Question

How many natural numbers n satisfy the inequality: 1/7 < n/10 < 4/5 ?

Answer 1

ANSWER

Five natural numbers.

EXPLANATION

The given inequality is

$\frac{1}{7} \: < \: \frac{n}{10} \: < \: \frac{4}{5}$

We multiply each term in the inequality by 10 to obtain,

$\frac{1}{7} \times 10\: < \: \frac{n}{10} \times 10\: < \: \frac{4}{5} \times 10$

This gives us,

$\frac{10}{7} \: < \: n \: < \: \frac{40}{5}$

We simplify further to obtain,


$1\frac{3}{7} \: < \: n \: < \: 8$

The natural numbers that satisfy the inequality are;


$2,3,4,5,7$


Hence 5 natural numbers satisfy the given inequality.