9 40. Divide 18 × 5 × 6 by 7 × 4 × 5. Cancel the common factor 5 from both dividend and divi 3 18 × 5 × 6 7×4×5 7 2 27 = = 39 sor, and the common factor 2 from 6 in the dividend and 4 in the divisor. Cancel the remaining factor 2 from the 4 in the divisor with the factor 2 in 18 in the dividend. The product of the factors remaining in the dividend is 27, and of those in the divisor, 7. 27 divided by 7 gives the quotient 34. Divide 9 × 2 × 6 by 6 × 6 × 3. NOTE. When the divisor equals the dividend, the quotient is 1. This result will be found when all the factors of the dividend and the divisor are canceled. 1. How many pounds of sugar at 6 cents a pound can be bought for 9 yards of calico at 12 cents a yard? 9 × 12 6 9 × 12 cents equals the cost of the = 18 calico. As many pounds of sugar must be given for the calico as there are 6 cents in 9 x 12 cents. 2. How many pairs of shoes at $3.00 a pair, must be given in exchange for 30 bushels of potatoes at 50 cents a bushel? 3. A farmer sold to a grocer 19 bushels of apples at 75 cents a bushel, and took his pay in coffee at 30 cents a pound. How many pounds did he receive? 4. A milkman sells daily 50 quarts of milk at 6 cents a quart. How many yards of carpet at 90 cents a yard can be bought for the milk sold in 7 days? 5. For 12 days' work of 8 hours each a workman received $24. How much at that rate would he receive for 18 days' work of 9 hours each? 6. Mr. Jones sold 121 pounds of beef at 14 cents a pound, and took his pay in potatoes at 77 cents a bushel; how many bushels did he receive? 7. On each of 6 days a grocer sold 150 pounds of sugar at 8 cents a pound. How many pounds of tea must he sell on each of 4 days at 60 cents a pound to equal the amount he received for the sugar? 8. Make a problem for 24 divided by 3 × 2. 9. Make a problem for 45 divided by 3 × 5. 1. A Fraction is one or more of the equal parts of a unit. One of the equal parts into which the unit is divided is a fractional unit. The value of a fraction depends both upon the size of the fractional unit and the number of fractional units expressed. How many halves in a dollar? an apple? a bushel? a mile? How many thirds in an orange? a loaf of bread? How many sevenths in a peck? in a quart? 2. A fraction is expressed by two numbers, one written under the other, with a horizontal line between them; as, 3, 1, 3, etc. The number below the line shows the number of equal parts into which the unit is divided; it is called the Denominator. The number above the line shows the number of equal parts taken in the fractional number; it is called the Numerator. The numerator and denominator are called the Terms of a fraction. 3. Read the following fractions. In each case tell into how many parts the unit is divided. 4. A Proper Fraction is one whose value is less than one; as,,,. The numerator of a proper fraction is less than the denominator. 5. An Improper Fraction is one whose value is equal to, or greater than, one; as, 4, 3, . The numerator is equal to, or greater than, the denominator. 6. A Mixed Number is an integer and a fraction united; as, 31, 43, 295. 7. To reduce integers and mixed numbers to fractions. How many fourths in an orange? How many fourths in 6 oranges ? How many fifths in a melon? In 3 melons? In one melon there are five fifths; in 3 melons there are three times five fifths. How many sevenths in 4? In 6? In 8? In one loaf there are three thirds. In three loaves there are nine thirds. Nine thirds and one third are ten thirds. There are ten thirds in 33 loaves of bread. How many sixths in 4? 34? 51? How many sevenths in 4? 6? 8? How many tenths in 3? 6? 5? How many ninths in 14 apples? Reduce to improper fractions: 1.25.94, 7. 136 10. 98% 13. 671% 16.143.13 4 2. 36 5.86 8. 3423 11. 873 13 14.924 17. 294.5% 15. 78236 18. 6731880 300 99 18. 14 14 times = 136, 136 + 3 = 133. Ans. Reduce: 1. 18 to thirds. 3. 284 to fifths. 2. 25 to sixths. 4. 493 to sevenths. 5. 533 to ninths. 6. 647 to twelfths. Write a rule for reducing a mixed number to a fraction. |