Adding and subtracting decimals

The single rule that saves all decimal arithmetic: line up the decimal points before you add or subtract. Everything else is ordinary column addition or subtraction.

Idea

To add or subtract two decimals:

1. Write them one below the other so the decimal points align.
2. Pad any shorter number with trailing zeros so all numbers have the same number of decimal places.
3. Add (or subtract) column by column, starting from the rightmost column, just like whole numbers.
4. Place the decimal point in the answer directly below the column.

For example, to add $5.3$ and $2.47$:

  5.30
+ 2.47
------
  7.77

For subtraction, the borrowing rules work exactly as for whole numbers. To compute $7 - 2.5$, treat $7$ as $7.0$:

  7.0
- 2.5
-----
  4.5

Common traps: do not right-align the digits. $5.3 + 2.47$ is not "$5.3$ above $2.47$ with the $3$ above the $7$" , you must align the points.

A second trap: borrowing across the decimal point. To compute $5.02 - 2.7$, pad: $5.02 - 2.70$. The hundredths column ($2 - 0 = 2$) is fine; the tenths needs borrowing ($0 - 7$ can't be done, so borrow from the ones).

Worked examples

Example 1. Add $2.34$ and $5.6$.

Pad: $5.60$. Then $2.34 + 5.60 = 7.94$.

Example 2. Subtract $4.07$ from $9$.

Pad $9$ as $9.00$. Then $9.00 - 4.07 = 4.93$.

Example 3. Find the sum of $0.5, 1.25, 3$, and $0.125$.

Pad to $3$ places: $0.500 + 1.250 + 3.000 + 0.125$. Adding: $0.500 + 1.250 = 1.750,\quad 1.750 + 3.000 = 4.750,\quad 4.750 + 0.125 = 4.875.$

Example 4. A bottle holds $1.5$ L of juice. After pouring out $0.85$ L, how much remains?

$1.5 - 0.85 = 1.50 - 0.85 = 0.65$ L.

Try it yourself

1. Add: $3.4 + 2.7$.
2. Subtract: $8.0 - 3.45$.
3. Add: $12.5 + 0.075 + 1.25$.
4. Subtract: $5.6 - 2.07$.
5. A pencil costs $\rupee 7.50$ and an eraser $\rupee 3.25$. Total cost?
6. Aman walked $1.2$ km and ran another $0.85$ km. Total distance?
7. A jug had $2$ L of water; $0.65$ L was drunk. Remaining?
8. Find the missing number: $5.2 + \square = 8.07$.

Activity

Make a "pricing" game. Write ten product names with decimal prices ($\rupee 12.50$, $\rupee 7.95$, etc.). Pick any three and add the total. Then pick any two and find the change from a $\rupee 100$ note.