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Extra resources for Algebra I (Cliffs Quick Review)
Therefore, if 1 + 3 = 4 and 4 = 2 + 2, then 1 + 3 = 2 + 2. Chapter 4: Equations, Ratios, and Proportions 41 ■ Additive axiom: If a = b and c = d, then a + c = b + d. Therefore, if 1 + 1 = 2 and 3 + 3 = 6, then 1 + 1 + 3 + 3 = 2 + 6. ■ Multiplicative axiom: If a = b and c = d, then ac = bd. Therefore, if 1 = 2/2 and 4 = 8/2, then 1(4) = (2/2)(8/2) Solving equations Remember that an equation is like a balance scale with the equal sign (=) being the fulcrum, or center. Thus, if you do the same thing to both sides of the equal sign (say, add 5 to each side), the equation will still be balanced.
In this instance, the system is unsolvable. Example 4: Solve for p and q. 3p + 4q = 9 2p + 2q = 6 Multiply the second equation by 2. (2)2p + (2)2q = (2)6 4p + 4q = 12 Now subtract the equations. 3p + 4q = 9 ^ - h 4p + 4q = 12 -p = -3 p = 3 52 CliffsQuickReview Algebra I Now that you know p = 3, you may plug in 3 for p in either of the two original equations to find q. 3p + 4q = 9 3(3) + 4q = 9 9 + 4q = 9 4q = 0 q=0 Answer: p = 3, q = 0 Substitution method Sometimes a system is more easily solved by the substitution method.
Decimals. Changing terminating decimals to fractions To change terminating decimals to fractions, simply remember that all numbers to the right of the decimal point are fractions with denominators of only 10, 100, 1000, 10,000, and so forth. Next, use the technique of read it, write it, and reduce it. Example 17: Change the following to fractions in lowest terms. 07 (negative seven hundredths) Write it: –7⁄100 (can’t reduce this one) All rules for signed numbers also apply to operations with decimals.