Fraction Addition & Subtraction
Practice fraction addition and subtraction with a free, browser-based math game. Includes step-by-step strategy, common mistakes, and classroom tips.
MathExpanded Form
Every digit in a number carries a weight: thousands, hundreds, tens, units. Writing the weights out is called expanded form. Below: why the parts can be shuffled without changing the answer, and the digit that trips people up.
Choose your difficulty
Pick a level to start playing. You can switch at any time.
How to play
Add the place-value parts, then tap the number they form.
Tip: your progress and best score are saved in this browser only.
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MathWhat you are actually practicing
Every digit in a number carries a weight. In 3,475 the 3 means three thousands, the 4 means four hundreds, the 7 means seven tens and the 5 means five units. Writing those weights out — 3,000 + 400 + 70 + 5 — is called expanded form.
The point is not the notation. It is that place value explains why the digit 3 is worth three thousand and not three, which is the idea the rest of arithmetic is built on.
How the game works
You are shown a number broken into place-value parts, and four candidate numbers. Pick the number the parts form. A wrong pick reveals it immediately.
Easy uses three-digit numbers in order. Medium and hard use four and five digits, with the parts shuffled.
The relationships worth knowing
Descending order is the usual form: 3,000 + 400 + 70 + 5 = 3,475.
Shuffling changes nothing: 70 + 3,000 + 5 + 400 is the same number, because addition is commutative.
Zeros do not appear as parts: 4,050 is 4,000 + 50 — the empty hundreds place contributes nothing.
Strategies that actually raise your score
Count the parts before you add. Three parts means the answer has at least three non-zero digits, which rules out most wrong options immediately.
Read the largest part first. It fixes the number of digits in the answer. If the largest part is 3,000, the answer is a four-digit number starting with 3.
Watch for the missing place. 4,000 + 50 is 4,050, not 4,500. A gap in the parts means a zero in the answer, and this is the single most common error.
Add largest to smallest. Working down from the thousands keeps the running total clear, and the last small part only ever changes the final digit.