OPERATION. 96 544 5 480 64|96|1 32 6412 By this process, it is found that 32 are the greatest common divisor of 96 and 544. Therefore the fraction, reduced to its lowest terms, is 32, Ans. 544 NOTE. By inspecting the above process, it will be seen that 32 are the measure of 64, the first remainder, and 96. Therefore they will be the measure of 96×5+64. As 32 are the measure of 96, they will be the measure of 96, multiplied by any number, and that product increased by 32 taken any number of times. Thus, 32 are the measure of 96×2+32. And universally, any number that is a measure of the remainder and divisor will be a measure of the dividend; and also of the divisor multiplied by any number, and that product increased by the remainder taken any number of times. 2. Reduce to its lowest terms. Ans. 4. Ans. 4. to its lowest terms. Ans. II. TO REDUCE A MIXED NUMBER TO AN IMPROPER FRACTION. Multiply the whole number by the denominator, and to the product add the numerator; the sum will be the numerator of the improper fraction, and the denominator will be the same as before. 1. Reduce 13 to an improper fraction. OPERATION. 13 6 83=83,* Ans. 2. Reduce 197 to an improper fraction. 3. Reduce 62 to an improper fraction. Ans. 182. III. TO REDUCE AN IMPROPER FRACTION TO A WHOLE, OR MIXED NUMBER. Divide the numerator by the denominator, and the quotient will be the whole number. If there be a remainder, write it over the divisor, at the right hand of the quotient. 1. Reduce 182 to a whole, or mixed number. OPERATION. 4|189 471, Ans. In this example, the unit is divided into fourths. Every fourths make a unit. Therefore, as many times as 4 are contained in 189, so many units there will be. I find that 4 are contained in 189, 47 times, and there is 1 remainder. There are, then, in 189, 47 units and of a unit. 6. Reduce 1000000 to a whole number. Ans. 1000000. * This process consists simply in ascertaining the number of sixths in 13 and §. In one unit there are six sixths, and in 13 units there are thirteen times as many sixths as in 1 unit. Hence, 13×6, or 78, express the number of sixths in 13. To 78 add 5, because in there are 5 sixths, and the amount, 83, expresses the number of sixths in 13g. IV. TO REDUCE A COMPOUND FRACTION TO A SIMPLE ONE. Multiply the numerators together for a new numerator, and the denominators for a new denominator. If there be mixed numbers, reduce them to improper fractions, and proceed as the rule directs. 1. Reduce of of to a simple fraction. 글 OPERATION. 1X7X 9 63 The propriety of this process may be seen from the following analysis. One eighth of is nine eightieths; 7 of are seven times as much as one eighth of seven times are 83. of § ; and is 8%, Ans. 2. Reduce of off of 1 to a simple fraction. 160, Ans. 3. Reduce of of of to a simple fraction. * Ans. 25 4. Reduce of of 265 to a mixed number. Ans. 84. 5. Reduce 71⁄2 of 34 of 8041 to a whole number. Hence the compound fraction now is, 140 of 0 of 18=4,}}}, Ans. The first part of this process consists in clearing the numerators and denominators of fractions. This is done by multiplying all the terms of the mixed fraction by the denominators. It is plain that the value of the expression is not changed in doing this, because all the terms are multiplied by the same number. TO MULTIPLY A WHOLE NUMBER BY A FRACTION. Multiply the whole number by the numerator, and divide by the denominator; or divide by the denominator, and multiply by the numerator. The last process may be analyzed thus: one fourth of 87 is 213; and of 87 are 3 times 212, or 654. The first process amounts to this: one fourth of 261 is equal to of 87. As of 1 are equal to 1x3+4=2; or 14x3; so 87X3-4-651; or 87÷4X3=651. 2. Multiply 8756 by 3. Multiply 45 by 7. 4. Multiply 75 by 4. 5. Multiply 84 by . Ans. 7164. Ans. 31. Ans. 324. Ans. 58 VI. TO DIVIDE A WHOLE NUMBER BY A FRACTION. Multiply the whole number by the denominator of the frac tion, and divide the product by the numerator. In example first, I wish to ascertain how many times is contained in 6. It is evident that it is contained in 6 as many times as there are halves in 6. Therefore, 6×2=12, Ans. In the second example, the divisor is . Had the divisor been, then 8×4, or 32, would have been the quotient. But as the divisor is, 32 are three times as large as the true quotient. Therefore, divide 32 by 3, and the quotient, 10, is the answer. Again. is contained in 8 as many times as there are fourths in 8. And are contained in 8 as many times as there are in 8. In 8 there are 32 fourths; as are three times as much as, therefore, there will be as many three fourths as there are one fourths in 8. Therefore, 8x4÷3, show how many times tained in 8. 3. Divide 89 by r 4. Divide 15 by f 5. Divide 27 by r 6. Divide 128 by T. 7. Divide 98 by VII. are con Ans. 139. Ans. 112. Ans. 578. Ans. 1920. Ans. 1666. TO MULTIPLY A FRACTION BY A WHOLE NUMBER. Multiply the numerator by the whole number, or divide the denominator by the whole number, when this can be done with out a remainder. |