## MATH - SCIENCE INTEGRATION

### 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

 To multiply rational numbers you multiply (across)        numerator       times     numerator      over             denominator     times     denominator

• 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, fractions, and repeating and terminating decimals can all be written in the form a/b , so the are all rational numbers. You are not going to change the value of the number just the way it looks.

• 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.