(4/7+2/3):13/3
To solve the expression \((\frac{4}{7} + \frac{2}{3}) : \frac{13}{3}\), we first need to simplify \(\frac{4}{7} + \frac{2}{3}\) and then divide that result by \(\frac{13}{3}\).
Finding a common denominator for \(\frac{4}{7} + \frac{2}{3}\): The least common multiple of 7 and 3 is 21.
\(\frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21}\)
\(\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}\)
Now, we can add the two fractions:
\[ \frac{12}{21} + \frac{14}{21} = \frac{12 + 14}{21} = \frac{26}{21} \]
Now we divide \(\frac{26}{21}\) by \(\frac{13}{3}\): Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{26}{21} \div \frac{13}{3} = \frac{26}{21} \times \frac{3}{13} \]
Performing the multiplication:
\[ = \frac{26 \times 3}{21 \times 13} = \frac{78}{273} \]
Simplifying \(\frac{78}{273}\): We can simplify this fraction by finding the greatest common divisor (GCD). The GCD of 78 and 273 is 3:
\[ \frac{78 \div 3}{273 \div 3} = \frac{26}{91} \]
Thus, the final result is:
\[ \frac{26}{91} \]
