Question
1. Write the ratios in simplest form: 1.1. \( 12: 18 \)
Ask by Guerrero Lynch. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplest form of the ratio \( 12 : 18 \) is \( 2 : 3 \).
Solution
To simplify the ratio \( 12 : 18 \), follow these steps:
1. **Find the Greatest Common Divisor (GCD):**
- The GCD of 12 and 18 is the largest number that divides both without leaving a remainder.
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18
- The common factors are 1, 2, 3, and 6.
- **GCD = 6**
2. **Divide Both Terms by the GCD:**
\[
\frac{12}{6} : \frac{18}{6} = 2 : 3
\]
3. **Simplified Ratio:**
\[
2 : 3
\]
**Answer:** The simplest form of the ratio \( 12 : 18 \) is \( 2 : 3 \).
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Simplify this solution Extra Insights
To simplify the ratio \(12:18\), we can divide both numbers by their greatest common divisor (GCD), which is 6. So, \(12 \div 6 = 2\) and \(18 \div 6 = 3\). Thus, the simplified form of the ratio is \(2:3\). For any ratio, remember that you can always simplify by finding the GCD of the numbers involved. Just like reducing fractions, this technique helps make ratios easier to understand and compare!
