Numbers

Predecessor(Before)  :
Examples:
     Case 1: The number before a number in a given sequence                   of  numbers.
                   5,   7 ,   0,   9,   10, -4, -2
      Predecessor of 0 is 7             Predecessor of -2  is -4
      Predecessor of 10 is 9           Predecessor of 7 is 5 
 
       Case 2 : on a number line
   
           Predecessor of 2 is 1            Predecessor of  4 is 3
         Predecessor of -3 is -4          Predecessor of -6 is -7
Successor(After)  :
Examples:
     Case 1: The number after a number in a given sequence                    of  numbers.
                   5,   7 ,   0,   9,   10, -4, -2
      Successor of 0 is 9               Successor of -4 is -2
      Successor of 5 is 7               Successor of  10 is -4 
 
       Case 2 : on a number line
   
           Successor of 2 is 3            Successor  of  4 is 5
         Successor of -3 is -2          Predecessor of -6 is -5
Give the predecessor of the following numbers (on a number line) :
1. 90
2. -35
3. -1000
4. 0
5. 30
Give the successor of the following numbers
(on a number line) :
1. -5
2. 3
3. 6
4. 30
5. -1000
Addition of positive and negative numbers
 
Examples:
    +3 + (+2) = 3 + 2 = +5    
(2 +ve numbers, addition,  results in +ve number)
         
     +3 + (-2) = 3 – 2 = +1
(1 +ve and 1 negative, subtraction , result takes the sign of the  biggest number. Since 3 is bigger than 2, result takes the sign of 3 which is +ve)
 
   +2 + (-3) = +2 – 3 = -1
(1 -ve and 1 +ve, subtraction, result takes the sign of the  biggest number. Since 3 is bigger than 2, result takes the sign of 3 which is -ve)
 
   -3 + (-2) =  – 3  – 2 = -5
(2 -ve numbers, addition, result in -ve number)
 
Subtraction of positive and negative numbers
 
Examples:

 
Addition of positive and negative numbers :
1. [-9] + [+5] =
2. [+68] + [-68] =
3. [0] + [+6] =
4. [-32] + [-56] =
5. [-200] + [-200] + [+400] =
Subtraction of positive and negative numbers :
1. [+2] – [-2] =
2. [-40] – [-20] =
3. [+23] – [+100] =
4. [-32] – [-45] =
5. [-2] – [+4] – [-6] =

How much:

Examples:

   case 1: Positive numbers

 

 

    Case 2 : Negative numbers

      

              -1   + -4 =  -5

              – 7  + -2 = -9

 

       

How much to
1. 2 + = 5
2. 10 + = 12
3. + + 3 = 5
4. -2 + = -5
5. + 5 = 95
Write tbe numbers in place value table :
Tens Ones 1/10
1. 30.1 =
2. 4.2 =
3. 8.9 =
4. 40 =
5. 0.8 =

Example

Write tbe numbers in place value table :
 Hundreds
[100]		Tens
[10]		Ones
[1]		Tenths
[1/10]		Hundredths
[1/100]		 
1. 400.38 =
2. 37.00 =
3. 60.16 =
4. 2.08 =
5. 19.60 =

 

Write tbe numbers in place value table :
Thousands
[1000]		 Hundreds
[100]		 Tens
[10]		 Ones
[1]		 Tenths
[1/10]		 Hundredths
[1/100]		 Thousandths
[1/1000]
1. 200.932 =
2. 1005.001 =
3. 9499.000 =
4. 5.008 =
5. 8.123 =
1. 0.9, 0.8
2. 1.62, 1.60
3. 2, 0.9
4. 2.531, 2.521
5. 6.75, 6.705
Which decimal is greater or equal
                  
Examples:
   In all cases, the denominators should be made equal and then the numerators are compared. 
    Case 1a:  0.4  or 0.8
      0.4 = 4/10                                     0.8 = 8/10

       8 is greater than 4 so 0.8 is greater than 0.4

    Case 1b:  0.40   or  0.8

      0.40 =  40/100                             0.8 = 8/10  = 80/100

       80 is greater than 40 so 0.8 is greater than 0.40

   Case 1c:   0.40   or   0.999
       0.40 = 40/100  =  400/1000              0.999 = 999/1000
      999 is greater than 400  so 0.999 is greater than 0.40
 
   Case 1d:   1.5   or 1.50
       1.5 =15/10 = 150/100                1.50 = 150/100
          since the numerator is the same, 1.5  = 1.50
   
    Case 1e:
      3.3  or  3.300
       3.3 =  33/10
             = 33 * 10/10 * 10  = 330 /100 
             = 330*10 /100*10 = 3300/1000
 
      3.300 = 3300/1000
      so   3.3  = 3.300  
Decimals to Fractions :

     4444/10000    444/1000    44/100   4/10 
                          
0.4444        0.444           0.44      0.4
                          
Examples:
    Case 1a: 1 digit after the decimal
      0.4 = 4/10                                     0.9 = 9/10
 
    Case 1b: 2 digits after the decimal
      0.40 =  40/100                       0.90 = 90/100

   Case 1c: 3 digits after the decimal
       0.400 = 400/1000         0.999 = 999/1000
 
   Case 1d: 4 digits after the decimal
   0.4000 = 4000/10000    0.9999= 9999/10000
     
Fractions to Decimals:
 
            0.040       0.4444            0.444          0.44       0.4
         40/1000    4444/10000    444/1000    44/100   4/10 
Examples:
    Case 1a: /10  (putting the decimal before 1 digit right to left)
      5/10 = 0.5                                    8/10 = 0.8
 
Case 1b: /100  (putting the decimal before 2 digits right to left)
       5111/10000 = 0.5111                 9222/10000 = 0.9222
   50/100 = 0.05                           90/100 = 0.09
Case 1c: /1000  (putting the decimal before 3 digits right to left)
       567/1000 = 0.567                    999/1000 = 0.999
 
Case 1d: /10000(putting the decimal before 4 digits right to left)
    10/1000 = 0.010                  67/10000 = 0.0067    Exceptional case : adding zero before
    123/10 = 12.3                       9999/100 = 99.99
         
 
      50/100 = 0.05                           90/100 = 0.09
Case 1c: /1000  (putting the decimal before 3 digits right to left)
       567/1000 = 0.567                    999/1000 = 0.999
 
Case 1d: /10000(putting the decimal before 4 digits right to left)
    10/1000 = 0.010                  67/10000 = 0.0067
   
 
         
Write the following decimals as fractions:
1. 0.4 =
2. 4.9 =
3. 5.369 =
4. 109.5 =
5. 42.111 =
6.100.08=
Write the following fractions as decimals:
1. 4/10 =
2. 19/100 =  
3. 531/10 =  
4. 1089/100 =  
5. 10/1000 =
6. 20023 / 10 =  
Decimals to Fractions  (expanded form):
                                         Examples:
 
   1.2 = 1 + 2/10           
   11.2 = 10 +1 + 2/10       
   111.2 = 100 +10 +1 + 2/10   
   45.22 = 40 +5 +2/10 + 2/100    
   1.227 = 1 + 2/10 + 2/100 + 7/100
   534.7839 = 500 + 30+ 4 + 7/10 + 8/100 + 3/1000 + 9/10000 
Fractions to Decimals (expanded form):
Examples:

    

      0+5/10 = 0.5                                    

      0+8/10 = 0.8

      30 + 0 + 0/10+ 50/100 = 30.050           

      9 + 0/10+ 9/100 = 9.09

     300 + 0 + 2 + 6/10 +7/100 = 302.67      
     
     900 + 0 +0 + 9/10+9/100 = 900.99
     1000 + 200+30+3+ 2/10+1/100+ 4/1000= 1233.214
Write the following decimals as fractions(expanded form):
1. 0.47 = +
2. 40.9 = + +
3. 5.369 = + + +
4. 19.53 = + + +
5. 2.1567= + + + +
Write each of the following as decimals :
1. 40 + 7 + 1/10 =
2. 30 + 0 + 2/10 + 6/100 =
3. 300 + 30 + 8+ 0/10 + 8/100=
4. 1000 + 0 + 0 + 3 + 0/10 + 0 /100 + 5/1000=
5. 600 + 0 +3 + 1/10 =
millimeters to centimeters
                                         Examples:
  1 mm = 1/10 cms   = 0.1 cms
  9mms = 9/10 cms = 0.9 cms
  10mms =  10/10 cms=  1 cms
 200mms = 200/10 = 20.0 cms 
2456 mms = 2456/10 = 245.6 cms
centimeters to millimeters
Examples:
    1cm = 10 mm
    20 cms = 20*10 = 200mms
    115 cms = 115*10= 1150mms
    350cms = 350*10 = 3500mms
 
mm to cm : 1 mm = 1/10 cm or 0.1 cm
1. 3 mms = cm or cm
2. 5 mms = cm or cm
3. 20 mms = cm or cm
4. 100 mms = cm or cm
5. 1000 mms = cm or cm
1 cm = 10 mm
1. 45 cms = mm 
2. 58 cms = mm 
3. 3 cms = mm 
4. 158 cms = mm 
5. 349 cm = mm 
centimeters to meters
                                         Examples:
  1 cm = 1/100 m   = 0.01 mts
  0.9cms = 9/10/100= 9/1000 mts = 0.009mts
  10cms =  10/100 mts= 0.1 mts
 200cms = 200/100 = 2 mts 
2456 cms = 2456/100 = 24.56 mts
meters to centimeters
Examples:
    1mt = 100 cms
    20 mts = 20*100 = 2000 cms
    115 mts= 115*100= 11500 cms
    3.50cms = 3.50*100 = 3500.0cms = 3500 cms
    1.008cms = 1008*100 = 100.800 cms = 100.8 cms
 
1 cm = 1/100 m   one-hundredth of a metre
1. 45 cm = m
2. 58 cm = m
3. 3 cm = m 
4. 158 cm = m 
5. 349 cm = m 
1 mt = 100cms   
1. 4 mts =  cms 
2. 5.8 mts =  cms 
3. 2.01 mts =  cms
4. 9.008 mts =  cms 
5. 0.999 mts =  cms

grams to kilograms

                                         Examples:

  1 gram = 1/1000kg   = 0.001 kg
  0.5 grams = 5/10/1000= 5/10000 mts = 0.0005 kg
  10.5 grams =  10.5/1000 kgs= 0.0105 kg
 200 grams = 200/1000 = 0.2 kgs 
2 kg 2 grams  = 2 + 2/1000 = 2 + 0.002 = 2.002 kgs

kilograms to grams

Examples:

    1 kg= 1000 grams

    20 kgs = 20*1000 = 20000 grams
    1 kg 15 grams= 1000 +  15 = 1015 grams
    0.50kgs = 0.50*1000 = 500 grams
 
1 g = 1/1000 kg = 0.001 kg
1. 7 g = kg = kg
2. 220 g = kg = kg
3. 5000 g = kg = kg
4. 3 kg 2 g = kg = kg
5. 15 kg 9 g = kg = kg
1 kg = 1000 grams
1. 9 kgs =  grams 
2. 10 kgs =  grams
3. 1.5 kgs =  grams
4. 4 kg 40 g =  grams
5. 12 kg 94 g =  grams

Addition of decimal numbers 

                                         Examples

                            0.009 + 9 + 15.08 = 24.089

      +       

                              
                Place the numbers under the corresponding column and then add zeros

Subtraction of decimal numbers 

                                         Example

               8.21 – 1.00 = 7.21                       2.000  – 0.001 = 1.999

      

        Place the numbers under the corresponding column and then add zeros
1. 0.009 + 9 + 15.08 =  
2. 15.356 + 0.001 + 0.001 =  
3. 0.75 + 1.02 + 2 =  
4. 189.07 + 189.07 + 0.1 =  
5. 2 + 2 + 0.001 =  
1. 9.22 – 0.01 =  
2. 17.01 – 5.01 =  
3. 2 – 0.001 =  
4. 15.75 – 9.995 =  
5. 4.001 – 0.001 =