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Let's break down the exercise and solve each question:

### Given problem:
"Calculate **the sum of the quotient of 30,176 by 92** and **the product of 532 by 174**."

#### Question 1: **Donne l'expression qui traduit la phrase écrite entre les guillemets.**
We need to write the mathematical expression for the given phrase.

- Quotient of 30,176 by 92: \( \frac{30,176}{92} \)
- Product of 532 by 174: \( 532 \times 174 \)

The sum of these two expressions can be written as:
\[
\frac{30,176}{92} + (532 \times 174)
\]

#### Question 2: **Donne un ordre de grandeur du résultat.**
We need to estimate the result of this expression.

- Approximate \( \frac{30,176}{92} \): This is roughly \( \frac{30,000}{100} = 300 \).
- Approximate \( 532 \times 174 \): This is roughly \( 500 \times 200 = 100,000 \).

So, the estimated result is:
\[
300 + 100,000 = 100,300
\]

#### Question 3: **Peux-tu calculer cette expression en ligne sans poser d’opération ou es-tu obligé d’utiliser la calculatrice?**
This question asks if we can calculate the expression mentally or if we need a calculator. Given the size of the numbers, performing exact calculations mentally might be challenging, especially for \( 532 \times 174 \). Hence, using a calculator or manual steps would be more efficient.

Now, let’s calculate the exact result.

- \( \frac{30,176}{92} = 328 \)
- \( 532 \times 174 = 92,568 \)

So, the final result is:
\[
328 + 92,568 = 92,896
\]

Would you like further explanation on any step or have any questions?

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Here are 5 related questions to expand on this topic:

1. How can we quickly estimate products and quotients to save time?
2. What are the steps to perform long division manually?
3. How do you know when it's necessary to use a calculator for large numbers?
4. What is the importance of rounding and estimation in real-life calculations?
5. Can you express the result using different numerical representations (e.g., scientific notation)?

**Tip:** Always start with a rough estimate before performing detailed calculations—it helps catch potential mistakes early.

On veut calculer : « la somme du quotient de 30 176 par 92 et du produit de 532 par 174 »

Learn how to solve an arithmetic problem involving division and multiplication. This problem requires calculating the sum of the quotient 30,176 ÷ 92 and the product 532 × 174. Suitable for students in Grades 7-9, this exercise also involves estimating the result.

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