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### Question 17:
**Work out**  
\[ 2 \frac{1}{2} \times \frac{3}{4} \]  
*You must show all your working and give your answer as a mixed number in its simplest form.*

#### Solution:
1. Convert the mixed number \( 2 \frac{1}{2} \) to an improper fraction:
   \[
   2 \frac{1}{2} = \frac{5}{2}
   \]

2. Multiply the two fractions:
   \[
   \frac{5}{2} \times \frac{3}{4} = \frac{5 \times 3}{2 \times 4} = \frac{15}{8}
   \]

3. Convert \( \frac{15}{8} \) to a mixed number:
   \[
   15 \div 8 = 1 \text{ remainder } 7
   \]
   So, \( \frac{15}{8} = 1 \frac{7}{8} \).

**Answer**:  
\( 1 \frac{7}{8} \).

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### Question 18:
The diagram shows an **isosceles triangle**.  
- One base angle is \( 36^\circ \).
- The other two angles are marked as \( x \).

**Find the value of \( x \).**

#### Solution:
In an isosceles triangle, two angles are equal. The sum of the interior angles of a triangle is always \( 180^\circ \).

Let the two equal angles be \( x \).  
We have one known angle of \( 36^\circ \).  
Thus, the equation becomes:
\[
36 + x + x = 180
\]
Simplifying:
\[
36 + 2x = 180
\]
\[
2x = 180 - 36
\]
\[
2x = 144
\]
\[
x = \frac{144}{2} = 72
\]

**Answer**:  
\( x = 72^\circ \).

---

### Question 19:
**Expand and simplify**:  
\[ (y - 6)(y + 5) \]

#### Solution:
Apply the distributive property (FOIL method):
\[
(y - 6)(y + 5) = y \times y + y \times 5 - 6 \times y - 6 \times 5
\]
This simplifies to:
\[
y^2 + 5y - 6y - 30
\]
Now combine like terms:
\[
y^2 - y - 30
\]

**Answer**:  
\( y^2 - y - 30 \).

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Would you like further details on any of these problems?

### Related Questions:
1. How do you convert between mixed numbers and improper fractions?
2. What are the properties of isosceles triangles, and how do they affect angle calculations?
3. What is the general process for expanding binomials?
4. Can you explain the importance of simplifying fractions in mathematical expressions?
5. How do you solve equations involving angles in different types of triangles?

### Tip:
Always check if an answer can be simplified further or written in a more concise form. For instance, improper fractions should often be expressed as mixed numbers when possible.

Work out 2 1/2 x 3/4, Find the value of x in the isosceles triangle with a base angle of 36°, Expand and simplify (y - 6)(y + 5).

Solve problems involving multiplying fractions, calculating angles in an isosceles triangle, and expanding and simplifying algebraic expressions. Step-by-step explanations suitable for Grades 6-8.

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