Check whether the following numbers are in proportion or not :
20, 18, 5, 6

Answer

To determine whether the numbers 20, 18, 5, and 6 are in proportion, we need to check if the ratio of the first pair (20 and 18) is equal to the ratio of the second pair (5 and 6).

### Step-by-Step Solution:

1. **Identify the pairs**:
We have two pairs of numbers:
- A = 20, B = 18
- C = 5, D = 6

2. **Set up the ratios**:
We need to find the ratios A/B and C/D.
- A/B = 20/18
- C/D = 5/6

3. **Simplify the first ratio**:
- A/B = 20/18 can be simplified.
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
\[ \frac{20 \div 2}{18 \div 2} = \frac{10}{9} \]
- So, A/B = 10/9.

4. **Simplify the second ratio**:
- C/D = 5/6 is already in its simplest form.

5. **Compare the two ratios**:
- Now we compare the two simplified ratios:
- A/B = 10/9
- C/D = 5/6

6. **Cross-multiply to check for equality**:
- To check if the two ratios are equal, we can cross-multiply:
\[ 10 \times 6 \quad \text{and} \quad 9 \times 5 \]
- Calculate:
- 10 × 6 = 60
- 9 × 5 = 45

7. **Conclusion**:
- Since 60 is not equal to 45, the ratios are not equal.
- Therefore, the numbers 20, 18, 5, and 6 are **not in proportion**.