Find the least fraction between `(6)/(7) and (7)/(9)`

Answer

To find the least fraction between \( \frac{6}{7} \) and \( \frac{7}{9} \), we can use the method of cross-multiplication. Here are the steps:

### Step 1: Set up the fractions
We have two fractions:
- \( \frac{6}{7} \)
- \( \frac{7}{9} \)

### Step 2: Cross-multiply
To compare the two fractions, we will cross-multiply:
- Multiply the numerator of the first fraction by the denominator of the second fraction:
\[ 6 \times 9 = 54 \]
- Multiply the numerator of the second fraction by the denominator of the first fraction:
\[ 7 \times 7 = 49 \]

### Step 3: Compare the results
Now we compare the two products obtained from cross-multiplication:
- \( 54 \) (from \( 6 \times 9 \))
- \( 49 \) (from \( 7 \times 7 \))

Since \( 49 < 54 \), we conclude that:
\[ \frac{7}{9} < \frac{6}{7} \]

### Step 4: Conclusion
Thus, the least fraction between \( \frac{6}{7} \) and \( \frac{7}{9} \) is:
\[ \frac{7}{9} \]

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