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By Jerry Bobrow
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Additional resources for Algebra I (Cliffs Quick Review)
222... Changing infinite repeating decimals to fractions Infinite repeating decimals are usually represented by putting a line over (sometimes under) the shortest block of repeating decimals. This line is called a vinculum. 333 . . 515151 . . 1474747 . . Notice that only the digits under the vinculum are repeated. Every infinite repeating decimal can be expressed as a fraction. 7. 77777 . . 77777 . . Because 10n and n have the same fractional part, their difference is an integer. 7 9n = 7 Chapter 2: Signed Numbers, Fractions, and Percents 27 You can solve this problem as follows.
Eliminate the percent sign. 2. Move the decimal point two places to the left (sometimes, adding zeros will be necessary). 05 Changing fractions to percents To change fractions to percents, 1. Change to a decimal. 2. Change the decimal to a percent. 05 = 5% Changing percents to fractions To change percents to fractions, 1. Drop the percent sign. 2. Write over one hundred. 3. Reduce if necessary. 29 30 CliffsQuickReview Algebra I Example 25: Change to fractions. (a) 60% = 60⁄100 = 3⁄5 (b) 230% = 230⁄100 = 23⁄10 = 23⁄10 Finding the percent of a number To determine the percent of a number, change the percent to a fraction or decimal (whichever is easier for you) and multiply.
Example 3: Simplify. (a) (a7)3 = a2l (b) (x3y2)4 = x12y8 (c) (2x2y3)3 = (2)3 x6y9 = 8x6y9 Dividing monomials To divide monomials, subtract the exponent of the divisor from the exponent of the dividend of the same base. Example 4: Divide. (a) y 15 = y 11 or y 15 ' y 4 = y 11 y4 (b) x 5y 2 = x 2y x 3y (c) 36a 4 b 6 =- 4a 3b 5 (divide the numbers) - 9ab (d) fg 15 = fg 12 g3 (e) x 5 = 1 (may also be expressed x-3) x8 x3 (f ) - 3 ` xy j ` xy 2 j xy You can simplify the numerator first. - 3 ` xy j ` xy 2 j - 3x 2 y 3 = =- 3xy 2 xy xy Or, because the numerator is all multiplication, you can cancel.
Algebra I (Cliffs Quick Review) by Jerry Bobrow