To solve the division of the fractions [tex]\(\frac{4}{7} \div 1 \frac{3}{4}\)[/tex], we can follow these steps:
1. Convert the mixed number to an improper fraction:
The mixed number [tex]\(1 \frac{3}{4}\)[/tex] can be converted to an improper fraction.
[tex]\[
1 \frac{3}{4} = \frac{1 \cdot 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
\][/tex]
2. Recall that dividing by a fraction is the same as multiplying by its reciprocal:
So, [tex]\(\frac{4}{7} \div \frac{7}{4}\)[/tex] becomes [tex]\(\frac{4}{7} \times \frac{4}{7}\)[/tex].
3. Multiply the fractions:
To multiply two fractions, multiply their numerators and multiply their denominators:
[tex]\[
\frac{4}{7} \times \frac{4}{7} = \frac{4 \cdot 4}{7 \cdot 7} = \frac{16}{49}
\][/tex]
4. Simplify the fraction if possible:
Here, [tex]\(\frac{16}{49}\)[/tex] is already in its simplest form since 16 and 49 have no common factors other than 1.
Thus, the final simplified answer is [tex]\(\frac{16}{49}\)[/tex].
