Thanks ambrus for finding the problem with "hint". For some reason I don't understand at the moment, using return in the subroutine causes hint to not wait for a user response. I changed it to print, and it now waits for a user response. Also, I added a chance to try again and the correct answer when the user answer is false the second time.

#!/usr/bin/perl
use strict;
use warnings;
use feature qw(say);

local $\ = "\n";

my %math = (
  'addition' => {
    'result' => 'sum',
    'operator' => '+',
    'function' => sub {my ($i,$j) = @_; return $i + $j},
  },
  'subtraction' => {
    'result' => 'difference',
    'operator' => '-',
    'function' => sub {my ($i,$j) = @_; return $i - $j},
  },
  'multiplication' => {
    'result' => 'product',
    'operator' => '*',
    'function' => sub {my ($i,$j) = @_; return $i * $j},
  },
  'division' => {
    'result' => 'quotient',
    'operator' => '/',
    'function' => sub {my ($i,$j) = @_; return $i / $j},
  },
);

my $operation = (keys %math)[rand keys %math];

sub random_number {
  return 1 + int(rand(7));
}
my $random_number_1 = random_number();
my $random_number_2 = random_number();

sub math_answer {
  my ($answer,$loop) = @_;
  my $result = int($math{$operation}{'function'}->($random_number_1,$r
+andom_number_2));
  my $equation = qq($random_number_1 $math{$operation}{'operator'} $ra
+ndom_number_2);
  if ($answer eq "hint") {
    print $equation;
    my $user_answer = <>;
    math_answer($user_answer,1);
  }
  elsif ($answer == $result) {
    print "True";
  }
  else {
    if ($loop == 1) {
      print "False, why don't you try again? The equation is $equation
+.";
      my $user_answer = <>;
      math_answer($user_answer,++$loop);
    }
    else {
      print "False, the answer is $result.";
    }
  }
}

print qq(What is the $math{$operation}{'result'} of $random_number_1 a
+nd $random_number_2 to the nearest integer? (type "hint" to show the 
+equation));
my $user_answer = <>;
chomp $user_answer;

math_answer($user_answer,1);
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