4. INTEGERS
Whole numbers: whole numbers are the
numbers form 0 to infinite.
Ex : 0,2,3,4,8,9,99,100,156 etc.
Natural numbers: nutral numbers are
the numbers from 1 to infinite.
Ex :1,5,7,1056,89,174 etc.
Integers: integers is the combination of
positive and negative numbers.
Ex : -6,-7,-10,1,4,5,-111,143 etc.
5. FRACTIONS AND
DECIMALS
Fraction: is that represents a part of
whole.
Proper fraction: numerator is smaller
than denominator.
Improper fraction: denominator is
smaller than numerator.
Mixed fraction: combination of whole
number and fractions.
14. POINTS TO REMEMBER
WE HAVE LEARNT ABOUT FRACTIONS,
THEIR ADDITION, SUBSTRACTION,
MULTIPLICATION & DIVISION.
THE PRODUCT OF TWO PROPER FRACTION IS
LESS THAN EACH OF THE FRACTIONS
THE PRODUCT OF ONE PROPER AND ONE
IMPROPER FRACTION IS LESS THAN THE
IMPROPER FRACTION & GREATER THAN
PROPER FRACTION
A RECIPROCAL OF FRACTION IS OBTAINED
BY INVERTING IT UPSIDE DOWN
19. MULTIPLICATION OF
DECIMALS
WHEN A DECIMAL 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 OVER ONE.
EXAMPLES :-
0.07 X 10 = 0.7
2.97 X 100 = 297
2.38 X 1000 = 2380
;
20. DIVISIONS OF DECIMALS
WHILE DIVIDING A NUMBER BY 10, 100 OR
1000 , THE DIGITS OF THE NUMBER AND
QUOTIENT ARE SAME BUT THE DECIMAL
POINT IN THE QUOTIENT SHIFTS TO THE LEFT
BY AS MANY PLACES AS THERE ARE ZEROS
OVER 1
EXAMPLES :-
2.38 ÷ 10 = 0.238
2.38 ÷ 100 = 0.0238
2.38 ÷ 1000 = 0.00238
;
21. DIVISIONS OF DECIMALS BY WHOLE
NUMBERS
6.4 ÷ 4 = 64 X 1 = 16 = 1.6
10 4 10
12.96 ÷ 4 = 1296 X 1 = 324 =
3.24
100 4 100
;
22. DIVISIONS OF DECIMALS BY WHOLE
NUMBERS
6.4 ÷ 4 = 64 X 1 = 16 = 1.6
10 4 10
12.96 ÷ 4 = 1296 X 1 = 324 = 3.24
100 4 100
;
23. DIVISIONS OF DECIMALS BY ANOTHER
DECIMAL
6.4 ÷ 1.6 = 64 ÷ 16 = 64 X 10 = 4
10 10 10 16
22.5 ÷ 1.5 = 225 ÷ 15 = 225 X 10
= 15
10 10 10 15
;
24. POINTS TO REMEMBER
WHEN A DECIMAL 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 OVER ONE.
WHILE DIVIDING A NUMBER BY 10, 100 OR
1000 , THE DIGITS OF THE NUMBER AND
QUOTIENT ARE SAME BUT THE DECIMAL
POINT IN THE QUOTIENT SHIFTS TO THE LEFT
BY AS MANY PLACES AS THERE ARE ZEROS
OVER 1