Do the ratios 18:12 and 2:3 form a proportion?



To determine whether the ratios \(18:12\) and \(2:3\) form a proportion, we need to check if they are equivalent. Two ratios form a proportion if their cross products are equal.

### Step-by-Step Solution:

1. **Express the Ratios as Fractions:**

   The ratios \(18:12\) and \(2:3\) can be expressed as fractions:

   \[
   \frac{18}{12} \quad \text{and} \quad \frac{2}{3}
   \]

2. **Simplify the First Ratio:**

   Simplify \(\frac{18}{12}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 6:

   \[
   \frac{18 \div 6}{12 \div 6} = \frac{3}{2}
   \]

3. **Compare the Two Ratios:**

   Now, the two ratios are:

   \[
   \frac{3}{2} \quad \text{and} \quad \frac{2}{3}
   \]

   Clearly, \(\frac{3}{2} \neq \frac{2}{3}\).

4. **Check Cross Multiplication:**

   To confirm, we can cross multiply to see if the products are equal:

   \[
   18 \times 3 = 54, \quad \text{and} \quad 12 \times 2 = 24
   \]

   Since \(54 \neq 24\), the cross products are not equal.

### Conclusion:

The ratios \(18:12\) and \(2:3\) do not form a proportion because they are not equivalent.

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Would you like more details or have any questions?

Here are some related questions:
1. How do you find the GCD of two numbers?
2. What is a proportion in mathematics?
3. How can you determine if two fractions are equivalent?
4. What are some practical applications of ratios and proportions?
5. How do you simplify ratios with larger numbers?

**Tip:** When comparing ratios, always simplify them first to see if they are equivalent.

Do the ratios 18:12 and 2:3 form a proportion?

Explore whether the ratios 18:12 and 2:3 form a proportion with a detailed, step-by-step solution. Learn key mathematical concepts like cross multiplication and simplifying fractions, perfect for students in Grades 6-8.

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