you want to double it for 8 servings: \[ 2.5 \times 2 = 5.0 \] You would need 5 cups of flour.
Division:
- If you want to find out how many servings you can get from a certain amount of ingredients, use division. If a recipe calls for 1.25 cups of sugar for 5 servings and you have 5 cups of sugar: \[ 5 \div 1.25 = 4 \] You can make 4 batches of the recipe.
3. Shopping Discounts
Multiplication:
- To find out how much you'll save with a percentage discount, you can multiply. If a $200 jacket is on sale for 30% off: \[ 200 \times 0.30 = 60 \] You save $60, bringing the jacket's price down to $140.
Division:
- If you want to know the original price of an item after discount, you can re-arrange the discount formula. If you paid $70 after a 15% discount: \[ 70 = X \times (1 - 0.15) \] Therefore, solving for X gives: \[ X = 70 \div 0.85 \approx 82.35 \] The original price was approximately $82.35.
4. Travel and Time Calculations
Multiplication:
- To estimate travel costs, you might multiply the distance by the cost per mile. If you plan to drive 150 miles and it costs $0.12 per mile: \[ 150 \times 0.12 = 18.00 \] Your travel cost will be $18.00.
Division:
- To find out how long a journey will take, divide the total distance by the speed. If you're traveling 300 miles at a speed of 60 miles per hour: \[ 300 \div 60 = 5 \] The trip will take 5 hours.
5. Area and Volume Calculations
Multiplication:
- In construction or home projects, calculating area requires multiplying length by width. For a rectangular garden that is 10.5 feet long and 6.25 feet wide: \[ 10.5 \times 6.25 = 65.625 \] The area is 65.625 square feet.
Division:
- When measuring materials, division can help calculate how many units fit in a certain space. If you have 12.5 cubic feet of soil and need to fill pots that each require 2.5 cubic feet: \[ 12.5 \div 2.5 = 5 \] You can fill 5 pots.
In summary, using decimal multiplication and division allows for precise calculations that are essential in everyday life, from budgeting and recipe adjustments to travel planning and measuring spaces.
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