Are the following statements true?
99 kg : 45 kg = 44:20

Answer

To determine whether the statements \( 99 \, \text{kg} : 45 \, \text{kg} = 44 : 20 \) are true, we will compare the two ratios by converting them into fractions and simplifying them.

### Step-by-Step Solution:

1. **Write the Ratios as Fractions:**
- The left-hand side (LHS) is \( 99 \, \text{kg} : 45 \, \text{kg} \). We can write this as a fraction:
\[ \frac{99}{45} \]
- The right-hand side (RHS) is \( 44 : 20 \). We can write this as a fraction:
\[ \frac{44}{20} \]

2. **Simplify the LHS:**
- To simplify \( \frac{99}{45} \), we find the greatest common divisor (GCD) of 99 and 45. The GCD is 9.
- Now, divide both the numerator and the denominator by 9:
\[ \frac{99 \div 9}{45 \div 9} = \frac{11}{5} \]

3. **Simplify the RHS:**
- To simplify \( \frac{44}{20} \), we find the GCD of 44 and 20. The GCD is 4.
- Now, divide both the numerator and the denominator by 4:
\[ \frac{44 \div 4}{20 \div 4} = \frac{11}{5} \]

4. **Compare the Simplified Ratios:**
- Now we have:
- LHS: \( \frac{11}{5} \)
- RHS: \( \frac{11}{5} \)
- Since both sides are equal, we conclude that:
\[ 99 \, \text{kg} : 45 \, \text{kg} = 44 : 20 \]

5. **Final Conclusion:**
- Therefore, the statement is true.

### Summary:
The statement \( 99 \, \text{kg} : 45 \, \text{kg} = 44 : 20 \) is true because both ratios simplify to \( \frac{11}{5} \).