Answer :

Certainly! Let's go through the steps to estimate the values, broken down clearly:

### Part a: Estimate the value of [tex]\(50.25 \times 0.49\)[/tex]

1. Approximate the numbers:
- 50.25 is close to 50.
- 0.49 is close to 0.5.

2. Multiply the approximations:
- [tex]\(50 \times 0.5\)[/tex]

3. Perform the multiplication:
- [tex]\(50 \times 0.5 = 25.0\)[/tex]

So, the estimated value of [tex]\(50.25 \times 0.49\)[/tex] is 25.0.

### Part b: Estimate the value of [tex]\(197 \div 0.399\)[/tex]

1. Approximate the numbers:
- 197 is close to 200.
- 0.399 is close to 0.4.

2. Divide the approximations:
- [tex]\(200 \div 0.4\)[/tex]

3. Perform the division:
- [tex]\(200 \div 0.4 = 500.0\)[/tex]

So, the estimated value of [tex]\(197 \div 0.399\)[/tex] is 500.0.

### Summary
- The estimated value of [tex]\(50.25 \times 0.49\)[/tex] is 25.0.
- The estimated value of [tex]\(197 \div 0.399\)[/tex] is 500.0.

That concludes our step-by-step estimation for both parts of the question!

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Rewritten by : Barada