Subtraction by Addition — Definition, Formula & Examples

Subtraction by addition is a method for finding the difference between two numbers by figuring out what you need to add to the smaller number to reach the larger one. Instead of subtracting directly, you count up from the smaller number.

Given two numbers $a$ and $b$ where $a > b$ , subtraction by addition determines $a - b$ by finding the value $d$ such that $b + d = a$ . The unknown addend $d$ equals the difference.

Key Formula

a - b = d \quad \Longleftrightarrow \quad b + d = a

Where:

$a$ = The larger number (minuend)
$b$ = The smaller number (subtrahend)
$d$ = The difference (unknown addend)

How It Works

Start with the smaller number and add up until you reach the larger number. Whatever you added is the answer to the subtraction problem. For example, to solve

15 - 9

, ask yourself: "9 plus what equals 15?" Since

9 + 6 = 15

, the answer is 6. This method is especially handy when making change with money or when direct subtraction feels awkward.

Worked Example

Problem: Find 83 − 47 using subtraction by addition.

Step 1: Start at 47 and add up to the nearest ten.

47 + 3 = 50

Step 2: Add from 50 up to 83.

50 + 33 = 83

Step 3: Combine the amounts you added.

3 + 33 = 36

Answer:

83 - 47 = 36

Why It Matters

Cashiers use this method every day when counting change back to a customer. If something costs $3.47 and you pay with a $5 bill, the cashier counts up from $3.47 to $5.00 to find your change of $1.53. It builds strong number sense that supports mental math in everyday life.

Common Mistakes

Mistake: Forgetting to add all the partial jumps together at the end.

Correction: Keep track of each amount you add along the way, then sum them all to get the final difference.