Multiply decimals and whole numbers: word problems

key notes :

Understanding Decimals

• Decimals represent fractions or parts of a whole.
• Place values include tenths, hundredths, and thousandths.

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Multiplication Basics

• When multiplying a decimal by a whole number, ignore the decimal at first.
• Multiply as if dealing with whole numbers.
• Count the total decimal places in the original decimal number.
• Place the decimal in the product accordingly.

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Word Problem Strategies

• Identify the given numbers (whole numbers and decimals).
• Determine what operation is required (e.g., finding total cost, total distance, etc.).
• Set up the multiplication equation based on the problem.
• Perform the multiplication correctly.
• Check for reasonableness (Does the answer make sense in context?).

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Common Scenarios in Word Problems

• Money-related problems (e.g., cost of multiple items).
• Distance and speed problems (e.g., total distance traveled).
• Measurement problems (e.g., calculating total weight, volume, or area).

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Examples

• A book costs $4.75. What is the total cost of 6 books?
  • Solution: 4.75×6=28.50 → The total cost is $28.50.
• A runner jogs 2.3 km every day. How far does she jog in 8 days?
  • Solution: 2.3 × 8 = 18.4 → She jogs 18.4 km in total.

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Common Mistakes to Avoid

• Misplacing the decimal in the final answer.
• Forgetting to align numbers correctly in multiplication.
• Ignoring units in word problems (e.g., dollars, meters).

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Checking Your Work

• Use estimation to verify if the answer is reasonable.
• Use a calculator for confirmation if needed.

Learn with an example