fractions and decimals

1. B.J.P.S Samiti’s
M.V.HERWADKAR ENGLISH MEDIUM HIGH SCHOOL
FRACTIONS AND DECIMALS
Program:
Semester:
Course: NAME OF THE COURSE
Sandhya S.Kulkarni 1

2. Fractions and Decimals
Proper fraction: Example 3/4
Improper fraction: 7/4
Mixed fraction: 1 ¾
Equivalent fractions of 3/5 are 6/10,12/20, 24/40
Compare 4/5 and 3/7.Equalise denominators as
4X7/5X7=28/35 and 3X5/7X5=15/35. 4/5 is larger
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 2

3. Addition and Subtraction of Fractions
• 3/4 +1/4= (3+1)/4=4/4=1
•7/3+9/2=(7X2/3X2)+(9X3/2X3)=14/6+27/6 = 41/6
•7/3-9/2=(7X2/3X2)-(9X3/2X3)=14/6-27/6 = -13/6
•21/2 + 3 = 5/2+3=5/2+(3X2/1X2)=5/2+6/2=11/2=51/2
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 3

4. MULTIPLICATION OF FRACTIONS
Multiplication of a Fraction by a Whole Number
a. (3/4)X3=9/4 b.(5/4)X3=15/4
To multiply a mixed fraction to a whole number, first
convert the mixed fraction to an improper fraction
and then multiply
c.(11/4)X4= (5/4)X4=20/4=5
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 4

5. MULTIPLICATION OF FRACTIONS
Multiplication of a Fraction by a Fraction
a. (3/4)X(1/5)=(3X1)/(4X5)= 3/20
b.(5/4)X(7/3)=35/12
Product of two proper fractions is less than each
fraction
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 5

6. MULTIPLICATION OF FRACTIONS
Ex:Lipika reads a book for 31/4hours everyday. She
reads the entire book in 6 days.How many hours
in all were required by her to read the book?
Total number of hours required to read the book
= (31/4 )X6= (13/4)X6= 78/4=39/2=191/2 hours
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 6

7. MULTIPLICATION OF FRACTIONS
Ex:A car runs 16 km using 1 litre of petrol. How much
distance will it cover using 23/4 litres of petrol?
Distance covered= 16X(23/4)=16X(11/3)=176/3=582/3 km
.
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 7

8. DIVISION OF FRACTIONS
Division of Whole Number by a Fraction
To divide a whole number by any fraction, multiply that whole
number by the reciprocal of that fraction.
Ex:3÷(1/4)=3X(4/1)=12
Ex:3÷(1/2)=3X(2/1)=6
Ex:4÷(22/3)=4X(8/3)=32/3
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 8

9. Division of a Fraction by a Whole Number
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 9
DIVISION OF FRACTIONS
To divide fraction a by any whole number, multiply that fraction
by the reciprocal of that whole number.
Ex: (3/4) ÷ 5= (3/4) X(1/5) = (3X1)/(4X5) = 3/20
Ex: (2/3) ÷ 7= (2/3) X(1/7) = (2X1)/(3X7) = 2/21

10. DIVISION OF FRACTIONS
Division of a Fraction by Another Fraction
Take reciprocal of the divisor fraction and multiply as follows
Ex: (1/3) ÷ (2/5) = (1/3)X(5/2) = 5/6
Ex: (1/3) ÷ (6/5) = (1/3)X(5/6) = 5/18
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 10

11. B.J.P.S Samiti’s
M.V.HERWADKAR ENGLISH MEDIUM HIGH SCHOOL
FRACTIONS AND DECIMALS
Program:
Semester:
Course: NAME OF THE COURSE
Sandhya S.Kulkarni 11

12. A decimal number 263.456 is written using its place value expansion given in the table
above.
Or given number 263.456 it can be written in expanded form as
263.456=2X100+6X10+3X1+4X(1/10)+5(1/100)+6X(1/1000)
Thousands
(1000)
Hundreds
(100)
Tens
(10)
Ones
(1)
Tenths
(1/10)
Hundredths
(1/100)
Thousandth
s
(1/1000)
Number
2 6 3 4 5 6 263.456
4 5 3 2 5 7 8 4532.578
M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 12
DECIMAL NUMBERS

13. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 13
DECIMAL NUMBERS
Decimals are used to convert the units
Example:Money from Paise to Rupees
10 paise= 10/100=0.1 Rupee
Example: Length from centimeter to meter
50 cm=50/100= 0.5 m
Example:Weight from gram to kilogram
100 gm=100/1000 =0.1 kg

14. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 14
DECIMAL NUMBERS
Addition of decimal numbers Subtraction of decimal numbers
23.45 56.95 83.45 56.95
+45.42 +32.26 -41.22 -32.26
---------- -------- ---------- --------
68.87 89.21 42.23 24.69

15. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 15
DECIMAL NUMBERS(Continued)
MULTIPLICATION OF DECIMAL NUMBERS
Example: 0.1X0.1= (1/10)X(1/10)=1/100=0.01
Example: 0.2X0.3=(2/10)X(3/10)=6/100=0.06
Example: 1.2X0.6=(12/10)X(6/10)=72/100=0.72
Observe 0.3X0.4=0.12
Number of digits on right side of the decimal point in product = Sum of
the number of digits on right side of the decimal point in each
multiplying number

16. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 16
DECIMAL NUMBERS(Continued)
Multiplication of Decimal Numbers by 10, 100 and 1000
Example: 1.56X10=(156/100)X(10)=156/10=15.6
Example: 1.56X100=(156/100)X(100)=156
Example: 1.56X1000=(156/100)X(1000)=1560
When a decimal number is multiplied by 10, 100 or 1000, the digits in
the product are same as in the decimal number but the decimal point in
the product is shifted to the right by as many of places asthere are
zeros over one.

17. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 17
DECIMAL NUMBERS(Continued)
Multiplication of Decimal Numbers by 10, 100 and 1000
Example: 1.56X10=(156/100)X(10)=156/10=15.6
Example: 1.56X100=(156/100)X(100)=156
Example: 1.56X1000=(156/100)X(1000)=1560
When a decimal number is multiplied by 10, 100 or 1000, the digits in
the product are same as in the decimal number but the decimal point
in the product is shifted to the right by as many of places as there are
zeros after one. Hence by observation answer can be written directly.

18. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 18
DECIMAL NUMBERS(Continued)
DIVISION OF DECIMAL NUMBERS
Division by 10, 100 and 1000
Example:31.5 ÷ 10 =(315/10)X1/10=315/100=3.15
Example:31.5 ÷ 100 =(315/10)X1/100=315/1000=0.315
Example:31.5 ÷ 1000 =(315/10)X1/1000=315/10000=0.0315
When a decimal number is divided by 10, 100 or 1000, the digits in the
quotient are same as in the decimal number but the decimal point in
the quotient is shifted to the left by as many of places as there are
zeros after one. Hence by observation answer can be written directly.

19. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 19
DECIMAL NUMBERS(Continued)
DIVISION OF DECIMAL NUMBERS
Division by a Whole Number
Example: 6.4 ÷2=(64/10)X(1/2)=(1/10)X(64/2)=(1/10)X(32)=3.2
Example:
16.48÷4=(1648/100)X(1/4)=(1/100)X(1648/4)=(1/100)X(412)=4.12
Or, divide 1648 by 4. You get 412. There are two digits to the right of
the decimal point in 16.48. Making similar placement of the decimal
in 412, you will get 4.12.

20. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 20
DECIMAL NUMBERS(Continued)
DIVISION OF DECIMAL NUMBERS
Division of a Decimal Number by another Decimal number
Example: 25.5 ÷ 0.5=25.5/0.5
Convert the denominator to whole number as
25.5X10/0.5X10 = 255/5 = 51
Example: 7.75 ÷ 0.25 = 7.75X100/ 0.25X100 =775/25= 31

21. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 21
DECIMAL NUMBERS(Continued)
Exersise: The length of a rectangle is 7.1 cm and its breadth is
2.5 cm. What is the area of the rectangle?
Solution: Length of the rectangle = 7.1 cm
Breadth of the rectangle = 2.5 cm
Therefore, area of the rectangle = 7.1 × 2.5 cm2 = 17.75 cm2

22. M.V.HERWADKAR ENGLISH MEDIUM SCHOOL 22
DECIMAL NUMBERS(Continued)
Exersise: Each side of a regular polygon is 2.5 cm in length. The
perimeter of the polygon is 12.5cm. How many sides does the
polygon have?
Solution: The perimeter of a regular polygon is the sum of the lengths of
all its equal sides = 12.5 cm.
Length of each side = 2.5 cm.
Thus, the number of sides =12.5 ÷2.5 = 125/25 =5
The polygon has 5 sides.