improper fractions. 1. How many halves are there in 1 apple? In 4 apples? In 6 apples? 2. How many thirds are there in 1 orange? In 3 oranges? In 5 oranges? 3. How many fourths are there in 2? In 3? In 4? 4. How many fifths are there in 3? In 4? In 6? 5. How many fourths are there in 14? In 23? RULE.—Multiply the integers by the given denominator, to this product add the numerator of the fractional part, if there be any, and write the result over the given denominator. 2. Change 51 to fourths. 4. Reduce 131 to sixths. REDUCTION. 6. Change 5 to ninths. To eighteenths. 7. Change 65 to twelfths. To twenty-fourths. Reduce to improper fractions: 165. To reduce improper fractions to integers or mixed numbers. 1. How many days are there in 6 half-days? In 8 halfdays? In 14 half-days? 2. How many yards are there in 9 thirds of a yard? In 15 thirds? In 18 thirds? 3. If a boy pick bushel of peaches per hour, how many bushels can he pick in 10 hours? How many are 10 halves? 4. If a man can earn of a dollar per hour, how much How many are 12 fourths? can he earn in 12 hours? 5. How many units are there in 15? 36? 32? 61? 81? 응? 6. How many dollars are there in $37? $47? $118? $109? RULE.-Divide the numerator by the denominator. 167. To reduce dissimilar fractions to similar fractions. 1. How many fourths are there in of an orange? 2. How many sixths of a field are there in of a field? 3. How many eighths in ? How many ninths in ? 4. Express each of the fractions 3, 4, and 1⁄2 as twelfths. 5. Express each of the fractions and as twentieths. 6. If is divided into 3 equal parts, how large is each part? 7. If is divided into 2 equal parts, how large is each part? 8. When and are divided into equal parts, what parts are common to both? 9. When and are divided into equal parts, what parts are common to both ? 10. What equal parts are common to both and †? 11. When, and are divided into equal parts, what parts are common to all? 12. Change,,, to equivalent fractions having the same fractional unit. Express the resulting fractions in equivalent fractions having their least common denominator. 168. Similar Fractions are those that have the same fractional unit. 169. Dissimilar Fractions are those that have not the same fractional unit. 170. Similar fractions have a Common Denominator. 171. When similar fractions are expressed in their smallest terms they have their Least Common Denominator. 172. PRINCIPLES.—1. A common denominator of two or more fractions is a common multiple of their denominators. 2. The least common denominator of two or more fractions is the least common multiple of their denominators. WRITTEN EXERCISES. 173. 1. Reduce and to similar fractions. PROCESS. ANALYSIS. Since similar fractions have a common denominator, to make these fractions similar we must change them to equivalent fractions having a common denominator. Since a common denominator of two or more fractions is a common multiple of their denominators (Prin.), we find a common multiple of the denominators 4 and 8, which is 32. We then multiply the terms of each fraction by such a number as will change the fraction to thirty-seconds. 2. Reduce, and to similar fractions having their least common denominator. RULE. Find the common, or least common multiple of the denominators for a common, or least common denominator. Divide this denominator by the denominator of each fraction and multiply both terms of the fraction by the quotient. Reduce all mixed numbers to improper fractions and all fractions to their smallest terms. Change the following to similar fractions having their least common denominator: 174. 1. James has 2 fifths of a dollar, and his brother has 4 fifths of a dollar. How many fifths have both? 2. George spent $3 on Monday, and $2 on Tuesday. How much did he spend in both days? How many sevenths are and ? |