Pancakes for six

A recipe for four people, scaled for six and for five. A third of a cup of sugar shows how Raku keeps fractions exact.

The recipe is for four people. Six are coming, or maybe only five. The program works out how much of everything you need.

Before you run it

The recipe needs a third of a cup of sugar. How will the program print the amount of sugar for five people? And what does the very last line print?

The text

# Pancakes for four people. Six are coming, or maybe five.
my %pancakes =
    flour => 250,    # grams
    milk  => 500,    # millilitres
    eggs  => 3,
    sugar => 1/3;    # cups

sub scale($amount, :$from = 4, :$to = 4) {
    return $amount * $to / $from;
}

for %pancakes.keys.sort -> $item {
    my $six  = scale(%pancakes{$item}, to => 6);
    my $five = scale(%pancakes{$item}, to => 5);
    say "$item: $six for six, $five for five";
}

my $sugar = scale(%pancakes<sugar>, to => 5);
say "Sugar for five: {$sugar.nude.join('/')} cup";

my $back = scale($sugar, from => 5);
say "Back to four: {$back.nude.join('/')} cup";
say $back == %pancakes<sugar>;

eggs: 4.5 for six, 3.75 for five
flour: 375 for six, 312.5 for five
milk: 750 for six, 625 for five
sugar: 0.5 for six, 0.416667 for five
Sugar for five: 5/12 cup
Back to four: 1/3 cup
True

Words

• 1/3 — a fraction. Raku keeps it as one third, a Rat, not as 0.3333… with a limited number of digits.
• :$from = 4 — a named parameter with a default value. If the caller does not say from => …, $from is 4.
• to => 6 — passes a named argument. Named arguments can come in any order, and you can leave out the ones that have defaults.
• %pancakes<sugar> — the value for the key sugar. < > is a short way to write %pancakes{'sugar'} when the key is a plain word.
• .nude — gives the numerator and the denominator of a fraction, as a list of two numbers: (5 12) for 5/12.

Reading notes

my %pancakes =
    flour => 250,    # grams
    milk  => 500,    # millilitres
    eggs  => 3,
    sugar => 1/3;    # cups

The recipe is a hash. The comments give the units, so the numbers stay plain numbers that the program can calculate with.

sub scale($amount, :$from = 4, :$to = 4) {
    return $amount * $to / $from;
}

scale has one positional parameter, the amount, and two named ones. Both named parameters are 4 by default, because the recipe is for four. A call only has to say what is different: to => 6 for six people, from => 5 to go back from five.

for %pancakes.keys.sort -> $item {
    my $six  = scale(%pancakes{$item}, to => 6);
    my $five = scale(%pancakes{$item}, to => 5);
    say "$item: $six for six, $five for five";
}

When you divide whole numbers with / in Raku, the result is a fraction, not a rounded number. 250 * 6 / 4 is exactly 375, and 3 * 6 / 4 is exactly 4.5. Raku prints whole results without a decimal point.

The sugar for five is 1/3 × 5/4 = 5/12. When Raku prints a fraction like this as a decimal number, it rounds it to six digits after the point, so you see 0.416667. That is only how it is printed. The value in $five is still exactly five twelfths.

my $sugar = scale(%pancakes<sugar>, to => 5);
say "Sugar for five: {$sugar.nude.join('/')} cup";

Cooks measure in fractions of a cup, so the program prints the fraction: .nude gives (5 12), and .join('/') makes 5/12 of it.

my $back = scale($sugar, from => 5);
say "Back to four: {$back.nude.join('/')} cup";
say $back == %pancakes<sugar>;

Scaling 5/12 from five people back to four gives 1/3 again. Nothing was lost on the way, so the comparison with the original amount is True.

Questions

1. Why are the items printed in the order eggs, flour, milk, sugar?
2. What does scale(500, to => 2) return?
3. What does scale(3, from => 2, to => 3) return, and what does it mean in the kitchen?

Try this

Print the sugar for six as a fraction too. What does .nude give for a whole number, like the flour for six?