Adding And Subtracting Decimals

Addition of decimals is the process of finding the sum of numbers that contain decimal points. Subtraction of decimals is the process of finding the difference between such numbers.

In these methods, check whether the decimal numbers have the same number of digits after the decimal point (i.e., check if they are "like decimals"). If not, convert the unlike terms to like terms by adding additional zeroes after the decimal point.

Example:

• \(3.6 + 1.34 = 4.94\)
• \(9.481 + 14.701 = 24.182\)
• \(4 - 9.6 = -5.6\)
• \(16.73 - 9.81 = 6.92\)

As we have learned, decimal numbers can be classified as like or unlike. To find the sum of two decimals, we need to apply the following steps:

1. Check whether the decimal points are vertically aligned.

2. If necessary, add trailing zeros to make the numbers have the same number of digits after the decimal point.

3. Add as whole numbers, then place the decimal point in the result directly under the other decimal points.

Adding Unlike Decimals

In unlike decimals, the values always have a different number of digits after the decimal point. They can be easily converted to like decimals by adding extra zeroes after the decimal point. Note that adding extra zeros does not change the value of the number.

Add 10.22 and 3.5

Step 1: Here, the given decimal values are not aligned correctly, so they are unlike.

\(\begin{array}{r@{\,.\,}l} 10 & 22 \\ +\quad 3 & 5 \\ \hline \\ \end{array}\)

Step 2: To make them alike, we add extra zeroes as shown below:

\(\begin{array}{r@{\,.\,}l} 10 & 22 \\ +\quad 3 & 5\mathbf{0} \\ \hline \\ \end{array}\)

Step 3: We now add the values to find the sum.

\(\begin{array}{r@{\,.\,}l} 10 & 22 \\ +\quad 3 & 5\mathbf{0} \\ \hline 13 & 72 \\ \end{array}\)

Examples:

• Adding 6.4 and 3.25
  \(\begin{array}{r@{\,.\,}l} 6 &4\mathbf{0} \\ +\quad 3 & 25 \\ \hline 9 & 65 \\ \end{array}\)
   
• Adding 12.5 and 4.123
  \(\begin{array}{r@{\,.\,}l} 12 & 5\mathbf{00} \\ +\quad 4 & 123 \\ \hline 16 & 623 \\ \end{array}\)
   
• Adding 7.8 and 0.55
  \(\begin{array}{r@{\,.\,}l} 7 & 8\mathbf{0} \\ +\quad 0 & 55 \\ \hline 8 & 35 \\ \end{array}\)

Adding Like Decimals

Since like decimals have the same number of digits after the decimal point, they can be aligned correctly and added just like whole numbers. The decimal point must be placed accurately in the final result.

Examples: Add 95.7 and 82.3

• Adding 4.3 and 2.5
  \(\begin{array}{r@{\,.\,}l} 4 & 3 \\ +\quad 2 & 5 \\ \hline 6 & 8 \\ \end{array}\)
   
• Adding 10.15 and 8.42
  \(\begin{array}{r@{\,.\,}l} 10 & 15 \\ +\quad 8 & 42 \\ \hline 18 & 57 \\ \end{array}\)
   
• Adding 0.725 and 0.151
  \(\begin{array}{r@{\,.\,}l} 0 & 725 \\ +\quad 0 & 151 \\ \hline 0 & 876 \\ \end{array}\)
   
• Adding 95.7 and 82.3
  \(\begin{array}{r@{\,.\,}l} 95 & 7 \\ +\quad 82 & 3 \\ \hline 178 & 0 \\ \end{array}\)

To find the difference between two decimals, we use the following steps:

• Verify if the decimal point of the number is correctly aligned in a vertical line.

• Place zeroes where the numbers differ in length.

• Now, we find the difference between the numbers by subtracting them.

Subtraction of Like Decimals

The subtraction of like decimals is calculated in the same way as whole numbers; by subtracting the smaller number from the larger one.

Examples

• Subtracting 2.4 from 8.9
  \(\begin{array}{r@{\,.\,}l} 8 & 9 \\ -\quad 2 & 4 \\ \hline 6 & 5 \\ \end{array}\)
   
• Subtracting 3.28 from 15.65 (Requires borrowing)
  \(\begin{array}{r@{\,.\,}l} 15 & 65 \\ -\quad 3 & 28 \\ \hline 12 & 37 \\ \end{array}\)
   
• Subtracting 0.42 from 0.95
  \(\begin{array}{r@{\,.\,}l} 0 & 95 \\ -\quad 0 & 42 \\ \hline 0 & 53 \\ \end{array}\)

Subtraction of Unlike Decimals

To subtract unlike decimals, first, add extra zeroes to the shorter decimal. Then, subtract the numbers in the same way as like decimals. 

Examples:

• Subtracting 4.23 from 9.5 (We add a zero to 9.5 to make it 9.50)
  \(\begin{array}{r@{\,.\,}l} 9 & 5\mathbf{0} \\ -\quad 4 & 23 \\ \hline 5 & 27 \\ \end{array}\)
   
• Subtracting 3.45 from 12 (12 is a whole number, so we add a decimal and two zeros: 12.00)
  \(\begin{array}{r@{\,.\,}l} 12 & \mathbf{00} \\ -\quad 3 & 45 \\ \hline 8 & 55 \\ \end{array}\)
   
• Subtracting 1.2 from 6.75 (We add a zero to the bottom number for alignment)
  \(\begin{array}{r@{\,.\,}l} 6 & 75 \\ -\quad 1 & 2\mathbf{0} \\ \hline 5 & 55 \\ \end{array}\)

Adding and subtracting decimals relies on visual organization and a solid understanding of place value. While the basic arithmetic mirrors whole numbers, the crucial step of aligning the decimal point—especially when dealing with numbers of varying lengths—can often present a challenge. To ensure accuracy and build confidence in solving these problems, here are a few tips and tricks to help.
 

• Use Graph Paper for Alignment: One of the biggest hurdles is keeping columns straight. Have students write their problems on graph paper (grid paper) with one digit per box and the decimal point on the line. This visual aid forces proper alignment and prevents place value errors better than a standard adding and subtracting decimals worksheet.
   
• Connect the Concept to Money: Money is the most intuitive way to explain decimals. Use coins and bills as adding and subtracting decimals examples to show why 5.5 (5 dollars and 50 cents) is different from 5.05 (5 dollars and 5 cents). This real-world connection makes the abstract concept of "unlike decimals" concrete and easier to grasp.
   
• Turn Calculations into Stories: Move beyond dry numbers by creating adding and subtracting decimals word problems based on the student's interests. For instance, if they like sports, ask them to calculate the difference in race times. If they like baking, have them add up ingredient weights. Context helps them understand why they are doing the math.
   
• Scaffold with Structured Resources: Start with a guided worksheet that has pre-printed decimal points and grids. Once the student gains confidence with the alignment, transition them to standard blank adding and subtracting decimals worksheets where they have to set up the problem themselves. This gradual release of support builds independence.
   
• Teach Estimation First: Before they solve the problem, ask the student to estimate the answer. If the problem is 4.2 + 5.9, the estimate should be around 10. If they get an answer like 47.9, their estimation skills will immediately alert them that something is wrong.
   
• Use Technology as a Verifier: Allow students to use an adding and subtracting decimals calculator only after they have attempted the problem by hand. This turns the device into a feedback tool rather than a crutch. If the calculator gives a different answer, challenge them to find the specific step where their manual calculation went off track.
   
• Consistent Low-Stakes Drills: Decimal mastery requires muscle memory. Short, daily adding and subtracting decimals practice sessions (5–10 minutes) are more effective than long, infrequent cramming. Frequent repetition helps the rule of "lining up the decimal" become second nature.

Decimals are significant components of mathematics. They are widely used in real-life scenarios beyond math, where the precision of numbers matters. Here are a few real-life applications of addition and subtraction of decimals:

• Shopping: We use decimals in shopping to calculate the exact amount of money spent or the discount amount.

• Cooking: In cooking, precise measurement of ingredients is often required in decimals.

• Distance/height measurements: They can be applied in measuring the accurate distance or height.

• Fuel consumption: Decimals help calculate fuel consumption or estimate the required fuel amount by using addition or subtraction.

•  Time: We use decimals to measure time in sports or when going on a trip.