Question 537014
Of course, you see at first sight that the number is 2. Let's pretend that we need algebra to solve this problem.
Let that mystery number be x.
{{{(3+x)/(4+x)=5/6}}}
Multiply by 6 and multiply by (4+x) to eliminate denominators. We can do it in any order, and we will end up with
{{{6(3+x)=5(4+x)}}}
Multiply (apply distributive property)
{{{18+6x=20+5x}}}
Subtract 18 from both sides
{{{6x=2+5x}}}
Subtract 5x from both sides
{{{x=2}}}
Verify
{{{(3+x)/(4+x)=(3+2)/(4+6)=5/6}}}