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

\( 0.6+0.7= \)

+=

Examples with solutions for Addition and Subtraction of Decimal Fractions

Step-by-step solutions included
Exercise #1

Determine whether the exercise is correctly written or not.

3.05+53.2

Step-by-Step Solution

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

Answer:

Not true

Video Solution
Exercise #2

Determine whether the exercise is correctly written or not.

3.05+213.22

Step-by-Step Solution

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

Answer:

Not true

Video Solution
Exercise #3

Determine whether the exercise is correctly written or not.

True or false:

The positions of the decimal points correspond.

21.52+3.4

Step-by-Step Solution

First let's fill in the zeros in the empty spaces as follows:

21.52+03.40 21.52\\+03.40\\ Note that the decimal points are written one below the other.

Therefore, the positions of the decimal points correspond and thus the exercise is written in the correct form.

Answer:

True

Video Solution
Exercise #4

Determine whether the exercise is written correctly:

Is the position of the decimal point correct in each number?

6.31+216.222

Step-by-Step Solution

First let's fill the zeros in the empty space as follows:

006.310+216.222  006.310\\+216.222\\\

Here We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.

Answer:

Yes

Video Solution
Exercise #5

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

312.54+1203.22

Step-by-Step Solution

To determine if the addition problem is set up correctly, we need to analyze how the numbers are aligned.

The given numbers for addition are 312.54312.54 and 1203.221203.22. When aligning these numbers for addition:

312.54+1203.22\begin{array}{r} 312.54 \\ +1203.22 \\ \hline \end{array}

We examine how the decimal points are positioned. For a correct setup, the decimal points should be aligned vertically. However, in the visual provided:

  • The decimal point in 312.54312.54 is positioned one place to the right compared to the decimal in 1203.221203.22.

  • The alignment should have appeared as amp;00312.54amp;+1203.22 \begin{aligned} &\phantom{00}312.54 \\ &+1203.22 \end{aligned} to be correct, but it does not.

Since the decimal points are not vertically aligned, the addition is set up incorrectly.

Therefore, the statement regarding the positioning of the decimal points is Not true.

Answer:

Not true

Video Solution

Frequently Asked Questions

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

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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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