Adding And Subtracting Decimals
2026-02-21 20:29 Diff
https://brightchamps.com/en-us/math/numbers/addition-and-subtraction-of-decimals

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
    \(\begin{array}{r@{\,.\,}l} 95 & 7 \\ +\quad 82 & 3 \\ \hline 178 & 0 \\ \end{array}\)