Decimal grid or area models can be used to understand the process of addition and subtraction using decimal numbers.

**Operations on Decimal Numbers**

Already we are familiar with decimal
numbers. We know how to represent a decimal number as a fraction and the place values
of digits. Now, let us learn the operations on decimal numbers.

__Addition and Subtraction of Decimal Numbers__

Iniya has purchased notebooks for ₹ 46.50
and a pencil box for ₹ 16.50. How much she will get as balance if she paid ₹ 100
to the shop keeper?

Price of a note book = ₹ 46.50 ; Price
of a pencil box= ₹ 16.50

To find the amount to be paid, we have
to add the price of both the items.

To get the balance amount we have to
subtract the total expense from ₹ 100. To know the total expenses and the balance
money, we need to understand addition and subtraction of decimals.

** **

__Addition and subtraction
of decimals through models__

Decimal grid or area models can be used
to understand the process of addition and subtraction using decimal numbers.

** **

__(i) Grid model__

We see below the grids to represent the
decimal numbers 1.0, 0.1 and 0.01.

Having these grids let us try to do addition
and subtraction of decimal numbers.

__Example 1.5__

Find
the sum of 0.16 and 0.77 using decimal grid models.

**Solution**

Here, 0.16= 16/100 and 0.77 =
77/100

First shade the region 0.16 and then
shade 0.77.

The total shaded area is the sum.

So, 0.16 + 0.77 = 0.93 .

__Example 1.6____ __

Find 0.52 – 0.08 using decimal grid models.

**Solution**

Here 0.52 =
52 / 100and 0 .08 = 8/100. First shade the region 0.52 then cross out 0.08, which
is 8/100 from the shaded area. The left out shaded region without cross marks is
the difference. So, 0.52 − 0.08 = 0.44 .

__Example 1.7____ __

Find the value of 0.72 − 0.51 by using
grids.

**Solution**

Take a square
of 100 boxes. Shade 72 boxes to represent
0.72.

Then strike
out 51 boxes out of 72 shaded boxes to subtract
0.51 from 0.72.

The left over
shaded boxes represent the required value.

Therefore,
0.72 – 0.51 = 0.21.

**Try this**

**Find the following using
grid models:**

**(i) 0.83 + 0.04 **

**Solution:**

0.83= 83/100 and 0.04 = 4/100

Shading the regions

0.83 and 0.04

The sum is the total shaded region.

S = 0.83 + 0.04 = 0.87

**(ii) 0.35 – 0.09**

Solution:

0.35 = 35/100 and 0.09 = 9/100

Shading the regions 0.35 by shading 35 boxes out of 100.
Striking off 9 boxes out of 35 shaded boxes to subtract 0.09 from 0.35.

The left over shaded boxes represent the required value.

0.35 - 0.09 = 0.26

** **

__(ii) Area model__

The whole number (unit place) which is a part of
decimals represents a square area and 1/10 th part of this square area which is
a thin rectangular strip represents the tenth
place of the decimal (0.1) and 1/100 ^{th} part of this rectangular strip represents the hundredth place
value (0.01) and the same process will be continued for the next place and so on.

Having these square and rectangular area
let us try to do addition and subtraction of decimal numbers.

__Example 1.8____ __

Add 3.2 + 6.4.

**Solution**

Here 3.2 is represented in Blue colour
and 6.4 is represented in Green colour. Hence, the sum of 3.2 and 6.4 is 9.6.

__Example 1.9 __

Subtract 7.5 – 3.4 .

**Solution**

First represent
the decimal number 7.5 using 7 squares and 5 rectangular strips. Cross out 3 squares
from 7 squares and 4 rectangular strips from 5 rectangular strips to get the difference
(see Fig. 1.5).

Hence, 7.5 – 3.4 = 4.1

**Try this**

Using the area models solve the following:

**(i) 1.2 + 3.5**

**Solution:**

Here 1.2 is represented in
blue colour and 3.5 is represented in Green colour. Sum of 1.2 and 3.5 is 4.7.

**(ii) 3.5 − 2.3**

**Solution:**

Representing 3.5 using 3
squares and 5 rectangular strips. Crossing out 2 squares from 3 squares and 3
rectangular strips from 5 to get the difference. So 3.5 - 2.3 = 1.2.

** **

__(iii) Place value grid
model__

So far we have
discussed grid models to do addition and subtraction of decimal numbers. Earlier
we have studied representation of decimal numbers in place value tables. Let us
use the same representation for addition and subtraction of decimal numbers.

For example,
while adding 4.83 and 1.67, we have

Therefore, 4.38 + 1.67 = 6.05.

__Example 1.10 __

Add the following : (i) 30.9
+ 52.73 (ii) 25.67 + 33.856

**Solution**

(i) 30.9 + 52.73

Let us use the place value grid.

(Since the
digits in the decimal place of 52.73 is 2 and 30.9 is 1, we should add 0 at the
hundredth place of 30.9 to equalise the digits in the decimal place)

Therefore, 30.9 + 52.73 = 83.63.

(ii) 25.67 + 33.856

Let us use the place value grid.

Therefore, 25.67 + 33.856 = 59.526.

**Note**

Adding zeros at the right
end of decimal digits will not change the value of the number.

__Example 1.11 __

Everyday Malar travels 1.820** ***km*** **by bus and 295 *m*** **by walk to reach the** **school. Find the distance
of school from her house in *km*.

**Solution**

1000 *m *=1 *km*; 1 *m = 1/*1000 *km*

Hence, 295 *m = 295/1000 km*

* *= 0.295 *km*

Distance travelled by bus =1.820 *km*

Distance covered by walk = 0.295 *km*

Total distance *= *1.820 + 0.295

=1.820 + 0.295

=2.115 *km*

Therefore, the school is situated at
the distance of 2.115 *km* from her house.

__Example 1.12 __

Subtract 2.85 from 4.97.

**Solution**

4.97 – 2.85 = ?

Let us use the place value grid.

Therefore, 4.97 – 2.85 = 2.12.

__Example 1.13 __

Subtract 3.09 from 12.7.

**Solution**

12.7 – 3.09 = ?

Let us use the place value grid.

Therefore, 12.7 – 3.09 = 9.61.

**Note**

1. We can equalize the decimal digits of given numbers by adding
zero at the right end of a decimal number that has only one decimal digit.

2. Zeros are added at the
right end of decimal digits of a decimal number that are to be added or subtracted.

__Example 1.14 __

Subtract 32.042 from 86.9.

**Solution**

Therefore, 86.9 – 32.042 = 54.858.

**Try this**

**Complete the magic square in such a way that rows, columns and diagonals
give the same sum 1.5.**

Solution

__Example 1.15 __

Naren bought 7.4 *kg*** **of mangoes. On the way home,
he gave 4.650** ***kg*** **of** **mangoes to his sister’s family. Find the weight of the remaining mangoes.

**Solution**

Mangoes bought by Naren = 7.4 *kg*

Mangoes given to Naren’s sister = 4.650
*kg*

Mangoes left for Naren’s family = 7.400
− 4.650

Weight of remaining mangoes = 2.750 *kg*

Therefore, the weight of the remaining
mangoes is 2.750 *kg.*

We use decimals every day, while dealing with money, weight, length etc. Decimal numbers are used in situations where more accuracy is required.

Tags : Number System | Term 3 Chapter 1 | 7th Maths , 7th Maths : Term 3 Unit 1 : Number System

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7th Maths : Term 3 Unit 1 : Number System : Addition and Subtraction of Decimal Numbers | Number System | Term 3 Chapter 1 | 7th Maths

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