Decimal Operations: Read Write Compare

Grade 5 · decimals · 89 practice problems · read aloud

🔊 Listen to this explanation

Decimal Operations: Adding & Subtracting

📊 What Are Decimal Operations?

Decimals help us represent parts of a whole number. We use decimal operations every day when working with money ($4.25), measurements (3.5 meters), and scores (9.75 points). Mastering decimals helps you handle real-world math problems!

🧮 Step-by-Step Guide

  1. Line up the decimal points - This is the most important step!
  2. Add zeros if needed to make numbers the same length
  3. Add or subtract just like with whole numbers
  4. Bring the decimal point straight down into your answer

🔢 Visual Examples

Example 1: Adding Decimals

3.45 + 2.6 = ?

Step 1: Line up decimals
3.45
+ 2.60
Step 2: Add zeros
Step 3: Add normally
Answer: 6.05

Example 2: Subtracting Decimals

7.8 - 2.35 = ?

Step 1: Line up decimals
7.80
- 2.35
Step 2: Add zeros
Step 3: Subtract normally
Answer: 5.45

⚠️ Common Mistakes

  • Forgetting to line up decimals: Always check alignment first!
  • Misplacing the decimal point: Count carefully when bringing it down
  • Forgetting to add zeros: 4.5 is the same as 4.50 - add zeros to help!

💡 Tips & Tricks

  • Money method: Think of decimals as dollars and cents ($3.25 = 3 dollars and 25 cents)
  • Zero power: Adding zeros after the decimal doesn't change the value (2.3 = 2.30)
  • Estimate first: Round decimals to check if your answer makes sense

🎯 Practice Suggestions

  • Create your own money problems ($12.45 + $3.75)
  • Use measurement word problems (3.2 cm + 4.15 cm)
  • Practice with grocery receipts or sports scores
  • Try online decimal games for extra practice

Remember: Practice makes perfect! Start with easier problems and work your way up.

Practice problems

6 of the 89, worked through step by step — try them before opening the answer.

1 0.75 × 1.2 = ?

Hint: When multiplying decimals, first multiply as if they were whole numbers, then count the total decimal places in both factors to determine where to place the decimal point in the product.

Show the answer

Answer: 0.9

  1. Write the problem. 0.75 × 1.2
  2. Convert decimals to fractions to make it easier. 0.75 = 75/100 1.2 = 12/10
  3. Multiply the fractions. (75/100) × (12/10) = (75 × 12) / (100 × 10)
  4. Calculate the numerator and denominator. 75 × 12 = 900 100 × 10 = 1000 So we have 900/1000.
  5. Simplify the fraction. 900/1000 = 90/100 (dividing numerator and denominator by 10) 90/100 = 9/10 (dividing numerator and denominator by 10 again)
  6. Convert back to decimal. 9/10 = 0.9 Therefore, 0.75 × 1.2 = 0.9

Let's multiply 0.75 by 1.2 step by step.

2 0.75 + 0.3 = ?

Hint: Remember to align the decimal points when adding numbers with different place values. For example, when adding 0.4 and 0.25, you would write them with the decimals lined up.

Show the answer

Answer: 1.05

  1. Write the problem clearly. 0.75 + 0.3
  2. Align the decimal points to add correctly. Think of it as: 0.75 + 0.30 (We can write 0.3 as 0.30 to make it easier to add)
  3. Add the digits in the hundredths place (the farthest right column). Hundredths place: 5 + 0 = 5 So, we write ._ _ 5
  4. Add the digits in the tenths place. Tenths place: 7 + 3 = 10 Since 10 tenths equals 1 whole, we write down the 0 in the tenths place and carry over the 1 to the ones place. So far we have .0 5
  5. Add the digits in the ones place. Ones place: 0 + 0 + 1 (the carried over 1) = 1 So, we write 1 to the left of the decimal.
  6. Combine the results. We have 1 from the ones place, and .05 from the decimal places. This gives us 1.05. Therefore, 0.75 + 0.3 = 1.05

Let's add 0.75 and 0.3 step by step.

3 0.65 × 1.8 = ?

Hint: When multiplying decimals, first multiply as if they were whole numbers, then count the total decimal places in both factors to determine where to place the decimal point in the product.

Show the answer

Answer: 1.17

  1. Multiply 0.65 × 1.8 as if they were whole numbers: 65 × 18
  2. 65 × 10 = 650
  3. 65 × 8 = 520
  4. 650 + 520 = 1170
  5. Count the decimal places: 0.65 has 2 decimal places, 1.8 has 1 decimal place, so total is 3 decimal places
  6. Place the decimal point in 1170 to get 3 decimal places: 1.170
  7. Remove the trailing zero: 1.17

The answer is 1.17.

4 2.75 + 1.3 = ?

Hint: Remember to align the decimal points when adding. Think about how you would add dollars and cents.

Show the answer

Answer: 4.05

  1. Write the numbers vertically, aligning the decimal points. 2.75 + 1.30 -------
  2. Add the numbers in the hundredths place: 5 + 0 = 5. Write 5 in the hundredths place.
  3. Add the numbers in the tenths place: 7 + 3 = 10. Write 0 in the tenths place and carry over 1 to the ones place.
  4. Add the numbers in the ones place: 2 + 1 + 1 (carried over) = 4. Write 4 in the ones place.
  5. Bring down the decimal point. The final answer is 4.05.

5 0.75 + 1.25 = ?

Hint: When adding decimals, align the decimal points and add each place value column from right to left, carrying over when necessary.

Show the answer

Answer: 2.00

  1. Write the numbers one above the other, aligning the decimal points. 0.75 + 1.25
  2. Start adding from the rightmost column (hundredths place). 5 hundredths + 5 hundredths = 10 hundredths. 10 hundredths = 1 tenth and 0 hundredths. Write 0 in the hundredths place, carry over 1 to the tenths place.
  3. Add the tenths place, including the carry-over. 7 tenths + 2 tenths = 9 tenths, plus the carried-over 1 tenth = 10 tenths. 10 tenths = 1 whole and 0 tenths. Write 0 in the tenths place, carry over 1 to the ones place.
  4. Add the ones place, including the carry-over. 0 ones + 1 one = 1 one, plus the carried-over 1 one = 2 ones. Write 2 in the ones place.
  5. Place the decimal point in the answer directly below the decimal points in the problem. The result is 2.00. So, 0.75 + 1.25 = 2.00.

Let's add 0.75 and 1.25 step-by-step.

6 0.85 + 1.47 = ?

Hint: Remember to align the decimal points when adding. Think about adding hundredths to hundredths and tenths to tenths.

Show the answer

Answer: 2.32

  1. Write the numbers with decimal points aligned: 0.85 + 1.47
  2. Add the hundredths place: 5 + 7 = 12. Write down 2 in the hundredths place and carry over 1 to the tenths place.
  3. Add the tenths place: 8 + 4 + 1 (carried over) = 13. Write down 3 in the tenths place and carry over 1 to the ones place.
  4. Add the ones place: 0 + 1 + 1 (carried over) = 2. Write down 2 in the ones place.
  5. Place the decimal point in the answer directly below the decimal points in the numbers being added. The final answer is 2.32.
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