Ch. 07. Fractions
लेखक
ॐ जितेन्द्र सिंह तोमर
M.A., B.Ed., DNYS, MASSCOM.
10/4/10/2/2022
7.1 Fractions
A fraction means a part of a whole. The whole means a single object or a group of objects.
A Part
Fraction = _________
Whole
Numerator
Fraction = ______________
Denominator
7.2 Name of a Part
1/2 = Half
1/4 = Quarter
7.3 In a fraction, upper part is called the Numerator and lower part is called Denominator.
in 3/5
3 is Numerator and
5 is Denominatorw
7.4 Types Of Fraction
a) Proper Fraction or Simple Fraction
Numerator > Denominator
In which fraction, the numerator is less than the denominator is called a Proper Fraction or Simple Fraction.
fractions
3/4, 1/2, 9/10, 0/3, 5/8
b) Improper Fractions
Denominator> Numerator
In which fraction, the numerator is more than the denominator is called a Improper Fraction.
5/4, 5/2, 13/10, 7/3, 15/8
c) Mixed Fraction
An improper fraction can be written as a combination of a whole and a part, and such fraction then called Mixed Fractions.
In other words whole with Fraction is called Mixed Fractions
Mixed Fractions = Whole + Fraction
R 9 1
Q ____ = ___ = 2 __
d 4 4
Converting Proper Fraction Into Mixed Fraction
N R
____ => Q ___
D d
Converting mixed Fraction Into Proper Fraction
(Whole × Denominator) + Numerator
Denominator
Standard or Simplest form of a Fraction
In which form of fraction, numerator and denominator both are co-prime (or have no common) factor is called standard form of fraction.
The standard form fraction is also called the simplest form of the fraction.
Simplest (Or Lowest) Form
A fraction is said to be in the simplest (or lowest) form if its numerator and the denominator have no common factor except 1.
Equivalent Fractions
Each proper or improper fraction has infinity number of equivalent fractions. To find anequivalent fraction of a given fraction, we may multiply or divide both the numerator and the denominator of the given fraction by the same number.
product of the cross multiplication are same in equivalent fraction.
Like and Unlike Fractions
Like Fractions
Fractions with same denominators are called like fractions.
Thus, 1/15, 2/15, 3/15, 8/15
Unlike Fractions
Fractions with different denominators are called unlike fractions.
Thus, 1/5, 2/11, 3/15, 8/11
Comparing Fractions
a) Comparing Like Fractions
In like fractions the fraction with greatest numerator is the greatest fraction and lowest numerator is lowest fraction.
b) Comparing Unlike Fractions
i) Unlike fractions with the same numerator :
Mind it that the fraction with the smaller denominator is greater
In unlike fractions having same Numerator the fraction with greatest denominator is the smallest fraction and lowest denominators is greatest fraction.
ii) Unlike fractions with the different numerator and denominator:
* Convert Fraction Into The Like Fraction
Convert fraction into the like fraction and then look the numerator and compare the fractions.
* As The Common Denominator
Using the LCM of the denominators of the fractions is preferred to make common denominator.
Law of Vinjeet
Addition And Subtraction Of
Like Fraction
* Addition Like Fraction
a c a + b
__ + __ = _______
b b b
* Subtraction Like Fraction
a c a – b
__ – __ = _______
b b b
* Addition & Subtraction of Mixed Like Fraction
b e b e
a __ ± d __ = (a ± d)+ ( __ ± __ )
c f c f
Unlike Fraction
* Addition unlike Fraction
* Subtraction unlike Fraction
* Addition & Subtraction of Mixed unlike Fraction
भिन्नों के कुछ महत्वपूर्ण नियम
जब दिए गए धनात्मक भिन्नो के अंश समान हो तो सबसे छोटे हर वाली भिन्न सबसे बड़ी तथा सबसे बड़े हर वाली भिन्न सबसे छोटी होता है।
जैसे:- 2/2, 2/4, 2/3, 2/7, 2/1 2/9 में
सबसे छोटा हर = 1,
इसलिए सबसे बड़ा भिन्न = 2/1
सबसे बड़ा हर = 9,
इसलिए सबसे छोटा भिन्न = 2/9
जब दिए गए धनात्मक विंडो के हर समानहो, तो सबसे बड़ा अंश वाला भिन्न सबसे बड़ा और सबसे छोटें अंश वाला भिन्न सबसे छोटा होता है.
जैसे:- 1/11, 7/11, 5/11, 3/11, 2/11, 13/11 में
सबसे बड़ा अंश = 13,
इसलिए सबसे बड़ा भिन्न = 13/11
सबसे छोटा अंश = 2,
इसलिए सबसे छोटा भिन्न =2/11
आरोही क्रम (Ascendimg Order) :
जब दो या अधिक भिन्नों को बढ़ते क्रम में रखा जाता हैं तब भिन्नों के इस क्रम को आरोही क्रम कहते हैं।
इस क्रम में सबसे छोटा भिन्न सबसे पहले तथा सबसे बड़ा भिन्न सबसे अंत में लिखा जाता हैं।
अवरोही क्रम (Descending Order) :
जब दो या अधिक भिन्नों को घटते क्रम में सजाया जाता हैं तब भिन्नों के इस क्रम को अवरोही क्रम कहते हैं।
इस क्रम में सबसे बड़ा भिन्न सबसे पहले तथा सबसे छोटा भिन्न सबसे अंत में लिखा जाता हैं।
*********** RTC ***********
Exercise 01
(01) Recognise the type of fraction
भिन्न के प्रकार को पहचानो।
1/2, 2/3, 7/6, 2⅕, 5/6, 8/3
1⅒, 2/3, 7/6, 2¾, ⅚, 5/3
2/7, 3⅞, 5/6, 12/3, 6⅐, 2/9
11/2, 12/3
*********** RTC ***********
Exercise 02
(02) Convert the followings into Standard Fraction
निम्न को मानक रूप में लिखिए
*********** RTC ***********
Converting Mixed Fraction Into Proper Fraction
*********** RTC ***********
Exercise 04
(04) Convert the followings into Mixed fraction
निम्न को मिश्र भिन्न में बदलो।
3/2, 5/3, 7/6, 22/3, 9/6, 8/3
11/2, 28/3, 8/6, 15/4, 11/4, 15/2
11/5, 12/7.
Addition And Subtraction Of Like Fractions
सामान्य अंकगणित ( भिन्नात्मक संख्याएं के जोड़)
(i) जब हर सामान हो तो
a c a – b
__ – __ = _______
b b b
दूसरे शब्दों में => अंशों को योग बटे हर
= अंश-1 – अंश-2
हर (कोई एक)
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Exercise 01
(01) Solved the followings
(1) 2 1
– __ या। 2/3 +1/3
3 3
Sol.
2 1 2 – 1
__ – __ = _______
3 3 3
2 – 1
= _______
3
1
= __
3
(2) 1 1
– __ या। 1/2 –1/2
2 2
(3) 3 1
– __ या। 3/4 –1/4
4 4
(4) 2 1
– __ या। 2/5 – 1/5
5 5
(5) 3 2
– __ या। 3/3 – 2/3
3 3
(6) 3 1
– __ या। 3/4 – 1/4
4 4
(7) 2 1
– __ या। 2/5 – 1/5
5 5
(8) 2 1
– __ या। 2/3 – 1/3
3 3
(9) 3 1
– __ या। 3/4 –1/4
4 4
(10) 4 1
– __ या। 4/7 – 1/7
7 7
(11) 2 1
– __ या। 2/7 – 1/7
7 7
(12) 3 2
– __ या। 3/7 – 2/7
7 7
(13) 3 2
– __ या। 3/5 – 2/5
5 5
(14) 5 2
– __ या। 5/6 – 2/6
6 6
(15) 3 2
– __ या। 3/6 – 2/6
6 6
(16) 3 2
– __ या। 3/5 – 2/5
5 5
(17) 7 3
– __ या। 7/8 – 3/8
8 8
(18) 5 4
– __ या। 5/9 – 4/9
9 9
(19) 7 3
– ___ या। 2/11 – 3/11
11 11
(20) 7 4
– ___ या। 3/12 – 4/11
12 12
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(ii) जब हर असामान हो तो
a c b.d(a/b) – b.d(c/d)
__ – __ = ____________________
b d b.d
a.d – b.c
= __________
b.d
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Exercise 02
(01) Solved the followings
निम्न को सरल करो
(1) 1 1
– __ या। 1/2 +1/3
2 3
Sol.
Sol.
2 1
__ – __
2 3
6 – 2
= _______
6
4
= __
6
2
= __
3
(2) 1 1
– __ या। 1/3 – 1/6
3 6
(3) 1 1
– __ या। 1/2 –1/4
2 4
(4) 1 1
– __ या। 1/5 –1/10
5 10
(5) 1 2
– __ या। 1/2 – 2/3
2 3
(6) 3 1
– __ या। 3/4 –1/2
4 2
(7) 2 1
– __ या। 2/3 – 1/5
3 5
(8) 2 1
– __ या। 2/5 –1/3
5 3
(9) 2 1
– __ या। 2/7 – 1/14
7 14
(10) 1 1
– __ या। 1/14 – 1/7
14 7
(11) 1 1
– __ या। 1/2 – 1/7
2 7
(12) 2 2
– __ या। 2/3 – 2/7
3 7
(13) 3 2
– __ या। 3/5 – 2/10
5 10
(14) 1 3
– __ या। 1/6 – 2/3
6 3
(15) 3 2
– __ या। 3/6 – 2/12
6 12
(16) 2 2
– __ या। 2/3 – 2/5
3 5
(17) 2 3
– __ या। 2/3 – 3/8
3 8
(18) 3 4
– __ या। 3/9 – 4/9
9 18
(19) 2 3
– __ या। 2/4 – 3/8
4 8
(20) 3 4
– __ या। 3/6 – 4/9
6 18
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Chapter-7
Fractions
Points to remember:
. A fraction is a part of whole or a part of collection
For example:
5-> numerator
7-> denominator
Different type of fractions are as follows:
(1) Proper fraction: where numerator is less than denominator.
For example: 237 3'5'9
(ii) Improper fraction: where numerator is more than denominator.
For example:
(iii) Mixed fraction: which has a whole number and a fractional part.
For example: 3.5.3
We can express a mixed fraction as an improper fraction for example 3
(iv) Like fractions: fractions with same denominator.
For example: 00 1357
(v) Unlike fractions: fractions with different denominator.
For example: 2321
(vi) Equivalent fractions: Two or more fractions representing the same of a whole.
For example:
To find an equivalent fraction of a given fraction, we multiply both numerator and denominator of the given fraction by the same non-zero number.
A fraction is said to be in the simplest form (or lowest form) if its numerator and denominator have no common factor except 1.
. Comparison of fractions: (1) For like fractions, smaller the numerator, smaller will be the fraction.
For example: <<
(ii) For fractions with same numerator, smaller the denominator, bigger will be
the fraction
For example:>>
(iii) For the fractions with different numerators and denominators, make their denominators equal before comparing the numerators.
While adding or subtracting like fractions, only numerators are operated upon (not the denominators).
For example: +¹=¹+¹==1
.
For adding or subtracting unlike fractions, convert them into like fractions. Mixed fraction is always greater than proper fraction.
For example: 1>
If numerator and denominator of a fraction are equal (same), then value of fraction is 1.
For example: = 1=1
A fraction can be converted to its simplest form by dividing the numerator and denominator with their HCF.
For example: 135+15 150+15 9 10
While adding mixed fractions, we can add the whole number parts separately and the fractional parts separately.
For example: 5+6
= 5 + 6 + +
= 11+ = 11 + 1 = 11²/1
OR
We can convert each mixed fraction into improper fraction and then add them.
For example: 5+6 ²/3
5X8+1 8 + 6X8+3 8
41 51
+ 41+51 <= 11 =
Questions:
1. Find the fraction representing the shaded portion.
Page 149
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