Addition and Subtraction of Decimals

Decimals are a way of representing numbers that are not whole. They are used for measurement, money, and many other things in daily life. Understanding how to add and subtract decimals is an essential skill that helps deal with real-world problems.

Understanding decimals

Decimal numbers have two parts: a whole number part and a fractional part. The decimal point separates these two parts. For example, in the number 3.45, "3" is the whole number part, and ".45" is the fractional part.

To understand decimals better, let's look at the structure of a decimal number:

Whole Number Part . Fractional Part 3 . 45

Place value in decimal

Each digit in a decimal number has a place value. In the decimal number system, place values are based on powers of ten. Consider the decimal number 4.567:

4.567 | | | | | +-- 7 is in the thousandths place | +---- 6 is in the hundredths place +------ 5 is in the tenths place

Here, 4 is in the units place. Moving right from the decimal, 5 is in the tenths place, 6 is in the hundredths place, and 7 is in the thousandths place.

Steps to add decimals

You can follow these simple steps to add decimals:

1. Line up the decimal points: Start by writing the numbers one below the other, making sure the decimal points line up.
2. Fill in the blanks with zeros: To make adding numbers easier, you can add zeros to the end of a number if it has fewer digits after the decimal point.
3. Add the numbers the same way you add whole numbers: start with the rightmost digit and move to the left, just like when adding whole numbers.
4. Place a decimal point in the answer: Make sure the decimal point in the sum is directly below the other decimal points.

Let's look at an example:

12.78 + 5.64 -------

1. Align decimal points:

12.78 + 5.64

2. In this example there is no missing digit after the decimal point.
3. Add as whole numbers:

12.78 + 5.64 ------- 18.42

Visual examples for addition

Suppose you add 3.25 and 1.5. We will approach this problem as follows:

3.25 +1.50 (add a zero for alignment) --------

Our visual example looks like this:

Steps to subtract decimals

Subtracting decimals is just like adding them. Here are the steps you should follow:

1. Line up the decimal points: Write the numbers so that the decimal points line up.
2. Fill in any blank spaces with zeros: This helps make the subtraction easier, since there aren't any blank spaces after the decimal point.
3. Subtract numbers the same way you subtract whole numbers: As with subtracting whole numbers, start with the rightmost digit and move left.
4. Place the decimal point in the answer: Make sure the decimal point in the difference is directly below the aligned decimal points.

Let's work through an example:

8.53 - 2.47 -------

1. Align decimal points:

8.53 - 2.47

2. There is no need to add any points.
3. Subtract as whole numbers:

8.53 - 2.47 ------- 6.06

Visual examples for subtraction

Consider subtracting 4.9 from 6.75. Visualize it like this:

6.75 - 4.90 (add zero for alignment) --------

Our styled visualization might look something like this:

Dealing with "borrowing" in subtraction

As with subtracting whole numbers, sometimes you may need to “borrow” from higher place values if your top digit is smaller than your bottom digit.

Here is how you can understand borrowing step-by-step:

3.41 - 1.73

Since 1 is smaller than 3 in the tenths place, borrow 1 from the units place:

3.311 - 1.73 --------- 1.68

After borrowing, 4 becomes 3 and you add 10 (as hundredths) to the 1, which makes it 11 in the hundredths place.

Practical example

Here are some practical examples of when you might use decimal addition and subtraction:

Example 1: Adding money

You go shopping and spend $12.95 at one store and $15.30 at another. How much did you spend in total?

12.95 + 15.30 ------- 28.25

You spent a total of $28.25.

Example 2: Subtracting measurements

You cut a piece of rope 6.7 m long from a rope 9.5 m long. How much rope is left now?

9.5 - 6.7 ----- 2.8

You have 2.8 meters of rope left.

Conclusion

Adding and subtracting decimals is a straightforward process once you understand the concepts of decimal place value and borrowing. Aligning the decimal points is important in ensuring that numbers are added or subtracted correctly. The next time you handle money, measurements, or any decimal-based calculations, you'll have a clear way to solve the problem!

Comments