Decimal Operations: Add Subtract Hundredths

Grade 5 · decimals · 86 practice problems · read aloud

🔊 Listen to this explanation

Decimal Operations: Adding and Subtracting

🔍 What Are Decimal Operations?

Decimal operations involve working with numbers that have a decimal point, like 4.25 or 10.8. We use decimals every day for money ($5.75), measurements (2.5 meters), and weight (3.4 kg). Learning to add and subtract them helps us solve real-world problems!

📝 Step-by-Step Guide

The golden rule for adding and subtracting decimals is to line up the decimal points!

  1. Write the problem vertically. Line up the decimal points directly under each other.
  2. Add zeros as placeholders so all numbers have the same number of digits after the decimal point.
  3. Add or subtract just like with whole numbers, working from right to left.
  4. Bring the decimal point straight down into your answer.

✨ Visual Examples

Example 1: Adding 3.45 + 12.6

1. Line up decimals and add a zero:
    3.45
   +12.60

2. Add:
    3.45
   +12.60
   16.05

Example 2: Subtracting 8.3 - 1.75

1. Line up decimals and add a zero:
    8.30
   - 1.75

2. Subtract (remember to regroup):
    78.120
   - 1.75
    6.55

⚠️ Common Mistakes

  • Misaligned Decimal Points: Forgetting to line up the decimals will give you the wrong answer every time!
  • Forgetting the Decimal Point: Don't leave the decimal point out of your answer.
  • Not Adding Zeros: It's much harder to subtract 8.3 - 1.75 if you don't write it as 8.30 - 1.75.

💡 Tips & Tricks

  • Decimal Point Detective: Always be on the lookout for the decimal point and line it up first!
  • Zero is a Hero: Adding zeros at the end of a decimal doesn't change its value (5.4 is the same as 5.40), but it makes adding and subtracting easier.
  • Estimate First: Round the decimals to the nearest whole number to get a rough idea of what your answer should be. If 3.45 + 12.6 is about 3 + 13 = 16, then 16.05 makes sense!

🎯 Practice Suggestions

The best way to get better is to practice!

  • Create your own problems about money. For example: "If I have $10.50 and earn $5.25, how much do I have now?"
  • Use grid paper to help you keep the numbers and decimal points neatly in line.
  • Ask a friend or parent to give you 5 problems a day to solve.
  • Play online math games that focus on decimal addition and subtraction.

Practice problems

6 of the 86, worked through step by step — try them before opening the answer.

1 7.45 + 3.28 = ?

Hint: When adding decimals, ensure the decimal points are aligned vertically before performing the operation.

Show the answer

Answer: 10.73

  1. Write the numbers one under the other, aligning the decimal points. 7.45 + 3.28 --------
  2. Start adding from the rightmost column (hundredths place). 5 hundredths + 8 hundredths = 13 hundredths. 13 hundredths is the same as 1 tenth and 3 hundredths. Write down the 3 in the hundredths place and carry over the 1 to the tenths place. Hundredths column result: 3 Carry over: 1
  3. Move to the tenths place. 4 tenths + 2 tenths = 6 tenths. Now add the carried-over 1 tenth: 6 tenths + 1 tenth = 7 tenths. Write down the 7 in the tenths place. Tenths column result: 7 Carry over: 0
  4. Move to the ones place. 7 ones + 3 ones = 10 ones. Write down the 0 in the ones place and carry over the 1 to the tens place. Ones column result: 0 Carry over: 1
  5. Move to the tens place. There is only the carried-over 1 ten. Write down the 1 in the tens place. Tens column result: 1
  6. Combine all digits, placing the decimal point in line with the original numbers. The result is 10.73. ANSWER: 10.73

Let's add 7.45 and 3.28 step by step.

2 7.85 + 4.29 = ?

Hint: When adding decimals, make sure to align the decimal points and add each place value separately, regrouping when necessary.

Show the answer

Answer: 12.14

  1. Write the numbers one above the other, aligning the decimal points. 7.85 + 4.29 --------
  2. Start adding from the rightmost column (hundredths place). 5 hundredths + 9 hundredths = 14 hundredths. 14 hundredths is the same as 1 tenth and 4 hundredths. Write down the 4 in the hundredths place and carry over the 1 to the tenths place. 7.85 + 4.29 -------- .4 (with 1 carried over to the tenths column)
  3. Add the tenths place, including the carry-over. 8 tenths + 2 tenths = 10 tenths, plus the carried-over 1 tenth = 11 tenths. 11 tenths is the same as 1 whole and 1 tenth. Write down the 1 in the tenths place and carry over the 1 to the ones place. 7.85 + 4.29 -------- 1 .4 (with 1 carried over to the ones column)
  4. Add the ones place, including the carry-over. 7 ones + 4 ones = 11 ones, plus the carried-over 1 one = 12 ones. Write down 12 in the ones place. 7.85 + 4.29 -------- 12.14
  5. Combine the result: 12 and 14 hundredths, which is 12.14. Final Answer: 12.14

Let's add 7.85 and 4.29 step-by-step.

3 7.45 + 3.89 = ?

Hint: When adding numbers with two decimal places, make sure to align the decimal points and add each column from right to left, carrying over when necessary.

Show the answer

Answer: 11.34

  1. Write the numbers one under the other, aligning the decimal points. 7.45 + 3.89 --------
  2. Start adding from the rightmost column (hundredths place). 5 hundredths + 9 hundredths = 14 hundredths. 14 hundredths = 0.14, which means 1 tenth and 4 hundredths. Write down the 4 in the hundredths place and carry over the 1 tenth to the next column. 7.45 + 3.89 -------- .4 (with 1 carried over to the tenths column)
  3. Add the tenths place, including the carry-over. 4 tenths + 8 tenths + 1 tenth (carried over) = 13 tenths. 13 tenths = 1.3, which means 1 whole and 3 tenths. Write down the 3 in the tenths place and carry over the 1 to the ones column. 7.45 + 3.89 -------- .34 (with 1 carried over to the ones column)
  4. Add the ones place, including the carry-over. 7 ones + 3 ones + 1 one (carried over) = 11 ones. Write 11 in the ones and tens places. 7.45 + 3.89 -------- 11.34
  5. Combine the result: 11 and 0.34 gives 11.34. Final Answer: 11.34

Let's add 7.45 and 3.89 step by step.

4 12.75 + 8.49 = ?

Hint: When adding decimals, align the decimal points and add each column from right to left, remembering to carry over when needed.

Show the answer

Answer: 21.24

  1. Write the numbers one under the other, aligning the decimal points. 12.75 + 8.49 --------
  2. Start adding from the rightmost column (hundredths place). 5 (hundredths) + 9 (hundredths) = 14 hundredths. 14 hundredths = 1 tenth and 4 hundredths. Write down the 4 in the hundredths place, and carry over the 1 to the tenths place. 12.75 + 8.49 -------- .4 (with 1 carried to the tenths place)
  3. Add the tenths place, including the carry-over. 7 (tenths) + 4 (tenths) = 11 tenths, plus the 1 carried over = 12 tenths. 12 tenths = 1 whole and 2 tenths. Write down the 2 in the tenths place, and carry over the 1 to the ones place. 12.75 + 8.49 -------- .24 (with 1 carried to the ones place)
  4. Add the ones place, including the carry-over. 2 (ones) + 8 (ones) = 10 ones, plus the 1 carried over = 11 ones. 11 ones = 1 ten and 1 one. Write down the 1 in the ones place, and carry over the 1 to the tens place. 12.75 + 8.49 -------- 1.24 (with 1 carried to the tens place)
  5. Add the tens place, including the carry-over. 1 (ten) + 0 (there is no tens digit in 8.49) = 1 ten, plus the 1 carried over = 2 tens. Write down the 2 in the tens place. 12.75 + 8.49 -------- 21.24 Final Answer: 21.24

Let's add 12.75 and 8.49 step-by-step.

5 15.67 + 9.84 = ?

Hint: Remember to line up the decimal points and add each place value separately, carrying over when needed.

Show the answer

Answer: 25.51

  1. Write the numbers with decimal points aligned: 15.67 + 9.84
  2. Add the hundredths place: 7 + 4 = 11. Write down 1 and carry over 1 to the tenths place.
  3. Add the tenths place: 6 + 8 + 1 (carried over) = 15. Write down 5 and carry over 1 to the ones place.
  4. Add the ones place: 5 + 9 + 1 (carried over) = 15. Write down 5 and carry over 1 to the tens place.
  5. Add the tens place: 1 + 1 (carried over) = 2.
  6. Bring down the decimal point. The final answer is 25.51.

6 15.78 + 9.45 = ?

Hint: When adding decimals, make sure to align the decimal points and add each place value separately.

Show the answer

Answer: 25.23

  1. Write the numbers vertically, aligning the decimal points: 15.78 + 9.45
  2. Add the hundredths place: 8 + 5 = 13. Write 3 in the hundredths place and carry over 1 to the tenths place.
  3. Add the tenths place: 7 + 4 + 1 (carried over) = 12. Write 2 in the tenths place and carry over 1 to the ones place.
  4. Add the ones place: 5 + 9 + 1 (carried over) = 15. Write 5 in the ones place and carry over 1 to the tens place.
  5. Add the tens place: 1 + 1 (carried over) = 2. Write 2 in the tens place.
  6. Bring down the decimal point. The final answer is 25.23.
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