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)

3. Basic Decimal Addition

Let’s start with adding decimals.

Example 1:

Add 1.25 and 2.3.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Add: Start adding from the rightmost digit.

  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:

Add 2.3 + 1.5

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Add: Start adding from the rightmost digit.

  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

2. 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

2. Divide as Whole Numbers:

 64 ÷ 8 = 8

3. 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.
2. Add: Start adding from the rightmost digit.

  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

3. 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.
2. Add: Start adding from the rightmost digit.

  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.
2. Add: Start adding from the rightmost digit.

  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.
2. Add: Start adding from the rightmost digit.

  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.
2. Add: Start adding from the rightmost digit.

  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

Add 6.58 and 4.73.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Add: Start adding from the rightmost digit.

  6.58
+ 4.73
------
 11.31

Diagram:

  6.58
+ 4.73
------
 11.31

Example27: Add 0.456 and 0.789.

Steps:

1. Align the Decimals: Write the numbers so that the decimal points are aligned.
2. Add: Start adding from the rightmost digit.

  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.
2. Add: Start adding from the rightmost digit.

  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.
2. Add: Start adding from the rightmost digit.

  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.
2. Add: Start adding from the rightmost digit.

  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.
2. Add: Start adding from the rightmost digit.

  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.
2. Add: Start adding from the rightmost digit.

  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

Tips

1. Addition: Line up the decimal points and add.
2. Subtraction: Line up the decimal points and subtract.
3. Multiplication: Multiply as whole numbers, then place the decimal point.
4. Division: Convert to whole numbers if necessary, then divide.

Summary

These additional examples should provide a comprehensive understanding of how to add, subtract, multiply, and divide decimals. Each example follows the same basic steps of aligning decimals for addition and subtraction, ignoring and then counting decimal places for multiplication, and converting to whole numbers for division. Using these methods consistently will help reinforce the concepts for kids.