Find the missing numbers:
`7:9 =square :18=42 :square = square :27`

Answer

To solve the problem step by step, we will find the missing numbers in the ratios given:

1. **First Ratio: 7:9 = square:18**
- Let the missing number be \( x \).
- We can set up the proportion:
\[ \frac{7}{9} = \frac{x}{18} \]
- Cross-multiply to solve for \( x \):
\[ 7 \times 18 = 9 \times x \]
- This simplifies to:
\[ 126 = 9x \]
- Now, divide both sides by 9:
\[ x = \frac{126}{9} = 14 \]

2. **Second Ratio: 7:9 = 42:square**
- Let the missing number be \( y \).
- Set up the proportion:
\[ \frac{7}{9} = \frac{42}{y} \]
- Cross-multiply:
\[ 7y = 9 \times 42 \]
- Calculate \( 9 \times 42 \):
\[ 7y = 378 \]
- Now, divide both sides by 7:
\[ y = \frac{378}{7} = 54 \]

3. **Third Ratio: 7:9 = square:27**
- Let the missing number be \( z \).
- Set up the proportion:
\[ \frac{7}{9} = \frac{z}{27} \]
- Cross-multiply:
\[ 7 \times 27 = 9z \]
- Calculate \( 7 \times 27 \):
\[ 189 = 9z \]
- Now, divide both sides by 9:
\[ z = \frac{189}{9} = 21 \]

**Final Answers:**
- The missing numbers are:
- For the first ratio: 14
- For the second ratio: 54
- For the third ratio: 21

---