Answer and Explanation :
1) Number \(\frac{65}{18}\)
Converting improper fraction into mixed fraction,
Divide 65 by 18
65 ÷ 18 = 3 with a remainder 11.
11 ÷ 4 = 2 with a remainder of 3
So, We write down the 3 and then write down the remainder 11 above the denominator 18.
i.e. \(\frac{65}{18}=3\frac{11}{18}\)
2) Number \(2\frac{5}{7}\)
Converting mixed into improper fraction,
Step 1 - Multiply the whole number part by the denominator
i.e. \(7\times 2=14\)
Step 2 - Add that to the numerator
i.e. \(14+5=19\)
Step 3 - The result is
\(2\frac{5}{7}=\frac{19}{7}\)
3) Perform the operation and write the answer in simplest form.
a) \(\frac{4}{7}\times\frac{3}{11}\)
Multiply,
\(\frac{4}{7}\times\frac{3}{11}=\frac{12}{77}\)
b) \(\frac{6}{10}\div\frac{12}{7}\)
Divide,
\(\frac{6}{10}\div\frac{12}{7}=\frac{6\times 7}{10\times 12}\)
\(\frac{6}{10}\div\frac{12}{7}=\frac{7}{20}\)
c) \(5\frac{1}{7}\times3\frac{1}{9}\)
First convert mixed into improper,
\(\frac{36}{7}\times\frac{28}{9}\)
Multiply,
\(\frac{36}{7}\times\frac{28}{9}=16\)
d) \(6\frac{3}{7}\div 1\frac{13}{14}\)
First convert mixed into improper,
\(\frac{45}{7}\times\frac{27}{14}\)
Divide,
\(\frac{45}{7}\times\frac{27}{14}=\frac{45\times 14}{7\times27}\)
\(\frac{45}{7}\times\frac{27}{14}=\frac{10}{3}\)
