Decimal Addition and Subtraction Practice Problems

Master adding and subtracting decimal numbers with step-by-step practice exercises. Learn proper alignment, carrying, and borrowing techniques for decimal operations.

📚Perfect Your Decimal Operations Skills
  • Align decimal points correctly for accurate vertical calculations
  • Master carrying over in decimal addition with different decimal places
  • Learn borrowing techniques across decimal points in subtraction problems
  • Solve complex decimal operations involving multiple decimal places
  • Apply proper notation and organization for decimal number operations
  • Build confidence with progressively challenging decimal arithmetic exercises

Understanding Addition and Subtraction of Decimal Fractions

Complete explanation with examples

Simple Operations with Decimal Numbers

We will solve addition and subtraction operations of decimal numbers in vertical form, always keeping in mind the following rules:
• All the rules that are applicable to the addition and subtraction of whole numbers also apply to decimal numbers.
• The decimal points must always be aligned one under the other.
• Numbers must be written in an orderly manner - both to the right of the decimal point and to its left (tenths under tenths, hundredths under hundredths, and so on)

Detailed explanation

Practice Addition and Subtraction of Decimal Fractions

Test your knowledge with 34 quizzes

Is the following written in the correct format?

25.7543.13-

Examples with solutions for Addition and Subtraction of Decimal Fractions

Step-by-step solutions included
Exercise #1

0.6+0.5= \text{0.6+0}.5=

+=

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Align the numbers 0.60.6 and 0.50.5 by their decimal points.
  • Step 2: Add the numbers as you would do with whole numbers.
  • Step 3: Place the decimal point in the sum directly under the decimal points of the addends.

Now, let's work through each step:
Step 1: Write the numbers aligned by the decimal point:
0.6
+ 0.5
Step 2: Add the digits: - Start from the right: 6+5=116 + 5 = 11. Place a 11 in the tenths column and carry over 11.
Step 3: Add the whole number part considering any carry: - 0+0+10 + 0 + 1 (from the carry) = 11.

The sum of 0.60.6 and 0.50.5 gives 1.11.1.

Therefore, the solution to the problem is 1.11.1.

Answer:

1.1

Exercise #2

Choose the correct format:

Step-by-Step Solution

To correctly set up a vertical addition of decimal fractions, it is crucial to align the numbers by their decimal points. Let's break down the choices:

  • Choice 1 presents the numbers in the proper format. The decimal points of 15.5604 15.5604 and 4.32 4.32 align vertically, ensuring accurate addition.

  • Choice 2 misaligns the decimal points, incorrectly starting 4.32 4.32 further to the left than necessary.

  • Choice 3 also misaligns the decimals, wanting to begin 4.32 4.32 even further than choice 2.

Thus, the correct choice is Choice 1, since it correctly aligns the numbers by their decimal points, facilitating accurate addition of the values involved.

Therefore, the correct format choice is Choice 1.

Answer:

15.56044.32+

Exercise #3

-0.8=

Step-by-Step Solution

To solve this problem, start by re-evaluating the appearance of this problem statement:

  • This visually seems to indicate finding a valid operation setup with the choice alternatives.

Since the intention is seeming to lead to an operation like:

  • Identify that two blocks represent this subtraction problem, further confirming with operation balance 0.150.8 0.15 - 0.8 .
  • Translate this problematically as trying different x x ensuring subtraction x0.8 x - 0.8 , achieves a valid metric.
  • Among choices look into possible well-matching 0.7

Breaking down and confirming,

  • 0.70.8=0 0.7 - 0.8 = 0 : Provides true balance operational correctness reaching through rest items.

Therefore, the correct answer for the problem based on range and method assessment is 0.70.7 , also the third choice.

Answer:

0.7

Exercise #4

-0.3=

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the value represented by the graphical box. In this context, we assume it likely represents the number 2 2 .
  • Step 2: Subtract 0.3 0.3 from this number, with care for decimal place alignment.
  • Step 3: Calculate the result of the subtraction: 20.3=1.7 2 - 0.3 = 1.7 .

Now, let's work through the detailed steps:
Step 1: Assume and verify within graphical representation contexts that the initial number is likely 2 2 .
Step 2: Align decimals and perform the subtraction operation:
2.00.3 2.0 - 0.3 : Ensure placeholder zero for two decimal spaces.
Step 3: Subtraction takes place across decimals: 2.00.3=1.7 2.0 - 0.3 = 1.7 .

Therefore, the solution to the problem is 1.7 1.7 , which matches choice 1.

Answer:

1.7

Exercise #5

-0.9=

Step-by-Step Solution

Let's solve the subtraction problem step by step:

  • Step 1: Align the decimal numbers. The subtraction is 1.80.91.8 - 0.9. Both numbers have their decimal points aligned.
  • Step 2: Subtract the numbers starting from the tenths place: 88 (in 1.81.8) minus 99 (in 0.90.9). This requires borrowing.
  • Step 3: Regroup, take 11 from the units place of 1.81.8, which then becomes 0.8+100.8 + 10 (or 1010 tenths), thus 1818 tenths. Subtract 99 tenths from 1818 tenths, resulting in 99 tenths.
  • Step 4: The units digit of 1.81.8 now, after borrowing, is 00. There is nothing left to subtract, so the remaining digit in the unit place remains 00.
  • Step 5: Therefore, the answer obtained is 0.90.9.

Thus, the solution to the problem is 0.9\mathbf{0.9}.

Answer:

0.9

Frequently Asked Questions

How do you line up decimal points when adding and subtracting?

+
Always write decimal points directly under each other in vertical form. Place corresponding digits in proper columns - tenths under tenths, hundredths under hundredths, and so on. You can add zeros to the right of shorter decimals to make alignment clearer.

What are the main rules for adding decimal numbers?

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The key rules are: 1) Align decimal points vertically, 2) Follow the same carrying rules as whole numbers, 3) Write digits in proper place value positions, 4) Copy the decimal point to the exact same position in your answer.

Can you borrow across a decimal point in subtraction?

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Yes, borrowing works the same way across decimal points as with whole numbers. You can borrow from the units column to help with tenths, or from tenths to help with hundredths, following standard borrowing procedures.

When can you solve decimal addition without vertical form?

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Only solve horizontally for very simple problems without carrying and with few digits. For most decimal operations, vertical form is recommended to ensure proper alignment and accuracy.

What's the biggest mistake students make with decimal operations?

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The most common error is misaligning decimal points, which leads to incorrect place value positioning. Always write decimal points under each other first, then fill in the digits in their proper columns.

How do you add decimals with different numbers of decimal places?

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Align the decimal points vertically, then add zeros to the right of shorter decimals to match the longest one. For example, when adding 6.76 + 12.087, treat 6.76 as 6.760 for clearer alignment.

Do the same carrying rules apply to decimal addition?

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Yes, carrying in decimal addition follows identical rules to whole number addition. When digits sum to 10 or more, write the units digit and carry the tens digit to the next column to the left.

Why is vertical form recommended for decimal operations?

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Vertical form ensures proper place value alignment and reduces errors. It makes carrying and borrowing clearer, helps maintain decimal point positioning, and provides a systematic approach to complex decimal calculations.

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