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How Do You Estimate Division with Compatible Numbers?

Published in Estimation Techniques 2 mins read

To estimate division using compatible numbers, you replace the original numbers with numbers that are easy to divide mentally and are close to the original values.

Understanding Compatible Numbers

Compatible numbers are numbers that divide evenly, making mental calculations easier. The goal is to find compatible numbers that are close to the original dividend and divisor so that the estimated quotient is close to the actual quotient.

Steps to Estimate Division with Compatible Numbers

Here's a step-by-step guide:

  1. Identify the Dividend and Divisor: Determine the number being divided (dividend) and the number dividing it (divisor).
  2. Find Compatible Numbers: Change the dividend and/or the divisor to numbers that are easy to divide mentally. These new numbers should be close to the original numbers. Consider rounding one or both numbers to create compatible numbers.
  3. Perform the Division: Divide the compatible dividend by the compatible divisor.
  4. Estimate the Quotient: The result of the division is your estimated quotient.

Examples

Let's look at a few examples:

Example 1: Estimate 142 ÷ 7.

  • Original problem: 142 ÷ 7
  • Compatible numbers: 140 ÷ 7 (140 is close to 142 and is easily divisible by 7)
  • Estimated quotient: 140 ÷ 7 = 20

Example 2: Estimate 253 ÷ 48.

  • Original problem: 253 ÷ 48
  • Compatible numbers: 250 ÷ 50 (250 is close to 253 and 50 is close to 48. They are also easy to divide)
  • Estimated quotient: 250 ÷ 50 = 5

Example 3: Estimate 8,321 ÷ 42

  • Original problem: 8,321 ÷ 42
  • Compatible numbers: 8,000 ÷ 40 (8,000 is close to 8,321 and 40 is close to 42)
  • Estimated quotient: 8,000 ÷ 40 = 200

Key Considerations

  • Closeness: The compatible numbers should be as close as possible to the original numbers to ensure a reasonably accurate estimate.
  • Ease of Calculation: The compatible numbers should be easy to divide mentally.
  • Flexibility: You might need to adjust both the dividend and the divisor to find suitable compatible numbers.

Estimating with compatible numbers is a useful strategy for quickly approximating the answer to a division problem. It helps to develop number sense and mental math skills.

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