## Basic Decimal Problems For Kids

Let’s dive into basic decimal problems for kids with examples and diagrams.

### 1. What is a Decimal?

Decimals are a way to represent parts of a whole number. For example, in the decimal number 3.25, “3” is the whole number part, and “.25” is the decimal part. The decimal part represents a fraction of 1.

### 2. Understanding Place Value

In decimals, each place to the right of the decimal point represents a fraction of 10:

• Tenths (0.1)
• Hundredths (0.01)
• Thousandths (0.001)

Example 1:

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  1.25
+ 2.30
------
3.55
``````

Explanation:

• Align the decimals to make sure each place value is correctly added.
• Add from right to left: 5 (hundredths) + 0 (hundredths) = 5
• 2 (tenths) + 3 (tenths) = 5
• 1 (whole number) + 2 (whole number) = 3
• The result is 3.55

Diagram:

``````  1.25
+ 2.30
------
3.55
``````

### 4. Subtracting Decimals

Now, let’s subtract decimals.

Example 2:

Subtract 3.75 from 5.8.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  5.80
- 3.75
------
2.05
``````

Explanation:

• Align the decimals.
• Subtract from right to left: 0 (hundredths) – 5 (hundredths) = 5 (borrow 1 from the tenths place)
• 7 (tenths) from 8 (tenths) = 1
• 3 (whole number) from 5 (whole number) = 2
• The result is 2.05

Diagram:

``````  5.80
- 3.75
------
2.05``````

Example 3:

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  2.30
+ 1.50
------
3.80
``````

Explanation:

• Add the tenths: 3 + 5 = 8
• Add the hundredths: 0 + 0 = 0
• The result is 3.80

Diagram:

``````  2.30
+ 1.50
------
3.80
``````

### 4. Basic Decimal Subtraction

Now, let’s subtract decimals.

Example 4:

Subtract 4.8 – 2.35

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  4.80
- 2.35
------
2.45
``````

Explanation:

• Subtract the hundredths: 80 – 35 = 45
• Subtract the tenths: 4 – 2 = 2
• The result is 2.45

Diagram:

``````  4.80
- 2.35
------
2.45
``````

### 5. Basic Decimal Multiplication

Let’s multiply decimals.

Example 5:

Multiply 0.6 × 0.4

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
``````  6
× 4
-----
24
``````
1. Count the Decimal Places: Both numbers have 1 decimal place. So, the result should have 2 decimal places.
``````0.24
``````

Explanation:

• Multiply the numbers: 6 × 4 = 24
• Place the decimal point in the result: 0.24

Diagram:

``````  0.6
× 0.4
------
0.24
``````

### 6. Basic Decimal Division

Lastly, dividing decimals.

Example 6:

Divide 6.4 by 0.8

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
``````6.4 ÷ 0.8 = 64 ÷ 8
``````
1. Divide as Whole Numbers:
`````` 64 ÷ 8 = 8
``````
1. Place the Decimal Point: The result is 8.

Explanation:

• Convert to whole numbers for easier division.
• The result is 8.

Diagram:

6.4 ÷ 0.8
= 64 ÷ 8
= 8

Example 7: Add 3.46 and 2.75.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  3.46
+ 2.75
------
6.21
``````

Explanation:

• Align the decimals.
• Add from right to left: 6 + 5 = 11 (write 1, carry 1)
• 4 + 7 + 1 (carry) = 12 (write 2, carry 1)
• 3 + 2 + 1 (carry) = 6
• The result is 6.21

Diagram:

``````  3.46
+ 2.75
------
6.21
``````

Example 8: Subtract 1.87 from 5.4.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  5.40
- 1.87
------
3.53
``````

Explanation:

• Align the decimals.
• Subtract from right to left: 0 – 7 (borrow 1 from the tenths place) = 3
• 3 (from borrowing) – 8 (tenths) = 5
• 5 (whole number) – 1 (whole number) = 4
• The result is 3.53

Diagram:

``````  5.40
- 1.87
------
3.53
``````

Example 9: Multiply 1.2 by 0.5.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: Both numbers have 1 decimal place. So, the result should have 2 decimal places.
``````  1.2
× 0.5
------
0.60
``````

Explanation:

• Multiply the numbers as if they were whole: 12 × 5 = 60
• Place the decimal point in the result: 0.60 (two decimal places)

Diagram:

``````  1.2
× 0.5
------
0.60
``````

Example 10: Divide 4.5 by 0.9.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````4.5 ÷ 0.9 = 45 ÷ 9
45 ÷ 9 = 5
``````
1. Place the Decimal Point: The result is 5.

Explanation:

• Convert 4.5 ÷ 0.9 to 45 ÷ 9 by moving the decimal point one place to the right in both numbers.
• Divide 45 by 9, which equals 5.
• The result is 5.

Diagram:

``````  4.5 ÷ 0.9
= 45 ÷ 9
= 5
``````

Example 11: Add 4.78 and 2.56.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  4.78
+ 2.56
------
7.34
``````

Diagram:

``````  4.78
+ 2.56
------
7.34
``````

Example 12: Add 3.007 and 1.23.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  3.007
+ 1.230
-------
4.237
``````

Diagram:

``````  3.007
+ 1.230
-------
4.237
``````

Example 13: Subtract 2.45 from 5.67.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  5.67
- 2.45
------
3.22
``````

Diagram:

``````  5.67
- 2.45
------
3.22
``````

Example 14: Subtract 0.59 from 3.14.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  3.14
- 0.59
------
2.55
``````

Diagram:

``````  3.14
- 0.59
------
2.55
``````

Example 15: Multiply 1.3 by 2.4.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: Both numbers have 1 decimal place. So, the result should have 2 decimal places.
``````  1.3
× 2.4
------
3.12
``````

Diagram:

``````  1.3
× 2.4
------
3.12
``````

Example 16: Multiply 0.75 by 0.6.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: Both numbers have 1 decimal place. So, the result should have 2 decimal places.
``````  0.75
× 0.60
------
0.45
``````

Diagram:

``````  0.75
× 0.60
------
0.45
``````

Example 17: Divide 4.8 by 0.6.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````4.8 ÷ 0.6 = 48 ÷ 6
48 ÷ 6 = 8
``````

Diagram:

``````  4.8 ÷ 0.6
= 48 ÷ 6
= 8
``````

Example 18: Divide 7.2 by 0.8.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````7.2 ÷ 0.8 = 72 ÷ 8
72 ÷ 8 = 9
``````

Diagram:

``````  7.2 ÷ 0.8
= 72 ÷ 8
= 9``````

Example 19: Add 5.63 and 3.47.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  5.63
+ 3.47
------
9.10
``````

Explanation:

• Align the decimals.
• Add from right to left: 3 + 7 = 10 (write 0, carry 1)
• 6 + 4 + 1 (carry) = 11 (write 1, carry 1)
• 5 + 3 + 1 (carry) = 9
• The result is 9.10

Diagram:

``````  5.63
+ 3.47
------
9.10
``````

Example 20: Add 0.75 and 1.25.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  0.75
+ 1.25
------
2.00
``````

Explanation:

• Align the decimals.
• Add from right to left: 5 + 5 = 10 (write 0, carry 1)
• 7 + 2 + 1 (carry) = 10 (write 0, carry 1)
• 0 + 1 + 1 (carry) = 2
• The result is 2.00

Diagram:

``````  0.75
+ 1.25
------
2.00
``````

Example 21: Subtract 4.52 from 9.8.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  9.80
- 4.52
------
5.28
``````

Explanation:

• Align the decimals.
• Subtract from right to left: 0 – 2 (borrow 1 from the tenths place) = 8
• 7 (from borrowing) – 5 (tenths) = 2
• 9 (whole number) – 4 (whole number) = 5
• The result is 5.28

Diagram:

``````  9.80
- 4.52
------
5.28
``````

Example 22: Subtract 2.89 from 6.05.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  6.05
- 2.89
------
3.16
``````

Explanation:

• Align the decimals.
• Subtract from right to left: 5 – 9 (borrow 1 from the tenths place) = 6
• 0 (from borrowing) – 8 (tenths) = 1 (borrow 1 from the whole number)
• 5 (from borrowing) – 2 (whole number) = 3
• The result is 3.16

Diagram:

``````  6.05
- 2.89
------
3.16
``````

Example 23: Multiply 0.9 by 1.4.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: Both numbers have 1 decimal place. So, the result should have 2 decimal places.
``````  0.9
× 1.4
------
1.26
``````

Explanation:

• Multiply the numbers as if they were whole: 9 × 14 = 126
• Place the decimal point in the result: 1.26 (two decimal places)

Diagram:

``````  0.9
× 1.4
------
1.26
``````

Example 24: Multiply 2.5 by 0.6.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: Both numbers have 1 decimal place. So, the result should have 2 decimal places.
``````  2.5
× 0.6
------
1.50
``````

Explanation:

• Multiply the numbers as if they were whole: 25 × 6 = 150
• Place the decimal point in the result: 1.50 (two decimal places)

Diagram:

``````  2.5
× 0.6
------
1.50
``````

Example 25: Divide 3.6 by 1.2.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````3.6 ÷ 1.2 = 36 ÷ 12
36 ÷ 12 = 3
``````

Explanation:

• Convert 3.6 ÷ 1.2 to 36 ÷ 12 by moving the decimal point one place to the right in both numbers.
• Divide 36 by 12, which equals 3.
• The result is 3.

Diagram:

``````  3.6 ÷ 1.2
= 36 ÷ 12
= 3
``````

Example 26: Divide 5.4 by 0.9.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````5.4 ÷ 0.9 = 54 ÷ 9
54 ÷ 9 = 6
``````

Explanation:

• Convert 5.4 ÷ 0.9 to 54 ÷ 9 by moving the decimal point one place to the right in both numbers.
• Divide 54 by 9, which equals 6.
• The result is 6.

Diagram:

``````  5.4 ÷ 0.9
= 54 ÷ 9
= 6``````

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  6.58
+ 4.73
------
11.31
``````

Diagram:

``````  6.58
+ 4.73
------
11.31
``````

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  0.456
+ 0.789
-------
1.245
``````

Diagram:

``````  0.456
+ 0.789
-------
1.245
``````

Example 28: Subtract 3.14 from 7.92.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  7.92
- 3.14
------
4.78
``````

Diagram:

``````  7.92
- 3.14
------
4.78
``````

Example 29: Subtract 1.234 from 5.678.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  5.678
- 1.234
-------
4.444
``````

Diagram:

``````  5.678
- 1.234
-------
4.444
``````

Example 30: Multiply 2.3 by 3.6.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: Both numbers have 1 decimal place. So, the result should have 2 decimal places.
``````  2.3
× 3.6
------
8.28
``````

Diagram:

``````  2.3
× 3.6
------
8.28
``````

Example 31: Multiply 1.25 by 0.4.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: The first number has 2 decimal places, and the second number has 1 decimal place. So, the result should have 3 decimal places.
``````  1.25
× 0.40
------
0.500
``````

Diagram:

``````  1.25
× 0.40
------
0.500
``````

Example 32: Divide 2.4 by 0.6.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````2.4 ÷ 0.6 = 24 ÷ 6
24 ÷ 6 = 4
``````

Diagram:

``````  2.4 ÷ 0.6
= 24 ÷ 6
= 4
``````

Example 33: Divide 7.2 by 0.3.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````7.2 ÷ 0.3 = 72 ÷ 3
72 ÷ 3 = 24
``````

Diagram:

``````  7.2 ÷ 0.3
= 72 ÷ 3
= 24
``````

Example 34: Add 8.907 and 5.324.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  8.907
+ 5.324
-------
14.231
``````

Diagram:

``````  8.907
+ 5.324
-------
14.231
``````

### Subtracting More Complex Decimals

Example 35: Subtract 3.789 from 8.561.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  8.561
- 3.789
-------
4.772
``````

Diagram:

``````  8.561
- 3.789
-------
4.772
``````

Example 36: Multiply 0.75 by 1.25.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: The first number has 2 decimal places, and the second number has 2 decimal places. So, the result should have 4 decimal places.
``````  0.75
× 1.25
------
0.9375
``````

Diagram:

``````  0.75
× 1.25
------
0.9375
``````

Example 37: Divide 9.36 by 0.12.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````9.36 ÷ 0.12 = 936 ÷ 12
936 ÷ 12 = 78
``````

Diagram:

``````  9.36 ÷ 0.12
= 936 ÷ 12
= 78``````

Example 38: Add 3.987 and 6.054.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  3.987
+ 6.054
-------
10.041
``````

Diagram:

``````  3.987
+ 6.054
-------
10.041
``````

Example 39: Add 1.234 and 2.789.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  1.234
+ 2.789
-------
4.023
``````

Diagram:

``````  1.234
+ 2.789
-------
4.023
``````

Example 40: Subtract 5.76 from 8.95.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  8.95
- 5.76
------
3.19
``````

Diagram:

``````  8.95
- 5.76
------
3.19
``````

Example 41: Subtract 4.678 from 9.123.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  9.123
- 4.678
-------
4.445
``````

Diagram:

``````  9.123
- 4.678
-------
4.445
``````

Example 42: Multiply 0.75 by 1.2.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: The first number has 2 decimal places, and the second number has 1 decimal place. So, the result should have 3 decimal places.
``````  0.75
× 1.2
------
0.900
``````

Diagram:

``````  0.75
× 1.2
------
0.900
``````

Example 43: Multiply 3.5 by 0.7.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: The first number has 1 decimal place, and the second number has 1 decimal place. So, the result should have 2 decimal places.
``````  3.5
× 0.7
------
2.45
``````

Diagram:

``````  3.5
× 0.7
------
2.45
``````

Example 44: Divide 5.4 by 1.2.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````5.4 ÷ 1.2 = 54 ÷ 12
54 ÷ 12 = 4.5
``````

Diagram:

``````  5.4 ÷ 1.2
= 54 ÷ 12
= 4.5
``````

Example 45: Divide 7.56 by 1.8.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````7.56 ÷ 1.8 = 756 ÷ 180
756 ÷ 180 = 4.2
``````

Diagram:

``````  7.56 ÷ 1.8
= 756 ÷ 180
= 4.2
``````

Example 46: Add 7.481 and 3.519.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  7.481
+ 3.519
-------
11.000
``````

Diagram:

``````  7.481
+ 3.519
-------
11.000
``````

Example 47: Subtract 2.345 from 6.789.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  6.789
- 2.345
-------
4.444
``````

Diagram:

``````  6.789
- 2.345
-------
4.444
``````

Example 48: Multiply 1.45 by 0.25.

Steps:

1. Ignore the Decimals: Multiply as if they were whole numbers.
2. Count the Decimal Places: The first number has 2 decimal places, and the second number has 2 decimal places. So, the result should have 4 decimal places.
``````  1.45
× 0.25
------
0.3625
``````

Diagram:

``````  1.45
× 0.25
------
0.3625
``````

Example 49: Divide 8.64 by 0.16.

Steps:

1. Convert to Whole Numbers: Move the decimal point to make the divisor a whole number.
2. Divide as Whole Numbers:
``````8.64 ÷ 0.16 = 864 ÷ 16
864 ÷ 16 = 54
``````

Diagram:

``````  8.64 ÷ 0.16
= 864 ÷ 16
= 54``````

Example 50: Add 12.34 and 7.891.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
``````  12.340
+  7.891
--------
20.231
``````

Explanation:

• Align the decimals.
• Add from right to left: 0 + 1 = 1
• 4 + 9 = 13 (write 3, carry 1)
• 3 + 8 + 1 (carry) = 12 (write 2, carry 1)
• 2 + 7 + 1 (carry) = 10 (write 0, carry 1)
• 1 + 1 (carry) = 2
• The result is 20.231

Diagram:

``````  12.340
+  7.891
--------
20.231
``````

Example 51: Subtract 6.789 from 15.632.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Subtract: Start subtracting from the rightmost digit.
``````  15.632
-  6.789
--------
8.843
``````

Explanation:

• Align the decimals.
• Subtract from right to left: 2 – 9 (borrow 1 from the tenths place) = 3
• 2 (from borrowing) – 8 (tenths) = 4
• 6 (from borrowing) – 7 (hundredths) = 8
• 15 (whole number) – 6 (whole number) = 9
• The result is 8.843

Diagram:

``````  15.632
-  6.789
--------
8.843``````