Mary bought of a yard of silk and used of it. What part of a yard did she use? of yd. =? 6 To reduce 12 to lower terms, both terms may be divided first by 3 and then by 2. 6 1/2 = 6 ÷ 3 12 ÷ 3' 2 ÷ 2 or 4.4 = 4 ÷ 2' or 1. The part of a yard used was. This problem could have been solved more quickly by dividing by the 3 and then by the 2 (necessary in the reduction) before finding the product of the numerators and of the denominators. Dividing a number in both numerator and denominator by crossing out, or canceling, the 3's, we have: Dividing a number in both numerator and denominator by 2, we have: × or 1. 2 This short method of multiplying is called cancellation. In cancellation, as in the reduction of a fraction to lower terms, always divide both the numerator and the denominator by the same number. Explain how the answer to the following problem was found: 1 × 1/2 × 1 = ? 15 84 2 In dividing, notice that when a quotient is 1 it is not usually written. In taking of, we think, but we write only=4. 2 1 8 II. MAKING CHRISTMAS PRESENTS [Use pencil only when needed.] 1. Fred is to make two kodak books for Christmas presents. The cover for one requires of a yard of linen; the cover for the other, of a yard. Find the cost of the linen at 80¢ a yard. Mirror 2. The boy's travel case 5 16 pictured here requires of a yard of canvas of a given width, and 1 roll of braid. How much must be paid for the material if 48¢ a yard is paid for the canvas and 5¢ a roll for the braid? 3. Six calendars are to be tied with silk cord. How many yards are required if of a yard is used for each? 4. From a piece of muslin containing 10 yards, 14 yards are used for one apron and 21 yards for another. How many yards are there left in the piece? 5. Eight candy boxes are to be made. How many sheets of cardboard are required for the boxes if of a sheet is used for each? 6. The work box pictured here is covered with ribbon and lined with silk. Find the cost of the material when of a yard of ribbon is bought at 48¢ a yard and of a yard of silk at $1.60 a yard. 7. Elizabeth dresses 3 dolls for Christmas presents. For each doll she uses of a yard of muslin, of a yard of lace, and of a yard of ribbon. Find the amount of each material used. *8. In buying material for Christmas presents, Margaret bought of a yard of silk at $1.25 a yard, of a yard of velvet ribbon at 80¢ a yard, and yard of silk braid at 30¢ a yard. Find the total cost. MIXED NUMBER AND INTEGER IN MULTIPLICATION 69 45. The Mixed Number and the Integer in Multiplication I Pantry shelves are each to be 42 feet long. How long a board of the right width is required for 3 shelves? At 9e a foot, how much must be paid for 83 feet of picture molding? To multiply a mixed number by an integer, or an integer by a mixed number: first, find the product of the fraction and the integer; next, find the product of the two integers; then, add the two products. [Use pencil only when needed.] 1. Multiply 3 ft. by 4; 121⁄2 in. by 5; 6¢ by 21; 8¢ by 51; 21 gal. by 7. 2. What is the length of 2 strips of wood, each 161⁄2 inches long? Of 4 strips, each 121 inches long? 3. Pegs 5 inches long are to be made for garden markers. How long a strip of wood the width and thickness of the pegs is required for 12 pegs? 4. A boy purchases 2 lb. of nails at 9¢ a pound; 13 doz. screws at 8¢ a dozen; and of a pound of putty at 8¢ a pound. Find how much he owed. *36. Find the sum of 12 × 7 and 163 x 5. II. IN A BOY's CARPENTER SHOP [Use pencil only when needed.] 1. The boards used in making the ends, sides, and roof of this bird house are each 8 inches wide. The board for the floor is 1 times as wide. What is its width? Find the length of board required: 2. For the 2 end pieces, each 111⁄2 inches long. 3. For the 2 side pieces, each 12 inches long. 4. For the 2 sides to the roof, each 18 inches long. 5. What is the entire length in inches of the board required for the ends, sides, and roof? What is the entire length in feet? |