Addition is the first piece of math most of us ever learn, and the one we use the most for the rest of our lives. This guide covers it properly — from the basics to decimals and negatives — and ends with how the ADDR app reimagines it.
What addition actually is
Addition combines two quantities into a single total, called the sum. The two numbers you add are the addends (or operands). When you write 2 + 2 = 4, the numbers 2 and 2 are the addends, the + is the addition operator, and 4 is the sum. That's the entire vocabulary you need.
Adding small whole numbers
For single-digit numbers, addition is memorization and intuition: 3 + 4 = 7, 6 + 2 = 8. Most people commit these "addition facts" to memory early, which makes larger sums faster because bigger problems break down into these small ones.
Adding larger numbers with place value
For multi-digit numbers, line them up by place value — ones under ones, tens under tens — and add each column from right to left. Consider 47 + 38:
- Add the ones column: 7 + 8 = 15. Write the 5, and carry the 1 to the tens column.
- Add the tens column plus the carry: 4 + 3 + 1 = 8.
- The sum is 85.
"Carrying" simply means a column overflowed past 9, so the extra ten moves to the next column. This same method scales to numbers of any size.
Adding decimals
Decimals work the same way — the key is to align the decimal points. For 3.5 + 2.25, write them so the points line up (you can think of 3.5 as 3.50), then add column by column to get 5.75. Keeping the decimal points aligned is the only rule that matters.
Adding negative numbers
Adding a negative number is the same as subtracting its positive version: 5 + (−3) = 2. If both numbers are negative, add their magnitudes and keep the negative sign: (−4) + (−6) = −10. A number line is the friendliest way to picture this — adding moves you right, adding a negative moves you left.
Three properties worth knowing
- Commutative: order doesn't matter. 2 + 9 equals 9 + 2.
- Associative: grouping doesn't matter. (1 + 2) + 3 equals 1 + (2 + 3).
- Identity: adding zero changes nothing. 7 + 0 = 7.
Making addition an experience
Here's where it gets fun. A plain calculator gives you the answer instantly and forgets it. ADDR takes the opposite view: every addition is escorted through an eight-stage pipeline, scored for confidence, assigned a risk level, and given commentary by NumberGPT. The sum is exactly the same one you'd compute by hand — ADDR just treats it with the ceremony usually reserved for far more complicated things.
The math is honest. The drama is optional. Both are part of the fun.
Quick reference
- Line numbers up by place value.
- Add right to left, carrying when a column exceeds 9.
- Align decimal points before adding decimals.
- Adding a negative is the same as subtracting.