Add/Subtract Decimals

Grade 4 · decimals · 78 practice problems · read aloud

🔊 Listen to this explanation

Adding & Subtracting Decimals

🧮 What is it and Why is it Useful?

Adding and subtracting decimals is just like working with whole numbers, but we have to pay special attention to the decimal point. We use this skill all the time in real life, like when we count money ($4.25 + $1.50), measure things (2.5 meters + 1.75 meters), or check our weight!

📝 Step-by-Step Guide

  1. Line up the decimals: Write the numbers vertically, making sure the decimal points are directly under each other.
  2. Fill in zeros: Add zeros to the end of any number so they all have the same number of digits after the decimal point. This is like giving every number the same "decimal places."
  3. Add or subtract: Work from right to left, just like with whole numbers.
  4. Bring down the decimal: Finally, bring the decimal point straight down into your answer.

🔍 Visual Examples

Example 1: Adding 3.25 + 1.4

Step 1 & 2: Line up decimals and add a zero.
  3.25
+ 1.40
-------
Step 3 & 4: Add and bring down the decimal.
  3.25
+ 1.40
-------
  4.65

Example 2: Subtracting 5.1 - 2.68

Step 1 & 2: Line up decimals and add zeros.
  5.10
- 2.68
-------
Step 3 & 4: Subtract and bring down the decimal.
  5.10
- 2.68
-------
  2.42

⚠️ Common Mistakes

Misaligned Decimals: The biggest mistake is not lining up the decimal points. If you don't, you might be adding tenths to hundredths!

Forgetting the Decimal: Always bring the decimal point straight down into your answer. Don't leave it out!

💡 Tips & Tricks

Think Money: Imagine the numbers are dollars and cents. $3.25 is 3 dollars and 25 cents. This makes it easier to understand!

The "Zeros are Heroes" Trick: Adding zeros at the end of a decimal doesn't change its value (3.4 is the same as 3.40), but it makes adding and subtracting much easier.

🎯 How to Practice

  • Use grid or graph paper to help you line up the numbers and decimal points perfectly in columns.
  • Create your own problems about money or measurements.
  • Ask a parent or friend to give you problems to solve. Start with two numbers, then try three!

Practice problems

6 of the 78, worked through step by step — try them before opening the answer.

1 3.75 + 2.15 = ?

Hint: When adding decimals, align the decimal points and add each place value separately, remembering to carry over when needed.

Show the answer

Answer: 5.90

  1. Write the numbers one under the other, aligning the decimal points. 3.75 + 2.15 _______
  2. Start adding from the rightmost column (hundredths place). The hundredths place: 5 + 5 = 10. Write down 0 in the hundredths place, and carry over 1 to the tenths place.
  3. Add the tenths place. Tenths place: 7 + 1 = 8, plus the carry-over 1 makes 9. Write down 9 in the tenths place.
  4. Add the ones place. Ones place: 3 + 2 = 5. Write down 5 in the ones place.
  5. Bring down the decimal point directly below the others in the answer. So we have: 5.90
  6. Since 5.90 is the same as 5.9, but we are adding money amounts (like dollars and cents), it's common to write two digits after the decimal. So the final answer is 5.90. ANSWER: 5.90

Let's add 3.75 and 2.15 step-by-step.

2 7.25 + 4.83 = ?

Hint: When adding numbers with decimal points, make sure to align the decimal points vertically before adding each column from right to left.

Show the answer

Answer: 12.08

  1. Write the numbers one under the other, aligning the decimal points. 7.25 + 4.83 --------
  2. Start adding from the rightmost column (hundredths place). Hundredths place: 5 + 3 = 8 Write 8 in the hundredths place of the answer.
  3. Move to the tenths place. Tenths place: 2 + 8 = 10 Since 10 is two digits, write 0 in the tenths place and carry over 1 to the ones place.
  4. Add the ones place, including the carry-over. Ones place: 7 + 4 = 11, plus the carried-over 1 gives 12. Write 2 in the ones place and carry over 1 to the tens place.
  5. Since there are no digits in the tens place of the original numbers, the carried-over 1 becomes the tens digit. So, the result is 12.08. Final answer: 12.08

Let's add 7.25 and 4.83 step by step.

3 12.75 + 8.25 = ?

Hint: When adding decimals, align the decimal points and add each place value separately, carrying over when needed.

Show the answer

Answer: 21.00

  1. Write the numbers one above the other, aligning the decimal points. 12.75 + 8.25 ---------
  2. Start adding from the rightmost column (hundredths place). The hundredths column: 5 (from 12.75) + 5 (from 8.25) = 10. Write down 0 in the hundredths place, and carry over 1 to the tenths place.
  3. Add the tenths place, including the carry-over. Tenths column: 7 (from 12.75) + 2 (from 8.25) + 1 (carried over) = 10. Write down 0 in the tenths place, and carry over 1 to the units (ones) place.
  4. Add the units (ones) place, including the carry-over. Units column: 2 (from 12.75) + 8 (from 8.25) + 1 (carried over) = 11. Write down 1 in the units place, and carry over 1 to the tens place.
  5. Add the tens place, including the carry-over. Tens column: 1 (from 12.75) + 0 (from 8.25, since there is no digit) + 1 (carried over) = 2. Write down 2 in the tens place.
  6. Combine all digits, placing the decimal point in the same aligned position. We have: 2 (tens), 1 (units), decimal point, 0 (tenths), 0 (hundredths) → 21.00 Final Answer: 21.00

Let's add 12.75 and 8.25 step-by-step.

4 12.75 + 8.34 = ?

Hint: When adding numbers with decimal points, make sure to align the decimal points vertically before adding each column from right to left.

Show the answer

Answer: 21.09

  1. Write the numbers one under the other, aligning the decimal points. 12.75 + 8.34 --------
  2. Start adding from the rightmost column (hundredths place). The hundredths place: 5 + 4 = 9 Write 9 in the hundredths place of the answer.
  3. Move to the tenths place. The tenths place: 7 + 3 = 10 Write 0 in the tenths place of the answer, and carry over 1 to the ones place.
  4. Add the ones place, including the carry-over. Ones place: 2 + 8 = 10, plus the carried-over 1 gives 11. Write 1 in the ones place, and carry over 1 to the tens place.
  5. Add the tens place. Tens place: 1 (from 12.75) + 0 (from 8.34) = 1, plus the carried-over 1 gives 2. Write 2 in the tens place.
  6. Place the decimal point in the answer, aligned with the decimal points in the problem. So far we have: 2 (tens), 1 (ones), decimal point, 0 (tenths), 9 (hundredths) → 21.09 Final Answer: 21.09

Let's add 12.75 and 8.34 step by step.

5 12.75 + 8.50 = ?

Hint: When adding decimals, make sure to line up the decimal points and add each place value carefully.

Show the answer

Answer: 21.25

  1. Write the numbers one under the other, aligning the decimal points. 12.75 + 8.50 --------
  2. Start adding from the rightmost column (hundredths place). 5 hundredths + 0 hundredths = 5 hundredths. Write 5 in the hundredths place. 12.75 + 8.50 -------- .05
  3. Move left to the tenths place. 7 tenths + 5 tenths = 12 tenths. 12 tenths is the same as 1 whole and 2 tenths. Write 2 in the tenths place and carry over 1 to the ones place. 12.75 + 8.50 -------- .25 (with 1 carried to ones)
  4. Add the ones place, including the carry. Ones: 2 + 8 + 1 (carry) = 11 ones. 11 ones means 1 ten and 1 one. Write 1 in the ones place and carry over 1 to the tens place. 12.75 + 8.50 -------- 1.25 (with 1 carried to tens)
  5. Add the tens place, including the carry. Tens: 1 + 1 (carry) = 2 tens. Write 2 in the tens place. 12.75 + 8.50 -------- 21.25
  6. Write the final answer with the decimal point in the correct position. ANSWER: 21.25

Let's add 12.75 and 8.50 step-by-step.

6 15.67 - 8.29 = ?

Hint: Remember to align the decimal points and regroup when necessary, similar to how you would solve 12.45 - 5.18.

Show the answer

Answer: 7.38

  1. Write the problem vertically with decimal points aligned: 15.67 - 8.29
  2. Subtract the hundredths place: 7 - 9. Since 7 is less than 9, regroup from the tenths place. The 6 becomes 5, and the 7 becomes 17. 17 - 9 = 8
  3. Subtract the tenths place: 5 - 2 = 3
  4. Subtract the ones place: 15 - 8 = 7
  5. Bring down the decimal point. The final answer is 7.38.
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