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Let's go through the math homework problems listed in the image step by step.

### **Exercice 1: Compléter (aucune justification n’est attendue)**

#### A) C’est le résultat du calcul de 7 – (–2 – 8) × 3 – 26
Let's solve it:
\[
7 - ( -2 - 8) \times 3 - 26
\]
First, calculate inside the parentheses:
\[
-2 - 8 = -10
\]
Then multiply by 3:
\[
-10 \times 3 = -30
\]
Now perform the full operation:
\[
7 - (-30) - 26 = 7 + 30 - 26 = 11
\]
**Résultat: 11**

#### B) C’est le nombre par lequel il faut multiplier 4 pour trouver 100
We solve:
\[
4x = 100 \implies x = \frac{100}{4} = 25
\]
**Nombre: 25**

#### C) C’est le résultat du produit de –4 par la somme de 12 et –17
First calculate the sum:
\[
12 + (-17) = -5
\]
Then multiply by -4:
\[
-4 \times (-5) = 20
\]
**Résultat: 20**

#### D) C’est le résultat de 4x² + 3 pour x = –5
Substitute \( x = -5 \) into the equation:
\[
4(-5)^2 + 3 = 4 \times 25 + 3 = 100 + 3 = 103
\]
**Résultat: 103**

#### E) C’est le résultat des deux-tiers de 24
\[
\frac{2}{3} \times 24 = 16
\]
**Résultat: 16**

#### F) C’est le numérateur du résultat simplifié de \( \frac{15}{7} \times \frac{3}{2} \)
First, multiply the fractions:
\[
\frac{15 \times 3}{7 \times 2} = \frac{45}{14}
\]
The numerator is **45**.

### **Exercice 2: Calculer en détaillant et donner le résultat sous forme d’une fraction irréductible**

For \( A = \frac{3}{4} + \frac{5}{6} \), find the least common denominator (LCD), then calculate:
\[
\text{LCD of 4 and 6 is 12.}
\]
Convert the fractions:
\[
\frac{3}{4} = \frac{9}{12}, \quad \frac{5}{6} = \frac{10}{12}
\]
Now add them:
\[
\frac{9}{12} + \frac{10}{12} = \frac{19}{12}
\]
This is already an irreducible fraction.

For \( B = \frac{5}{6} - \frac{2}{9} \), use the LCD:
\[
\text{LCD of 6 and 9 is 18.}
\]
Convert the fractions:
\[
\frac{5}{6} = \frac{15}{18}, \quad \frac{2}{9} = \frac{4}{18}
\]
Now subtract:
\[
\frac{15}{18} - \frac{4}{18} = \frac{11}{18}
\]
This is already an irreducible fraction.

---

Would you like further details on any of these steps or have any specific questions? 

Here are some follow-up questions you could explore:
1. What are the steps for finding the least common denominator (LCD)?
2. How do you simplify a complex fraction?
3. How do you solve for unknowns in basic algebraic equations?
4. What are the rules for multiplying and dividing fractions?
5. How does substitution work in algebraic expressions?

**Tip:** Always simplify your fractions as a final step to ensure they are in their lowest terms!

Devoir Maison 3ème Mathématiques - Exercice 1: Compléter les calculs et répondre aux questions. Exercice 2: Calculer et donner le résultat sous forme d’une fraction irréductible.

Step-by-step solutions for Grade 9 math homework covering calculations, fractions, and algebra. Includes detailed explanations for arithmetic operations, solving equations, and simplifying fractions.

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