Observe that this work is not different from that given under example II., page 111., except that the number of zeros to be annexed to the numerator is always two. Why? (a) Find the sum of the twenty decimals. (b) Find the sum of the twenty common fractions. (a) Find the sum of the nine decimals. (b) Find the sum of the nine common fractions. Fractions. III. Reduce to hundredths. NOTE. Such fractions as the following may be easily reduced to hundredths by dividing the numerator and the denominator of each by that number which will change the denominator to 100.* (a) Find the sum of the twelve results. (b) Find the sum of the twelve common fractions. NOTE.-Multiply the numerator and the denominator of each fraction by that number which will change the denominator to 100*. (a) Find the sum of the nine decimals. *Every common fraction can be changed to hundredths by annexing two zeros to the numerator and dividing by the denominator; but this method of reduction is not always the most simple. Take of the numerator and g of the denominator. + Multiply the numerator and the denominator by 22. Fractions. 205. DENOMINATE FRACTIONS. 1. One half inch is what part of a foot? 2. Two and inches are what part of a foot? 3. Five and inches are what part of a foot? 4. One half foot is what part of a rod? 5. Three and one half feet are what part of a rod? 6. Ten and one half feet are what part of a rod? 7. Sixty-four rods are what part of a mile? 8. Ninety-six rods are what part of a mile? 9. One hundred eighty rods are what part of a mile? 10. One and one half quarts are what part of a peck? 11. Two and one half quarts are what part of a gallon? 12. Twenty-four quarts are what part of a bushel ? 13. Fourteen ounces are what part of a pound? 14. Seven and one half ounces are what part of a pound? 15. One and one fourth ounces are what part of a pound? 16. Six hundred pounds are what part of a ton? 22. Thirty-two cubic feet are what part of a cord? 25. Seven and one half minutes are what part of an hour? Multiplying both members of the equation (See page 77, Art. 170, Statement 5) by 2, the denominator of the fraction in the equation, we have * Observe that the equation might have been cleared of fractions by multipl ing both its members by 6, the 1. c. m. of 2 and 3. Algebra. 207. PROBLEMS LEADING TO EQUATIONS CONTAINING ONE UNKNOWN QUANTITY WITHOUT FRACTIONS. EXAMPLE. John and Henry together have 60 oranges, and Henry has three times as many as John. Let then How many has each? and x+3x= the number they together have. But they together have 60. Therefore x + 3 x = 60. Therefore John has 15 oranges and Henry has 45 oranges. PROBLEMS. 1. The sum of two numbers is 275, and the greater is four times the less. What are the numbers? 2. Robert has a certain sum of money and Harry has five times as much; together they have $216. How many dollars has each ? 3. One number is four times another, and their difference is 270. What are the numbers? 4. Peter has a certain number of marbles and William has 8 more than Peter; together they have 96 marbles. How many has each? 5. Sarah has a certain number of pennies and her sister has nine more than twice as many; together they have 93. How many has each? 6. Two times Reuben's money plus three times his money equals 175 dollars. How many dollars has he? |