Languages
Back
Languages
Addition and Subtraction with Decimal Numbers
> ... Math > Rounding and Decimals > Addition and Subtraction with Decimal Numbers

Addition and subtraction with decimals are just the same as addition and subtraction with the whole number. The most important thing to remember is to line up the decimal points so that when you stack them, they are directly on top of each other. Doing this stacks the place values so that the ones are on top of the ones, the tens on the tens, the tenths on the tenths, and so forth. If there are any times when there aren’t as many digits after the decimal place in one number as there are in another, remember that you can fill in any places to the right of the decimal with a 0. In numbers, this looks like 3.15 = 3.150 = 3.150000000 and so on.

Steps for Addition (Combining Two Positive or Two Negative Numbers)

  1. Stack the numbers according to place value. (This will line up the decimals.)
  2. Add the numbers in the columns starting with the column on the right.
  3. Carry numbers into the next place value to the left as needed.
  4. Repeat this pattern for each remaining column.
  5. Bring the decimal down.
  6. Check the sign. (If both numbers were positive, the answer is positive. If both numbers were negative the answer is negative.)

Steps for Subtraction (Combining a Positive and Negative Number)

  1. Place the biggest number on top.
  2. Stack in columns according to place value. (This will line up the decimals.)
  3. Regroup when needed.
  4. Subtract in columns by place value starting on the right and going left.
  5. Bring the decimal down.
  6. The strongest wins. (If the bigger number was negative then the answer is negative. If the bigger number was positive then the answer is positive.)
Addition with Decimals

Video Source (06:14 mins) | Transcript

Subtraction with decimals

Video Source (08:49 mins) | Transcript

Additional Resources

Practice Problems

Evaluate the following expression:
  1. \(2.4 + 8.8 = ?\) (
    Solution
    x
    Solution: \(11.2\)
    Details:
    Using place values, we will add \(2.4\) and \(8.8\). Line up the numbers in their corresponding places.
    This is a box with two columns. The ones column and the left and the tenths column on the right. Number 2 is placed in the ones column and point 4 is placed in the tenths column. Below these two numbers there is an 8 in the ones column and a point 8 in the tenths column.

    Next, add the numbers in the tenth column. Since \(4 + 8 = 12\), place the 2 below the tenths place and the 1 on the ones place.
    This is the same as the previous image except there is now an addition symbol to the left of all the numbers and a blue solution box at the very bottom. In the tenths column of the solution box is the number point 2. The number 1 is also written at the very top of the numbers in the ones column.

    Finally, add the numbers in the ones place. Include the 1 carried over from the tenths place.
    \(1 + 2 + 8 = 11\)
    This is the same as the previous image except there is now the number 11 written below the numbers in the ones column in the solution box. The solution box now contains 11.2

    Our final answer: \(11.2\)
    Be sure to include the decimal point between the tenths place and the ones place.
    )
  2. \(8.12 + 9.81 = ?\) (
    Solution
    x
    Solution: \(17.93\)
    Details:
    Using place values, we will add \(8.12\) and \(9.81\). Line up the numbers in their corresponding place values.
    This is the same as the previous image except there is now the number 11 written below the numbers in the ones column in the solution box. The solution box now contains 11.2

    Next, add the numbers in the hundredths column. Since \(2 + 1 = 3\), place the 3 below the hundredths place.
    This is a box that has three column: Ones, Tenth, and Hundredths. Number 8 is placed in Ones Column, Number point 1 is placed in Tenth column, and Number 2 is placed in Hundredths column. Below Number 8, Number 9 is placed. Number point 8 is placed right below Number point 1. Number 1 is placed below Number 2. Add the numbers in the Hundredths column, then place 3 below the hundredths place.

    Next, add the numbers in the tenths column. Since \(1 + 8 = 9\), place the 9 below the tenths place.
    This image is the same as the previous image except there is now a point 9 in the tenths column.

    Finally, add the numbers in the ones column. Since \(8 + 9 = 17\), we put a 7 in the ones place and the 1 in the tens place.
    This is the same as the previous image except there is now a 7 in the ones column and a new column to the left of the ones labeled the tens column. In it there is a number 1. The solution under the horizontal line now reads 17.93

    Our final answer: \(17.93\)
    Be sure to include the decimal point between the tenths place and the ones place.
    )
  3. \(5.92 + 3.22 = ?\) (
    Video Solution
    x
    Solution: \(9.14\)
    Details:

    (Video Source | Transcript)
    )
  4. \(7.2 - 1.5 = ?\) (
    Solution
    x
    Solution:
    \(5.7\)
    )
  5. \(5.2 - 5.4 = ?\) (
    Solution
    x
    Solution:
    \(-0.2\)
    )
  6. \(39.6 - 88.88 = ?\) (
    Video Solution
    x
    Solution: \(-49.28\)
    Details:

    (Video Source | Transcript)
    )

Need More Help?

  1. Study other Math Lessons in the Resource Center.
  2. Visit the Online Tutoring Resources in the Resource Center.
  3. Contact your Instructor.
  4. If you still need help, Schedule a Tutor.
Place Values After the Decimal Point
Round a Number to the Nearest Whole Number or Integer