Adding Four Digit Numbers

How to add four digit numbers (for example 4529 + 6733):

• Place one number above the other so that the thousands', hundreds', tens' and ones' places are lined up. Draw a line under the bottom number.

    4529  
   +6733    

• Add the ones' place digits (9 + 3 = 12). This number is larger than 10 so place a one above the tens' place column and place the two below the line in the ones' place column.

      1  
   4529  
  +6733    
      2  

• Add the tens' place digits (1 + 2 + 3 = 6) and place the answer below the line and in the tens' place column.

       1 
     4529  
   + 6733    
       62

• Add the numbers in the hundreds' place column (5 + 7 = 12) and place the 2 below the line and before the other number below the line. Place the 1 from the twelve above the thousands' place column.

   1  1  
   4529  
  +6733   
    262

• Add the digits in the thousands' place column (1 + 4 + 6 = 11) and place the answer below the line in the thousands' place column.

     1  1
     4529 
   + 6733  
    11262

Addition of Time

How to add hours to a time:

• Add the number of hours to the hours portion of the time.
• If the number of hours is more than 12 do the following:
  • Subtract 12 from the number of hours.
  • If the time was AM change it to PM, if it was PM change it to AM.
  • Repeat this process if the number of hours is still more than 12.
• If the number of hours is equal to 12 change AM to PM or PM to AM.

Example: What time is 16 hours after 9:00 AM?

• Add the hours together. (16 hours + 9 hours = 25 hours)
• If the number of hours is more than 12 do the following:
  • Subtract 12 from the number of hours. (25 hours - 12 hours = 13 hours)
  • Change the AM to PM.
  • Repeat this process if the number of hours is still more than 12.
  • Subtract 12 hours from 13 hours. Change the PM to AM.
• Answer: 1:00 AM

Multiplying two digit by one digit numbers

How to multiply a two digit number by a one digit number
(for example 59 + 7).

• Place one number above the other so that the ones' place digits are lined up. Draw a line under the bottom number.

    59  
   x 7    

• Multiply the two ones' place digits (9 * 7 = 63). This number is larger than 9, so place the six above the tens' place column and place the three below the line in the ones' place column.

   6  
   59  
  x 7   
    3  

• Multiply the digit in the tens' place column (5) by the second number (7). The result is 5 * 7 = 35. Add the 6 to the 35 (35 + 6 = 41) and place the answer below the line and to the left of the 3.

     6
     59  
   x  7  
    413

Multiplication of Two Digit Numbers

How to multiply a two digit number by a two digit number (e.g. 29 x 67).

• Place one number above the other so that the tens' and ones' places are lined up. Draw a line under the bottom number.

      29 
    x 67    

• Multiply the two numbers in the ones' places. (9 * 7 = 63). This number is larger than 9 so place a 6 above the tens' place column and place 3 below the line in the ones' place column.

      6   
      29  
   x  67     
       3  

• Muliply the digit in the top tens' place column (2) by the digit in the lower ones' place column (7). The answer (2*7=14) is added to the 6 above the top tens' place column to give an answer of 20. The 20 is placed below the line.

     6   
     29  
  x  67    
    203

• After 29 has been multiplied by 7 as shown above, 29 is multiplied by the tens' place of the multiplier which is 6. The number 0 is placed in the ones place because we are multiplying by a tens' place number. The result would be 174:

     5  
     29  
  x  67   
    203  
   1740

• A line is drawn under the lower product (1740) and the products are added together to get the final answer of 1943.

     6  
     29  
   x 67   
    203  
  +1740  
   1943    

Division

How to divide a three digit number by a one digit number (e.g 413 ÷ 7).

• Place the divisor before the division bracket and place the dividend (413) under it.

           
   7)413   

• Examine the first digit of the dividend(4). It is smaller than 7 so it can't be divided by 7 to produce a whole number. Next take the first two digits of the dividend (41) and determine how many 7's it contains. In this case 41 holds five sevens (5*7=35) but not six (6*7=42). Place the 5 above the division bracket.

       5   
   7)413   

• Multiply the 5 by 7 and place the result (35) below the 41 of the dividend.

       5   
   7)413    
     35   

• Draw a line under the 35 and subtract it from 41 (41-35=6). Bring down the 3 from the 413 and place it to the right of the 6.

       5   
   7)413    
     35 
      63    

• Divide 63 by 7 and place that answer above the division bracket to the right of the five.

       59  
    7)413    
      35
       63   

• Multiply the 9 of the quotient by the divisor (7) to get 63 and place this below the 63 under the dividend. Subtract 63 from 63 to give an answer of 0. This indicates that there is nothing left over and 7 can be evenly divided into 413 to produce a quotient of 59.

       59  
    7)413
      35
       63
       63
        0    

Identifying Triangles by their Sides

Types of triangles based on their sides

• An EQUILATERAL triangle has all three sides the same length.
• An ISOSCELES triangle has two sides with the same length.
• A SCALENE triangle has all three sides different lengths.

Identifying Triangles by their Angles

Types of triangles based on their angles

• A RIGHT triangle has one 90o angle.
• An OBTUSE triangle has one angle that is greater than 90o.
• An ACUTE triangle has all three angles less than 90o.

Name	Sides	Angles
Triangle	3	3
Quadrilateral	4	4
Pentagon	5	5
Hexagon	6	6
Heptagon	7	7
Octagon	8	8
Nonagon	9	9
Decagon	10	10