# ADDITION AND SUBTRACTION OF DECIMALS

Addition and subtraction of decimals :

The process of adding and subtracting decimals are similar to adding and subtracting whole numbers.

The place value is important. It is important to arrange the digits one below the other according to the place values.

While adding 7235 with 47, we have to arrange the numbers as

aaaaaaaaaaaaaaaaaaa7 2 3 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa+        4 7 aaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaa-----------

Not asaaaaaaaaaaaaa7 2 3 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa+  4 7 aaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaa-----------

Let us see, how to add the decimals 0.24 and 0.15.

Observe the figure given below.

0.24 and 0.15 are shaded in two different colors. Now the sum of 0.24 and 0.15 is 0.39

That is,

3 tenths and 9 hundredths

Method 1 :

Therefore,

0.24 + 0.15  =  0.39

Method 2 :

Not asaaaaaaaaaaaaaaaaa0 . 2 4 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa+  0 . 1 5  aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaaaaaaaa0 . 3 9  aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------

Therefore,

0.24 + 0.15  =  0.39

Note :

In both the methods, arrange the decimal numbers according to the place values as we arrange in whole numbers. Then add them.

Not asaaaaaaaaaaaaaaaaa0 . 7 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa+  0 . 2 0  aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaaaaaaaa0 . 9 5  aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------

In the above addition of decimals, 0.2 is taken as 0.20, as the first decimal number has two digits on the right side of the decimal point.

## Subtraction of decimals

Let us see, how to subtract 0.14 from 0.25

Method 1 :

Therefore,

0.25 - 0.14  =  0.11

Method 2 :

Not asaaaaaaaaaaaaaaaaa0 . 2 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-  0 . 1 4  aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaaaaaaaa0 . 1 1  aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------

Therefore,

0.25 - 0.14  =  0.11

Note :

In both the methods, arrange the decimal numbers according to the place values as we arrange in whole numbers. Then subtract them.

Subtract 0.75 from 2

Not asaaaaaaaaaaaaaaaaa2 . 0 0 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa--  0 . 7 5 aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa   aaaaaaaaaaaaaaaaaaaaaaa1 . 2 5  aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------

In the above addition of decimals, 2 is taken as 2.00, as the second decimal number has two digits on the right side of the decimal point.

## Addition and subtraction of decimals - Practice problems

Questions :

Simplify the following decimals :

1)  0.36 + 0. 589

2)  1.26 + 1.369

3)  3.286 - 0.689

4)  0.55 - 0.25

5) 3.25 + 2.856

Solution :

1)  0.949

2)  2.629

3)  2.597

4)  0.30

5)  6.106

After having gone through the stuff given above, we hope that the students would have understood "Addition and subtraction of decimals".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6