Math Lecture: Dividing Decimals by Decimals

Introduction

• This lecture covers how to divide a decimal by a decimal.

Key Concept: Division Setup

• Dividend: Number being divided.
• Divisor: Number by which the dividend is divided.
• Important Question: Is the divisor a whole number?
  • If not, convert it to a whole number by multiplying by a power of 10.
  • Whatever you do to the divisor, you must do to the dividend.

Example 1: 5.76 ÷ 0.3

1. Setup
   • Dividend: 5.76
   • Divisor: 0.3
2. Conversion
   • Multiply divisor by 10 to make it a whole number (0.3 -> 3).
   • Do the same to the dividend (5.76 -> 57.6).
3. Division Process
   • Move decimal straight up in the answer area.
   • Use Divide, Multiply, Subtract, Bring Down, Repeat.
   • Calculate each stage:
     • 5 ÷ 3 = 1, remainder 2.
     • Bring down 7, 27 ÷ 3 = 9.
     • Bring down 6, 6 ÷ 3 = 2.
   • Final Answer: 19.2

Example 2: 86.4 ÷ 0.12

1. Setup
   • Dividend: 86.4
   • Divisor: 0.12
2. Conversion
   • Multiply divisor by 100 to make it a whole number (0.12 -> 12).
   • Do the same to the dividend (86.4 -> 8640).
3. Division Process
   • Division steps:
     • 8 ÷ 12 = 0.
     • 86 ÷ 12 = 7, remainder 2.
     • Bring down 4, 24 ÷ 12 = 2.
     • Bring down 0, 0 ÷ 12 = 0.
   • Final Answer: 720

Summary

• Ensure the divisor is a whole number by multiplying by the appropriate power of 10.
• Apply the same multiplication to the dividend.
• Then, perform the standard division process.

Conclusion

• Practice ensures familiarity with converting divisors to whole numbers and executing the division process.
• Remember to check if the divisor is whole before starting.
• Whatever change is applied to the divisor should be applied to the dividend.

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• I hope this explanation was helpful. Thanks for watching!