Subtracting Numbers: A Step by Step Guide

Subtracting Numbers: A Step by Step Guide

Subtraction is one of the fundamental operations in mathematics. It involves taking away smaller numbers from larger ones. Let's take a closer look at how it works step by step:

Understanding Place Value

Before you can start subtracting, you need to understand place value. In base ten numerals, each digit represents a certain power of ten. For example, the first digit indicates hundreds, the second tens, and so on. When subtracting, you have to consider these powers of ten when borrowing digits from the left column.

Setting Up the Problem

To set up a problem for subtraction, you first arrange your two numbers vertically with the larger number above the smaller one. Make sure all the digits line up correctly according to their place values.

Placing Digits Next To Each Other

The next step is placing your subtrahend (the number being taken away) directly underneath its corresponding minuend (the number being taken away from). If there isn't enough room beneath the minuend due to lack of space between them, you may draw lines through any empty spaces to separate the figures as needed.

Borrowing From Left Column

If you encounter zeroes in the rightmost position of both numbers, they will cancel out during the process of adding the digits together. However, if there's only a single zero present, this means you must borrow a one from the previous place value column to make it equal to eleven. This process is called 'borrowing', and it helps us solve multi-digit subtraction problems efficiently.

For instance, let's say we want to calculate (9 - 7). We can represent this visually as follows: [\begin{array}{c|ccc} &&&\ & 9 && \ - & 7 &&\end{array}\qquad 9;-;7=2]If we don't have sufficient zeros after the last digit of our numbers, we can imagine zeros hanging off the end. So if we wanted to do (9 - 5), we could rewrite this as (9-005 = 900{-}005), which becomes easier to perform using standard algorithms such as the method described below.

Aligning Right Side Zeros

In some cases, you might want to align right side zeros instead of having them flush against the left vertical edge. While it looks different, the principle remains the same. If you choose this method, remember to carry over and borrow accordingly.

Filling in the Result

Once you complete the steps outlined earlier, you fill in the result under the minuend. After doing so, check that what you wrote matches what you were asked to find.

Remember that while mental math tricks can help speed up calculations like double-digit subtraction, mastering traditional methods provides more reliable results especially when dealing with large numbers.