Question

Value of the expression

Answer 1

1/4 ÷ 4/10 + 5/7 ÷ 5/7

Note: 5/7 ÷ 5/7 = 1

This brings us to

1/4 ÷ 4/10 + 1

1/4 * 10/4 + 1

10/16 + 1

5/8 + 1

Answer: 13/8

Answer 2

$\bf \cfrac{1}{4}\div \cfrac{4}{10}~~+~~\cfrac{5}{7}\div \cfrac{5}{7}\implies \cfrac{1}{4}\cdot \cfrac{10}{4}~~+~~\cfrac{5}{7}\cdot \cfrac{7}{5}\implies \cfrac{1\cdot 10}{4\cdot 4}+\cfrac{5\cdot 7}{7\cdot 5} \\\\\\ \cfrac{10}{16}+\cfrac{35}{35}\implies \cfrac{10}{16}+1\implies \cfrac{(1\cdot 10)~+~16}{16}\implies \cfrac{26}{16}\implies \cfrac{13}{8}\implies 1\frac{5}{8}$