Estimating Quotients Worksheet for 4th Grade | Lesson Planet - Free Printable

Problem Overview:

The task involves estimating quotients using compatible numbers. Compatible numbers are numbers that are close to the original numbers and can be easily divided mentally. The goal is to estimate the division problems by rounding or choosing numbers that simplify the division process.

Steps to Solve:

1. Understand the Concept of Compatible Numbers:
- Compatible numbers are numbers that are easy to compute mentally.
- For example, instead of dividing 435 by 6, we might use 420 (a multiple of 6) because it is easier to divide.

2. Estimate Each Quotient:
- For each division problem, identify compatible numbers that are close to the original numbers and can be divided easily.
- Perform the division with these compatible numbers to get an estimated quotient.

3. Apply the Method to Each Problem:
- Follow the steps for each given division problem.

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Solution:

#### Problem 1: $ 5.29 \div 6 $
- Original Numbers: 5.29 and 6
- Compatible Numbers: Round 5.29 to 6 (since 6 is a multiple of 6 and close to 5.29).
- Division: $ 6 \div 6 = 1 $
- Estimated Quotient: 1

#### Problem 2: $ 2.53 \div 5 $
- Original Numbers: 2.53 and 5
- Compatible Numbers: Round 2.53 to 2.5 (since 2.5 is easy to divide by 5).
- Division: $ 2.5 \div 5 = 0.5 $
- Estimated Quotient: 0.5

#### Problem 3: $ 4.233 \div 5 $
- Original Numbers: 4.233 and 5
- Compatible Numbers: Round 4.233 to 4 (since 4 is easy to divide by 5).
- Division: $ 4 \div 5 = 0.8 $
- Estimated Quotient: 0.8

#### Problem 4: $ 2.753 \div 5 $
- Original Numbers: 2.753 and 5
- Compatible Numbers: Round 2.753 to 2.5 (since 2.5 is easy to divide by 5).
- Division: $ 2.5 \div 5 = 0.5 $
- Estimated Quotient: 0.5

#### Problem 5: $ 5.23 \div 9 $
- Original Numbers: 5.23 and 9
- Compatible Numbers: Round 5.23 to 5.4 (since 5.4 is a multiple of 9 and close to 5.23).
- Division: $ 5.4 \div 9 = 0.6 $
- Estimated Quotient: 0.6

#### Problem 6: $ 6.711 \div 5 $
- Original Numbers: 6.711 and 5
- Compatible Numbers: Round 6.711 to 7 (since 7 is close to 6.711 and easy to divide by 5).
- Division: $ 7 \div 5 = 1.4 $
- Estimated Quotient: 1.4

#### Problem 7: $ 2.160 \div 4 $
- Original Numbers: 2.160 and 4
- Compatible Numbers: Round 2.160 to 2 (since 2 is easy to divide by 4).
- Division: $ 2 \div 4 = 0.5 $
- Estimated Quotient: 0.5

#### Problem 8: $ 8.75 \div 9 $
- Original Numbers: 8.75 and 9
- Compatible Numbers: Round 8.75 to 9 (since 9 is a multiple of 9 and close to 8.75).
- Division: $ 9 \div 9 = 1 $
- Estimated Quotient: 1

#### Problem 9: $ 9.660 \div 6 $
- Original Numbers: 9.660 and 6
- Compatible Numbers: Round 9.660 to 10 (since 10 is close to 9.660 and easy to divide by 6).
- Division: $ 10 \div 6 \approx 1.67 $
- Estimated Quotient: 1.67

#### Problem 10: $ 9.233 \div 7 $
- Original Numbers: 9.233 and 7
- Compatible Numbers: Round 9.233 to 9 (since 9 is close to 9.233 and easy to divide by 7).
- Division: $ 9 \div 7 \approx 1.29 $
- Estimated Quotient: 1.29

#### Problem 11: $ 16.680 \div 7 $
- Original Numbers: 16.680 and 7
- Compatible Numbers: Round 16.680 to 16 (since 16 is close to 16.680 and easy to divide by 7).
- Division: $ 16 \div 7 \approx 2.29 $
- Estimated Quotient: 2.29

#### Problem 12: $ 12.150 \div 6 $
- Original Numbers: 12.150 and 6
- Compatible Numbers: Round 12.150 to 12 (since 12 is a multiple of 6 and close to 12.150).
- Division: $ 12 \div 6 = 2 $
- Estimated Quotient: 2

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Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & 1 \\
2. & 0.5 \\
3. & 0.8 \\
4. & 0.5 \\
5. & 0.6 \\
6. & 1.4 \\
7. & 0.5 \\
8. & 1 \\
9. & 1.67 \\
10. & 1.29 \\
11. & 2.29 \\
12. & 2 \\
\end{array}
}
\]