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Both these methods break up the subtraction as a process of one digit subtractions by place value. Starting with a least significant digit, a subtraction of the subtrahend: s j s j−1... s 1. from the minuend m k m k−1... m 1, where each s i and m i is a digit, proceeds by writing down m 1 − s 1, m 2 − s 2, and so forth, as long as s i ...
A subtraction problem such as is solved by borrowing a 10 from the tens place to add to the ones place in order to facilitate the subtraction. Subtracting 9 from 6 involves borrowing a 10 from the tens place, making the problem into +. This is indicated by crossing out the 8, writing a 7 above it, and writing a 1 above the 6.
For instance, if the number π is rounded to 4 decimal places, the result is 3.142 because the following digit is a 5, so 3.142 is closer to π than 3.141. [107] These methods allow computers to efficiently perform approximate calculations on real numbers. [108]
The nines' complement of a decimal digit is the number that must be added to it to produce 9; the nines' complement of 3 is 6, the nines' complement of 7 is 2, and so on, see table. To form the nines' complement of a larger number, each digit is replaced by its nines' complement. Consider the following subtraction problem:
Each row contains exactly one of each digit; Each column contains exactly one of each digit; Each bold-outlined group of cells is a cage containing digits which achieve the specified result using the specified mathematical operation: addition (+), subtraction (−), multiplication (×), and division (÷).
Mental subtraction 2: 12 "Nine Nits is all there's Room For" Addition and subtraction less than 10,000 3: 13 "Breaking up is Easy to Do" Multiplication 4: 14 "You Ain't Nothing but a Houndred" Multiplication of 3-digit numbers by single digits 5: 15 "Dividing we Stand" Dividing 3-digit numbers by 2-digit numbers 6: 16 "Double Digit Dating"