Question

Which number is between 1/7 and 0.2

Answer 1

0.2 is 1/5 so the number between 1/7 and 1/5 so the ANSWER is 1/6

Answer 2

let's convert the 0.2 to a fraction, and then let's put them both fractions using the same denominator.

we can convert any decimal by simply "using a denominator with as many zeros as there are decimals", so 0.2 has 1 decimal, so we use one zero, let's proceed,

$\bf 0.\underline{2}\implies \cfrac{02}{1\underline{0}}\implies \stackrel{simplified}{\cfrac{1}{5}}$

now, to put those two fractions with the same denominator, we simply "multiply each other by the other's denominator", let's see how that goes,

$\bf \stackrel{\textit{we multiply top and bottom by 5}}{\cfrac{1}{7}\implies \cfrac{1\cdot 5}{7\cdot 5}\implies \cfrac{5}{35}}\qquad \qquad \qquad \stackrel{\textit{we multiply top and bottom by 7}}{\cfrac{1}{5}\implies \cfrac{1\cdot 7}{5\cdot 7}\implies \cfrac{7}{35}} \\\\\\ ~~~~~~~~~~\boxed{\cfrac{5}{35}}\text{\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash}\cfrac{6}{35}\text{\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash}\boxed{\cfrac{7}{35}}$