function checkFraction(num, denom, ans) 
{  
   if ( num * 1.0 == 0 )
   {    alert("Invalid Numerator");  return false;  }
   if ( denom * 1.0 == 0 )
   {    alert("Invalid Denominator");  return false;  }
   var value = num + "/" + denom;
   var d = (num*1.0)/denom - ans;
   if ( d == 0 )
   {   alert("Fantastic!\n" + value + " is correct!");
       return true;
   }
   else 
   {   alert("Sorry!\n" +  value + " is not correct!\n Please try again.");
       return false;
   }
}

function checkAppNumber(value, ans, delta)
{  var d = eval(value) - ans;
   delta = delta*1;
   if (  d <  delta && d > -delta )
   {        alert("Fantastic!\n Good answer!");
            return true;
   }
   else if (d > 0) 
   {     alert("Try a smaller number.");   return false;   }
   else 
   { alert("Try a bigger number.");   return false;   }
}


function checkNumber(value, ans)
{  var d = eval(value) - ans;
   if (  d < 0.000001 && d > -0.000001 )
   {        alert("Fantastic!\nYou are absolutely correct!");
            return true;
   }
   else if (d > 0) 
   {     alert("Your answer is too big.");   return false;   }
   else 
   { alert("Your answer is too small.");   return false;   }
}

// check if sig^power == number and sig is proper

function checkScientific(sig, power, number)
{  if ( Math.abs(sig) >=0 && Math.abs(sig) < 10 )
   {  if ( power >= 0 ) 
         checkNumber(sig*myPower(10, power), number);
      else
         checkNumber(sig*myPower(0.1, Math.abs(power)), number);
   }
   else 
   {  alert(sig + " is out of range.");   return false;   }
}

function checkRealNumber(value, ans, delta)
{  var d = eval(value) - ans;
   if (  d < delta && d > -delta )
   {        alert("Fantastic!\n excellent estimation!");
            return true;
   }
   else if (d > 0) 
   {     alert("Your answer is too big.");   return false;   }
   else 
   { alert("Your answer is too small.");   return false;   }
}

function checkString(str, ans)
{  if ( str == ans )
   {  alert("Fantastic!\nYou are absolutely correct!");  return true;   }
   else 
   {  alert("Sorry, your answer is incorrect.");  return false;   }
}

function checkString2(str1, str2, ans)
{  if ( str1.toLowerCase() + str2.toLowerCase() == ans.toLowerCase() || str2.toLowerCase() + str1.toLowerCase() == ans.toLowerCase() )
   {  alert("Fantastic!\nYou are absolutely correct!");  return true;   }
   else 
   {  alert("Sorry, your answer is incorrect.");  return false;   }
}