3 Title

Beginning Algebra
Tutorial 8: Properties of Real Numbers

 Answer/Discussion to 1a  xy Using the commutative property of multiplication (where changing the order of a product does not change the value of it), we get  xy = yx (return to problem 1a)

 Answer/Discussion to 1b .1 + 3x Using the commutative property of addition (where changing the order of a sum does not change the value of it), we get .1 + 3x = 3x + .1 (return to problem 1b)

 Answer/Discussion to 2a (a + b) + 1.5 Using the associative property of addition (where changing the grouping of a sum does not change the value of it), we get  (a + b) + 1.5 = a + (b + 1.5) (return to problem 2a)

 Answer/Discussion to 2b 5(xy) Using the associative property of multiplication (where changing the grouping of a product does not change the value of it), we get  5(xy) = (5x)y (return to problem 2b)

 Answer/Discussion to 3a -2(x - 5)

 *Distribute -2 to EVERY term *Multiply

 Answer/Discussion to 3b  7(5a + 4b + 3c)

 *Distribute 7 to EVERY term *Multiply

 Answer/Discussion to 4a  -7 The opposite of -7 is 7, since -7 + 7 = 0. The reciprocal of -7 is -1/7, since -7(-1/7) = 1. (return to problem 4a)

 Answer/Discussion to 4b 3/5 The opposite of 3/5 is -3/5, since 3/5 + (-3/5) = 0. The reciprocal of 3/5 is 5/3, since (3/5)(5/3) = 1. (return to problem 4b)

Last revised on July 24, 2011 by Kim Seward.