Math Problem Statement

Division of whole number by Decimal

Solution

To divide a whole number by a decimal, follow these steps:

Example: Divide 45÷0.545 \div 0.5

  1. Convert the decimal into a whole number: Multiply both the divisor (0.50.5) and the dividend (4545) by the same power of 10 to eliminate the decimal. 0.5×10=5and45×10=4500.5 \times 10 = 5 \quad \text{and} \quad 45 \times 10 = 450 Now the problem becomes: 450÷5450 \div 5

  2. Perform the division: Divide the new dividend by the new divisor. 450÷5=90450 \div 5 = 90

  3. Conclusion: 45÷0.5=9045 \div 0.5 = 90

General Steps:

  1. Multiply both the dividend and divisor by 10 (or higher power) to eliminate the decimal in the divisor.
  2. Perform regular division with the new whole numbers.
  3. Simplify the result, if necessary.

Would you like a detailed example with another set of numbers or a step-by-step practice problem? Let me know!


5 Questions to Expand:

  1. How do you handle division when both numbers are decimals?
  2. What happens if the divisor is a very small decimal (e.g., 0.010.01)?
  3. How can this method be applied to real-world problems involving measurements?
  4. Can you demonstrate this with a visual representation or a number line?
  5. How do you ensure accuracy when dividing large numbers by decimals?

Tip:

Always double-check by multiplying your answer by the divisor to confirm it matches the original dividend.

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Math Problem Analysis

Mathematical Concepts

Division
Decimal Arithmetic
Multiplication

Formulas

To divide a whole number by a decimal: Multiply both the divisor and the dividend by the same power of 10 to eliminate the decimal, then perform standard division.

Theorems

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Suitable Grade Level

Grades 6-8