 # ADDITION AND SUBTRACTION OF DECIMAL UP TO 3 PLACES

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Adding decimals is very similar to adding whole numbers except with a few extra technical details and bookkeeping.  Recall that decimals are just fractions.  We add fractions by adding the whole number parts and the fractional parts separately, carrying the 1 from the fractional part if necessary, to the whole number part.  For decimals, we line up the decimal points so that the whole number parts line up and the decimal parts line up.  Then add each.

1) Line up the decimal points vertically. Fill in any 0’s where necessary.

2) Add or subtract the numbers as if they were whole numbers.

3) Place the decimal point in the sum or difference so that it lines up vertically with the numbers being added or subtracted.

EXAMPLE 1: Add 0.56 + 9 + 6.287

To add decimals, line up the decimal points vertically and fill in 0’s as shown:

0.560

9.000

+ 6.287

15.847 ← Place the decimal point in the sum so that it lines up vertically.

Solution

1. 93.59    Notice the decimal points in line.
4.7
2. 93.59        We added this 0 so both numbers have 2 digits to the right
4.70         of the decimal point.

1

3.   93.59
+  4.70
98.29

Add 135 + 44.571 + 2.01

Solution

1. 135.    Notice the decimal points in line.
44.571
2.01
2. 135.000        We added these 0s so all three numbers have 3 digits
44.571         to the right of the decimal point.
2.010
1
3.   135.000
44.571
+    2.010
181.581

Subtraction of Decimal

Subtraction of decimals is carried out in a similar way.  We line up the decimals vertically, tack on extra zeros to the right, and subtract downward.  More specifically, follow the steps below

Step 1:  Line up the numbers vertically so that the decimal points all lie on a vertical line.
Step 2:  Add extra zeros to the right of the number so that each number has the same number of digits to the right of the decimal place.
Step 3:  Subtract the numbers as you would whole numbers.  Place the decimal point of the result in line with the other decimal points.

EXAMPLE : Subtract 3.742 – 10.638

To subtract decimals, line up the decimal points vertically and add 0’s where shown. Remember to borrow when necessary.

10.638

–3.742

6.896

Subtract 34.91 – 14.214

Solution

1. 34.91    Notice the decimal points in line.
14.214
2.   34.910         We added this 0 so both numbers have 3 digits to the right
14.214         of the decimal point.
3.    34.8910110
–  14. 2   1  4
20. 6   9   6

Example

Subtract 12.00942 – 12.0087

Solution

1. 12.00942    Notice the decimal points in line.
12.0087
2. 12.00942        We added these 0 so all three numbers have 5 digits
12.00870         to the right of the decimal point.
3.     12.0089142
+  12.00 8  70
0 .00072        Notice the zeros to the right of the decimal point.

Example

Find the value of x if  x + 52.98  =  67.3
Solution

We want to determine what number must be added to 52.78 to get 67.3.  The is the reverse of an addition problem, that is a subtraction problem.

667.12310
–   5 2.   9  8
14.32

Exercises

1. 159.02 – 87.835
2. 198.9 – 198.132

Word Problem on Decimals

Example

A nurse needs to make sure that a patient receives 1.12 liters of fluid during a 24 hour period.  The IV bottle originally contained 2.1 liters of fluid.  How much fluid should be left in the IV bottle when the patient has been given the necessary amount of fluid for the day?

Solution

Since we are taking away 1.12 liters from a 2.1 liter bottle, this is a subtraction problem.

12.10110
–    1.   1  2
0.   9  8

The nurse should remove the IV when it has 0.98 liters of fluid left in it

If the decimals have opposite signs, place the larger decimal on top, line up the decimal points, subtract the numbers, and carry down the sign, as shown:

Quiz