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### Question 47: Simplify the ratio 40 : 160 : 240
We need to find the simplest form of this ratio.

1. Start by finding the greatest common divisor (GCD) of 40, 160, and 240.
   - The GCD of 40, 160, and 240 is **40**.

2. Now divide each part of the ratio by 40:
   - \( \frac{40}{40} = 1 \)
   - \( \frac{160}{40} = 4 \)
   - \( \frac{240}{40} = 6 \)

Thus, the simplest form of the ratio is **1 : 4 : 6**.

**Answer: 1 : 4 : 6**

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### Question 48: What is the size of angle \( x \)?
From the image, we see a diagram involving angles. There's a given angle of **32°**, and it appears that angle \( x \) and this angle are adjacent, forming a straight line.

- The sum of angles on a straight line is **180°**.
- Therefore, we can find \( x \) by subtracting 32° from 180°:

\[
x = 180° - 32° = 148°
\]

**Answer: \( x = 148° \)**

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Would you like a detailed explanation of these solutions or have any further questions?

### Related Questions:
1. How do you find the greatest common divisor of a set of numbers?
2. Can ratios involving three terms always be simplified in the same way as two-term ratios?
3. Why does the sum of angles on a straight line equal 180°?
4. How would you approach simplifying a ratio if one of the terms were negative?
5. How can we calculate unknown angles in a triangle using basic angle properties?

### Tip:
Always check for the GCD (greatest common divisor) when simplifying ratios, as this ensures you reduce them to their simplest form.

Fully simplify the following ratio (40 : 160 : 240). What is the size of angle x?

Learn how to simplify the ratio 40 : 160 : 240 by finding the greatest common divisor (GCD), and discover how to calculate the size of angle x using the supplementary angle theorem. Suitable for students in Grades 6-8.

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