Calculating aloud

01The operand boundary

The coordinating conjunction nela is mandatory between the two operands:

[operand 1] nela [operand 2] [operation]. [result] kelai.

This is a grammatical boundary, not an optional pause. Without it, adjacent operands can have the same form as one compound numeral: ta shao wi is five, so only ta shao nela wi unambiguously presents three and two as separate operands. nela never occurs inside a numeral. Part 1's hear-it-whole drill pays its rent here: precisely because ta shao wi arrives as one shape, the boundary between shapes must be spoken.

02The four operations, spoken

A plain equality uses the same boundary: ta shao ta nela ta shao ta kelai. means "Four equals four." A result question replaces the result with hina: ta shao nela wi sholei. hina kelai. means "Three plus two; what results?"

03Addition and subtraction: commensurable quantities

Addition and subtraction operate on the same kind of quantity. Classifiers remain optional, but when nouns or classifiers appear, both operands and the result must keep a compatible referent:

Long? Yes, deliberately: counting eggs into the bowl aloud is exactly this long in every language, and Phi declines to offer a shorter written form than the spoken truth. What the rule refuses is a different thing: two people and three bowls are not a sum. Use an ordinary sentence to relate them instead. The same rule applies to subtraction: the removed quantity and the remainder have the starting quantity's kind.

04Multiplication: quantity and factor

In multiplication, the first operand may name what is counted and the second is a bare factor. The product inherits the first operand's referent:

Requiring the same classifier on both operands would be wrong here: the factor two is not two bowls. It tells how many copies of the counted quantity the operation uses.

05Division: total, groups, quotient, remainder

Division is the household's daily arithmetic: portioning among. The first operand names the total being portioned and the second may name recipients or groups. The quotient inherits the total's kind, not the second operand's:

The remainder is a separate fact with a future: in this kitchen, wi lipha powea therilu. is tomorrow's breakfast. Whether the distribution is also sufficient, fair, or agreed to are separate sentences; equal portions state none of them.

06Comparing magnitudes

Two more verbs share the operand boundary: sharoi (exceed) and thenoi (fall short). No result clause follows, because the comparison is the whole claim:

The verbs measure magnitude and stop there: what exceeds is not thereby better, and what falls short is not thereby less. Negation states the inclusive readings: ta shao nela ta shao ma thenoi., three does not fall short of three.

07Current mathematical limits

Phi has internal exact integers from 0 through 242. It currently has no negative or fractional numeral syntax. A subtraction stated entirely in Phi therefore assumes a nonnegative result, and an uneven division uses an integer quotient plus remainder. Preserve negative values, fractions, out-of-range results, formulas, and exact technical calculations as source material outside the Phi passage when their form matters.

08Drill: narrate the calculations

Say each as full Phi sentences with nela, then check against the key in Part 9.

1. 4 + 3 = 7
2. 8 − 2 = 6
3. 3 × 3 = 9
4. 18 ÷ 2 = 9
5. Six bowls and two bowls gather; how many bowls result?
6. Nine guests portion among three tables; how many guests are assigned to each table?
7. Ask whether nine exceeds six.