MATH - SCIENCE INTEGRATION CONVERSION FACTORS AND DIMENSIONAL ANALYSIS Multiplying Rational Numbers Definition       A rational number is any number that can be written in the form a/b  where b  is not equal to zero. Review of Steps Practice Exercises What numbers are rational? Using the OGT Calculator Review of Steps

• Simplified Fraction
  

  5   x   7   =    5 x 7   =  35      8       11       8 x 11      88

  
  

  
   
• Reduce Fraction
  

  9    x    4   =    9 x 4    =   36   =  3     10         6        10 x 6        60       5

  (Reminder: There is no need to reduce before you multiply because your calculator will do this for you.)

  
  

  
   

Practice Exercises

Use the OGT calculator for each set of practice problems.   Hit next to check your answers.

• Ordered Exercises
  

  Ex 1.     4  x  10

  7       17

  Ex 2.      9  x  13      (Convert answer to an improper fraction.)

  5       6

  Ex 3.     -4  1  x 2  4

  2          9

  Ex 4.      9  x -12

  11

  Ex 5.    52.389 x  2

  3

  Ex 6.     817.65  x 1.263

  17.902        (Round answer to 3 places after the decimal.)

  Hit next to check your answers.

  
  

  
   
  • Solutions
    

    Ex 1.      40/119

    EX 2.     39/10

    EX 3.     -11

    Ex 4.     -9 9/11

    Ex 5.   34.926

    Ex 6.   57.686

    
    

    
     
• Mixed Exercises
  

  Ex 1.     6  x -82
  13
  Ex 2.    45.89 x  16    (Round answer to 2 places after the decimal .)
  9
  Ex 3.     - 3  x - 7
  10      16
  EX 4.    - 33  1  x 42
  7
  Ex 5.      542.71  x  68.31
  72.30       13.46
  (Round answer to 2 places after the decimal)
  Ex 6.     34  x  89       ( Convert answer to an improper fraction. )
  3        6
  Hit next to check your answers.

  
  

  
   
  • Solutions
    

    Ex 1.    -37 11/13

    Ex 2.    81.58

    Ex 3.    21/160

    Ex 4.    -1392

    Ex 5.    38.07

    Ex 6.    1513/9

    
    

    
     

What numbers are rational?

• Integers
  

  Integers can be written in the form a/b  by putting the integer over 1.

  - 3 =  - 3                                       6 =  6

  1                                               1

  
  

  
   
• Fractions
  

  Fractions are already in the form a/b  and can be either proper, improper, or mixed numbers.

  2                   13                         -5   7

  9                    7                               11

  
  

  
   
• Terminating Decimals
  

  All terminating and repeating decimals can be written in the form a/b .

  0.685 is 685 thousandths which is 685 over 1000.

  Answer:    685   =  137   Reduce

  1000       20    (Your calculator will do this for you.)

  
  

  
   
• Repeating Decimals
  

  Because of the extensive use of calculators this process is not used very much anymore, but some you should know by sight.

  
  

  
   

Using the OGT Calculator

The key you will need to multiply rational numbers with your calculator is the fraction key  .  It is in the third row and the fifth column.  This will allow you to input fractions, both proper and improper, and mixed numbers.  Your solution will be a proper fraction or mixed number. You can also change mixed number to improper fractions and improper fractions to mixed numbers using the inverse key  which is the second key in the first row, and the fraction key  . Also to input a negative number you use the  key in the last row to the left of the  key. You input the number first then the  key.

• Proper Fractions
  

  3    x    9    =                                      10        11

  Key Strokes:

  Display:  27  110

  Answer:    27/110

  
  

  
   
• Improper Fractions
  

  -7   x   28   =                                        4         21

  Key Strokes:

  (The calculator will change improper fractions into mixed)

  Display:   -2 _1   3

  Answer:  -2 1/3

  Do not clear the answer from the calculator.

  To change the answer into an improper fraction use  then  .

  Keystrokes:

  Display:  -7  3

  Answer:   -7/3

  
  

  
   
• Mixed Numbers
  

  You do not have to change mixed numbers to improper fractions before multiplying using the calculator, you can input them as mixed numbers using the  .

  -4  5   x   7  11        9             20

  Keystrokes:

  Display:  -34 _ 71  180

  Answer:  -34 71/180

  Do not clear the answer from the calculator

  To change the answer into an improper fraction use  then  .

  Keystrokes:

  Display: -6191  180

  Answer:  -6191/180

  
  

  
   
• Integers
  

  If you are multiplying an integer by a fraction you do not have to change the integer into fraction form with the calculator.

  4  x 6 =

  9

  Key Strokes :

  Display:   2 _2  3

  Answer:  2 2/3

  Do not clear the answer from the calculator

  To change the answer into an improper fraction use  then  .

  Keystrokes:

  Display:  -7 3

  Answer:   -7/3

  
  
  
  
  

  
   
• Decimals
  

  When using the calculator you do not have to change decimals to fraction form, but remember your answer will be in decimal form.

  7.38  x   -9    =                                                    11

  Keystrokes:

  Display:  -6.038181818

  Answer:  -6.04

  Make sure you read the directions to determine how many decimal places to round to, but 2 places after the decimal will usually be sufficient.

  
  

  
   
• Decimal over Decimal
  

  In the following problem you are not multiplying by a rational number. But since the fraction bar also represents a division problem there is no need to panic, you can easily use your calculator to find the answer. All you have to do is use the division key  instead of the fraction key  .

  3.67    x    9.25    =                                          11.27

  Keystrokes:

  Display:  3.12200532

  Answer:  3.12

  Make sure you read the directions to determine how many decimal places to round to, but 2 places after the decimal will usually be sufficient.