Remainders Everywhere

Converting 23/4 to 5 and 3/4 is really a division with remainder: 23 ÷ 4 = 5 remainder 3. Every mixed number is a division result in disguise — the whole part is the quotient, and the new numerator is the remainder.

The same whole-plus-remainder pattern shows up all over measurement: feet and inches, pounds and ounces, weeks and days. In each case a big count is split into full units plus whatever is left over — exactly what a mixed number does.