Multiplying and Dividing Numbers

Post  2     Multiplying and Dividing Numbers and special note on ZERO.

- 4 times 5 = -20      50  divided by -10 = - 5                     (- 8) 9 =-72      If multiplying or dividing by one positive number and one negative then the answer is negative.

- 4(- 8) = +32 or 32             (-7)(- 6) = +42 or 42                -18 divided by - 3 = 6     If multiplying or dividing by a negative number and another  negative then the answer is positive.

+4(+ 8) =+32    You know a positive number multiplied or divided by another positive number yields a positive answer.

HOW to write a Multiply in Algebra! In algebra we do NOT use the x or the dot for multiply.  We write the numbers next to each other; some times we use  parentheses.     3(6) or (3)(6)   means multiply 3 and 6.

You must use only two of the numbers at a time to determine their sign. Try these examples:          A.     -6(-7)(-4)  = +42(-4) = - 168.     The -6 times the -7 gives + 42. Then multiply by the -4.          B.     (-4)6(-2) = -24(-2) = +48  or 48. The -4 times the 6 gives -24. Then multiply by the -2.   The rules for  deciding the sign of the answer for multiplying and dividing are the same.  The / symbol means divide by or is the fraction bar.    It is also the divide key on the calculator.

FRACTIONS:       which ones are less than 1 whole?  5/8 or 8/5.   And 9/11 or 11/9?                                                                    And 14/7 or 7/14?             DO YOU KNOW?    5/8 means 5 divided by 8.  This should give you a decimal number that is less than 1 whole if you complete the division.  Do NOT confuse it with 8 divided by 5   or also called 8-fifths.          This is more than 1 whole.   It is 1 and 3/5. Be sure you know which "way" to divide.    Do the division for the 5/8 and send me your answer in an email Click: Susan O. Johnsey .

WHAT ABOUT ZERO in division?    Zero is well understood with adding, subtracting and multiplying.  But it is a bit peculiar, some would say, when it comes to division.        Look carefully:       0/4 = 0              4/4= 1           4/(-4)= -1                0/-4 = 0                   -4 / 4 = -1              -4/(-4) = 1           4/0 is undefined.     Division by zero    and   Division into zero are quite different.

A common fraction that most students know is 4/5, that is, 4-fifths.   4/5  means 4 divided by 5 .  Will the division give you a number larger than 1 or smaller than 1??  Can you read these fractions? Watch out!!     6/5 is read "6-fifths"    5/5 is read "5-fifths" and equals 1 whole    5/4 is read "5-fourths".      OK?    Keep going please:              5/3 is read_______    5/2 is read_________    5/1  is read__________                 5/3 is read 5-thirds   5/2 is read 5-halves   5/1  is read 5 wholes                       5/0 is read_______   oops what did you say here?   5- zeroths!!!                       what is that?    there is no such fraction!          And what about the 5/0?                         5/0  is undefined (have you ever heard of 5-zeroths?   I hope not! )    5/0 means 5 divided by 0. There is not a simple number answer that can be given.  This is studied in Calculus so I will tell you for now to just know  division BY zero is undefined.   Do not confuse it with division into zero.        0/4 = 0

 

All division BY zero is undefined:                     6 /0  or 6 divided by 0, and even,   0/0 are undefined. 0 divided  by 3 (zero-thirds) is 0,           but 3 divided by 0 (that is 3-zeroths) is undefined.