Grade: Grade 5 Subject: Mathematics Unit: Decimals SAT: Algebra ACT: Math

Guided Practice: Decimal Operations

Work through decimal problems step-by-step with hints and instant feedback. Build your confidence before tackling problems on your own!

How This Works

Practice with Support

Each problem comes with hints you can reveal if you get stuck. Try solving on your own first, then check your work!

Your Progress

0 of 12 problems completed correctly

Addition Practice

Beginner Line up those decimal points!

Problem 1: Addition

4.6 + 2.35 = ?
Hint:

Rewrite 4.6 as 4.60 so both numbers have the same number of decimal places. Then line up the decimal points and add.

 4.60
+2.35
 ?.??
Solution:

4.60 + 2.35 = 6.95

Remember: Add a zero to 4.6 to make 4.60, then add column by column from right to left!

Problem 2: Addition with Carrying

7.89 + 5.46 = ?
Hint:

Line up the decimals. When adding, 9 + 6 = 15, so write 5 and carry 1. Then 8 + 4 + 1 = 13, write 3 and carry 1.

Solution:

7.89 + 5.46 = 13.35

9+6=15 (carry 1), 8+4+1=13 (carry 1), 7+5+1=13

Subtraction Practice

Beginner Don't forget to borrow when needed!

Problem 3: Subtraction

9.4 - 3.27 = ?
Hint:

Rewrite 9.4 as 9.40. Then you need to borrow since you can't subtract 7 from 0.

 9.40
-3.27
Solution:

9.40 - 3.27 = 6.13

Borrow from 4: 10-7=3. Then 3-2=1. Finally 9-3=6.

Problem 4: Subtraction with Multiple Borrows

15.03 - 8.57 = ?
Hint:

You'll need to borrow twice! First, you can't subtract 7 from 3. Second, you can't subtract 5 from 0.

Solution:

15.03 - 8.57 = 6.46

Borrow from 0 (which borrows from 5): 13-7=6. Then 9-5=4. Finally 14-8=6.

Multiplication Practice

Intermediate Count those decimal places!

Problem 5: Simple Multiplication

0.7 x 0.8 = ?
Hint:

Step 1: Multiply as if there are no decimals: 7 x 8 = 56

Step 2: Count decimal places: 0.7 has 1, 0.8 has 1. Total = 2 places.

Step 3: Put 2 decimal places in your answer.

Solution:

7 x 8 = 56, but we need 2 decimal places, so 0.56

Problem 6: Multiplication with More Places

2.5 x 3.4 = ?
Hint:

Step 1: 25 x 34 = 850

Step 2: 2.5 has 1 place, 3.4 has 1 place. Total = 2 places.

Step 3: Place the decimal in 850 to get 2 decimal places.

Solution:

25 x 34 = 850. With 2 decimal places: 8.50 = 8.5

Problem 7: Three Decimal Places Total

1.25 x 0.4 = ?
Hint:

1.25 has 2 decimal places, 0.4 has 1 decimal place.

Total = 3 decimal places needed in the answer.

125 x 4 = 500, then add 3 decimal places.

Solution:

125 x 4 = 500. With 3 decimal places: 0.500 = 0.5

Division Practice

Intermediate Make the divisor a whole number first!

Problem 8: Simple Division

4.8 / 0.6 = ?
Hint:

Move the decimal in 0.6 one place right to get 6.

Move the decimal in 4.8 one place right to get 48.

Now divide: 48 / 6 = ?

Solution:

4.8 / 0.6 = 48 / 6 = 8

Problem 9: Division with Decimal Answer

7.5 / 2.5 = ?
Hint:

Move both decimals 1 place right: 75 / 25

Think: What times 25 equals 75?

Solution:

7.5 / 2.5 = 75 / 25 = 3

Problem 10: Two-Place Divisor

9.12 / 0.12 = ?
Hint:

Move both decimals 2 places right: 912 / 12

What is 912 divided by 12?

Solution:

9.12 / 0.12 = 912 / 12 = 76

Mixed Practice

Advanced Use all your skills together!

Problem 11: Mixed Operations

What is (3.5 + 2.75) x 2?

Problem 12: Order of Operations

What is 10.5 - (1.5 x 3)?

Key Takeaways

1

Addition/Subtraction

Line up decimal points, add zeros if needed

2

Multiplication

Count total decimal places in both factors

3

Division

Make divisor a whole number first

4

Check Your Work

Estimate first to catch big errors

Practice Makes Perfect: The more decimal problems you solve, the more automatic these steps become. Keep practicing until the rules feel natural!

Next Steps

  • If you got all 12 correct on your first try, move on to Word Problems!
  • If you needed hints, try this lesson again tomorrow for extra practice
  • Work on the problems you found hardest until they feel easy
  • Challenge yourself with longer decimal numbers