A fractional share is a part of a share held in less than one unit — 0.25 of a share, for example — which some brokers let you buy and which some reinvestment plans create. It is worth its fraction of the price, earns its fraction of the dividend and carries its fraction of the cost: it is a share, only smaller.
Where fractions come from
From two places. Buying by amount: at a broker that offers it, you buy $100 worth rather than 3 shares, and the remainder becomes a fraction. Reinvestment: when a dividend is reinvested in securities, the amount almost never lands on a whole number of shares, and some plans keep the fraction rather than the cash. Mutual fund units, for their part, have always been bought in fractions — ETFs and mutual funds mentions it in passing.
What a fraction does, and does not do
It behaves like a share, pro rata: 0.25 of a security at $40 is worth $10, receives a quarter of the dividend per share and counts for a quarter in the quantity. The average cost and the adjusted cost base are computed the same way, the quantity simply having decimals.
What it does not do: it does not travel. The fraction exists in the books of the broker that created it; when an account is transferred to another broker, fractions are generally sold before the transfer, and the proceeds move as cash. Outside a registered account, that sale realizes a gain or a loss, like any sale.
A neutral worked example
A $100 purchase of a fictional security at $40: 2.5 shares. The security pays $1 per share: $2.50 received. A year later, a purchase of 0.5 of a share at $44, that is $22, brings the quantity to 3 shares for $122: an average cost of $40.67. Nothing different from a whole lot, except the decimals.
What this changes for your tracking
Everyfolio accepts decimal quantities: a fraction is entered like any purchase, with its exact quantity and its price, and the average cost follows. A reinvested dividend is two operations for the app: the dividend received, then the purchase of the fraction, with its price and its date — each reinvestment is a purchase. At transfer time, the broker's sale of the fractions is a sale like any other: it is entered on its date, and its gain or loss is realized.
Informative, general content — not personalized advice. For your situation: your institution or an advisor.
Challenge: check my understanding
Four questions wait behind an account: they check what you understood, and the state stays from one visit to the next.