How to Add or Subtract Decimals

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Decimals are numbers that include a whole part and a fractional part separated by a decimal point. The whole part is greater than one, and the fractional part is less than one.

For example, the number 15.74 can be split into two parts:

The whole part: 15
The fractional part: 74

Terminating and Non-Terminating Decimals

Decimals can be categorized into two types:

Terminating Decimals: These are decimals that have an end. For example, 2.50 is a terminating decimal.
Non-Terminating Decimals: These are decimals that do not have an end. For example, 3.333333… is a non-terminating decimal.

The Concept of Preceding Powers of 10

The place value of digits in a decimal number decreases by a factor of 10 as you move from left to right. For example, the expanded form of 16.457 is:

10 + 6 + \(\frac{4}{10}\) + \(\frac{5}{100}\) + \(\frac{7}{1000}\)

Additionally, 16.457 can be represented as \(16 \frac{457}{1000}\) in mixed fraction terms.

How to Add or Subtract Decimals

To add or subtract two decimal numbers, follow these steps:

Line up the numbers by their decimal points.
Add zeros to the numbers if necessary to make them have the same number of digits.
Perform simple column addition or subtraction.

Exercises for Adding and Subtracting Decimals

114.334 – 62.120
```
  114.334
-  62.120
———
```
129.743 – 34.230
```
  129.743
-  34.230
———
```
121.373 + 31.220
```
  121.373
+  31.220
———
```
114.648 + 31.330
```
  114.648
+  31.330
———
```
129.494 + 56.750
```
  129.494
+  56.750
———
```
136.978 + 42.880
```
  136.978
+  42.880
———
```
136.712 – 16.530
```
  136.712
-  16.530
———
```

123.428 + ____ = 139.198
130.666 + ____ = 205.996
123.389 + ____ = 173.919

Answers

114.334 – 62.120 = 52.214
Solution:

First, line up the numbers by their decimal points:
```
  114.334
-  62.120
———
  052.214
```
Start with the thousandths place: \(4 – 0 = 4\), then the hundredths place: \(3 – 2 = 1\), and so on:
```
  114.334
-  62.120
———
  052.214
```
129.743 – 34.230 = 95.513
Solution:

First, line up the numbers by their decimal points:
```
  129.743
-  34.230
———
  095.513
```
Start with the thousandths place: \(3 – 0 = 3\), then the hundredths place: \(4 – 3 = 1\), and so on:
```
  129.743
-  34.230
———
  095.513
```
121.373 + 31.220 = 152.593
Solution:

First, line up the numbers by their decimal points:
```
  121.373
+  31.220
———
  152.593
```
Start with the thousandths place: \(3 + 0 = 3\), then the hundredths place: \(7 + 2 = 9\), and so on:
```
  121.373
+  31.220
———
  152.593
```
114.648 + 31.330 = 145.978
Solution:

First, line up the numbers by their decimal points:
```
  114.648
+  31.330
———
  145.978
```
Start with the thousandths place: \(8 + 0 = 8\), then the hundredths place: \(4 + 3 = 7\), and so on:
```
  114.648
+  31.330
———
  145.978
```
129.494 – 56.750 = 72.744
Solution:

First, line up the numbers by their decimal points:
```
  129.494
-  56.750
———
  072.744
```
Start with the thousandths place: \(4 – 0 = 4\), then the hundredths place: \(9 – 5 = 4\), and so on:
```
  129.494
-  56.750
———
  072.744
```

136.978 + 42.880 = 179.858
Solution:

First, line up the numbers by their decimal points:
```
  136.978
+  42.880
———
  179.858
```
Start with the thousandths place: \(8 + 0 = 8\), then the hundredths place: \(7 + 8 = 15\), and so on:
```
  136.978
+  42.880
———
  179.858
```
136.712 – 16.530 = 120.182
Solution:

First, line up the numbers by their decimal points:
```
  136.712
-  16.530
———
  120.182
```
Start with the thousandths place: \(2 – 0 = 2\), then the hundredths place: \(1 – 3 = 8\) (borrow 1 from the tenths place), and so on:
```
  136.712
-  16.530
———
  120.182
```
123.428 + _____ = 139.198
Solution:

To find the missing number, subtract 123.428 from 139.198:
```
  139.198
- 123.428
———
   15.770
```
So, 123.428 + 15.770 = 139.198
130.666 + _____ = 205.996
Solution:

To find the missing number, subtract 130.666 from 205.996:
```
  205.996
- 130.666
———
   75.330
```
So, 130.666 + 75.330 = 205.996
123.389 + _____ = 173.919
Solution:

To find the missing number, subtract 123.389 from 173.919:
```
  173.919
- 123.389
———
   50.530
```
So, 123.389 + 50.530 = 173.919