By William G. McCallum, Eric Connally, Deborah Hughes-Hallett
This e-book bargains a clean method of algebra that specializes in instructing readers how one can actually comprehend the rules, instead of viewing them in simple terms as instruments for other kinds of arithmetic. It is determined by a storyline to shape the spine of the chapters and make the cloth extra enticing. Conceptual workout units are incorporated to teach how the knowledge is utilized within the actual international. utilizing symbolic notation as a framework, enterprise execs will come away with a tremendously stronger ability set.
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Additional info for Algebra: Form and Function
4. 5. Equivalent Equations Versus Equivalent Expressions Let us compare what we have learned about expressions and equations. To transform an equation into an equivalent equation, we can use any operation that does not change the equality of the two sides. However, when we solve an equation, the expressions on either side of the equal sign may not be equivalent to the previous expressions. Consider the equation 2x + 5 = 13, whose solution is 4. If we subtract 5 from both sides of the equation, we get 2x = 8 whose solution is also 4.
This says that if the average of three tests counts for 60%, then each test alone counts for 20%. Whether you choose the form where the multiplication has been distributed or not depends on how you want to use an expression. Apago PDF Enhancer Example 8 Which of the two expressions in Example 7 would you use if you (a) knew all of the test scores and wanted to compute their contribution to your final grade? (b) wanted to know the effect on your final grade of getting 10 more points on the second test?
2b. 2b In general, we have: The Distributive Law For any numbers a, b, and c, a(b + c) = ab + ac. We say that multiplication by the number a distributes over the sum b + c. 34 Chapter 2 RULES FOR EXPRESSIONS AND THE REASONS FOR THEM Example 1 Use the distributive law to write two equivalent expressions for the perimeter of a rectangle, and interpret each expression in words. Solution Let l be the length and w the width of the rectangle. The perimeter is the sum of the lengths of the 4 sides. Since there are 2 sides of length l and 2 of length w, the perimeter is given by the expression 2l + 2w.