How it works
Integer division answers how many whole units fit, while the remainder operator answers what remains after that quotient. C# integer division truncates toward zero. This matters when an intermediate result can be negative: truncation is different from always rounding down. A negative remainder follows the sign of the left operand, so it is unsafe to assume that every remainder is a valid array index.
A useful first model is packaging. If each box holds four items, a shipment of seventeen items fills four complete boxes and leaves one item. Keep both values when reporting capacity; rounding a quotient before calculating the remainder loses information. Choose integer arithmetic when fractional units are not meaningful, and convert before division when a fractional answer is required.
Walk through the example. The example prints the complete boxes and loose items separately. The two negative expressions then expose truncation toward zero: negative seventeen divided by four produces negative four, and the remainder is negative one. The final calculation normalizes a possibly negative offset into the range zero through three by adding the modulus and taking the remainder again.
Watch the boundary. Dividing by zero throws rather than producing a special integer. Also consider the minimum signed integer divided by negative one, whose mathematical result does not fit the same signed type. Validate divisors at a boundary and choose a wider type when the domain needs it. Do not hide invalid input by silently replacing the divisor.
Practice independently. Write a function that describes how many complete trays and leftover pieces a nonnegative order needs. Test zero pieces, exactly one tray, one extra piece, and several trays. Reject a tray capacity of zero. Then implement a circular weekday offset that accepts both positive and negative movement, and predict its result before running each case.
A working example
using System;
using System.Collections.Generic;
using System.Linq;
using System.Globalization;
using System.Text;
using System.Text.Json;
using System.Text.Json.Serialization;
using System.Text.RegularExpressions;
int items = 17, capacity = 4;
Console.WriteLine($"boxes={items / capacity}; loose={items % capacity}");
Console.WriteLine(-17 / 4);
Console.WriteLine(-17 % 4);
int offset = -1;
Console.WriteLine((offset % 4 + 4) % 4);
Expected output
boxes=4; loose=1 -4 -1 3
Keep quotient and remainder together; normalize negative circular offsets explicitly.