Math 017 Materials With Exercises

Example 3.5 Replace with expressions such that the resulting statements are true. Use parentheseswhen needed.a) 2x y 5z 2xb) xyz z Solution:a) 2x y 5z y 5z 2x; y 5zb) xyz z(x)y ; (x) yCommutative property of multiplication. Rearranging factors results in equivalent expressionsMultiplication, like addition, is commutative. the result of multiplication does not depend on the order,35 53. In general, we haveCommutative Propertyof Multiplicationxy yx orx y y xThis means that, the rearrangement of the order of factors results in an equivalent expression.For example,3 32a a 2 , x y yx or ( a b)x x(a b).Factors can also be rearranged if we have more than two factors. For example,3ab ba 3,cdef dcef efdc fedc(or any other order of factors of c, d, e, and f)Example 3.6 Rewrite the expressiona different order.a 1y x in two equivalent forms by multiplying its factors inbSolution:We can rewrite the above expression in more than two equivalent forms. For example,a 1 a 1a 1 a 1a 1x y , x y , yx , x y , or y x . Any two would be theb b b bbcorrect answer.Applying rules of operations on fractions results in an equivalent expressionThe rules for addition and subtraction of fractions with common denominators areRule for Addition andSubtraction ofFractions with CommonDenominatorsacbca bca b a b , c 0c c c27