By Hart W.H.
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Additional resources for Intermediate Algebra for Colleges
L)(o - - 3) 3-Q = = 26. Multiplication and division of fractions To multiply one fraction by another, multiply the numerators for a new numerator and multiply the denominators for a new denominator. 3 ILLUSTRATION = 1. 5 ^ X 6 = = 18 a ^=- o a c ac ** i* j cr oo 7 To divide one fraction by another, invert the divisor dividend by this inverted divisor. 2. ILLUSTRATION o T 4 7 F^JT^K'Q O o i 4 . _ ' b _ a d _ ad be be d It is frequently useful to recall that as a fraction whose denominator any number can be expressed is 1.
333 ILLUSTRATION 6. , a unit in any place in the decimal notation is multiplied by 10, we obtain a unit in the next place to the left. If we divide a unit in any place by 10, we obtain a unit in the next place to the right. The preceding remarks justify the following convenient rules. If I. To multiply a number by the right in the II. left To a number by number. ILLUSTRATION To divide by 7. 67) 1000, which places to the left: move the decimal point one place to number. 7. 567. 021327. * 43. Addition of decimals In finding a sum of decimals, after they have been arranged with the decimal points in a column, it is desirable to add once going upward and then downward to check in each column.
36. g). -*- 2. 39. 2a. 43. || 3o 56 2c ... eg). | + 6. y * d. x 2c 3d ' 48. 12a 8 l_ - 60. 49. 5c - 15 INTRODUCTION TO FRACTIONS AND EXPONENTS d 9 7 -Ml 25 8 -H)H)H)H)- -(-SX-SX-8- 27. Positive integral exponents We write a2 to abbreviate a -a, 3 square of a and a the cube of ILLUSTRATION If 52 1. = and a8 for We a -a' a. call a2 the a. 5-5 = 53 25. = 5* 5' 5 = 125. m is any positive integer,* we define am by the equation 9 a m = a-a-a- (m -a. factors a) (1) am the mth power of the base a and call m the exponent of this power.