To solve the expression \( \frac{7}{9} \div \frac{4}{9} \), we can multiply by the reciprocal of the second fraction:
\[ \frac{7}{9} \div \frac{4}{9} = \frac{7}{9} \times \frac{9}{4} \]
Now, when multiplying, we can simplify:
\[ \frac{7 \times 9}{9 \times 4} = \frac{7}{4} \]
The fraction \( \frac{7}{4} \) is already in simplest form.
Next, we can separate the \( \frac{7}{4} \) into the form \( a \frac{b}{c} \). Here, \( 7 = 4 \times 1 + 3 \), so we can express it as:
\[ \frac{7}{4} = 1 \frac{3}{4} \]
Now looking at the answer options given:
- \( a = 1, b = 4, c = 3 \) (this represents \( \frac{4}{3} \))
- \( a = 1, b = 3, c = 4 \) (this correctly represents \( 1 \frac{3}{4} \))
- \( a = 1, b = 63, c = 36 \) (not in the correct form)
- \( a = 1, b = 36, c = 63 \) (not in the correct form)
Thus, the correct answer is:
a = 1, b = 3, c = 4.
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