DIVISION OF FRACTIONS 76. Division of Fractions I 111 [Use pencil for drawings only.] 1. Two pounds of candy are to be put into boxes holding one half pound each. How many boxes are needed? 2. How many lengths one half yard long can be cut from 1 yard of ribbon? From 3 yards? 3. How many times is contained in 1? In 2? In 3? 4. Three apples are each divided into quarters. How many quarters are there? 5. How many quarter-inches are there in 1 inch? In 2 inches? 6. How many times is contained in 1? In 2? In 3? 7. Four sheets of paper are each divided into thirds. How many thirds are there? 8. Show by a drawing how many times of a circle is contained in 2 circles of the same size. In 4 circles. (1) How many times are 3 inches contained in 4 inches? How many times are 3 fourths contained in 4 fourths or one whole? 3 inches are contained in 4 inches 13, or, times. (2) How many times are 2 thirds contained in 3 thirds, or one? It can be seen from the problems above that, in dividing 1 by a fraction, the terms of the fraction expressing the quotient are the same numbers as those in the divisor, but they are in a different position. They are inverted. (A boy standing on his head is inverted; the reflection of a tree in water shows the tree inverted; and a fraction turned upside down is inverted.) & inverted is ; inverted is 3; inverted is §; 2 (which equals †) inverted is . How many times is of a yard contained in 3 yards? of a yard is contained in 3 yards, 4 times. How many times is of a yard contained in of a yard? To divide a number by a fraction, invert the terms of the divisor, and proceed as in multiplication. [Use pencil only when needed.] 1. Divide 8 by ; 9 by ; 20 by ; 14 by ; by §. 2. How many Christmas presents can be wrapped with 6 sheets of paper, if each takes sheet? 3. Photographs are to be tied up with silver cord. How many can be tied up with 7 yards of cord, if each photograph takes of a yard? 4. Boxes are to be filled with candy. How many boxes are required to hold 6 pounds, if each box holds of a pound? (1) How many jelly glasses holding pint each are required for 3 pints of jelly? (2) How many cakes requiring 11⁄2 cups of sugar can be made from 4 cups of sugar? 41 ÷ 11 = ? 4/1/2 = 12/2. 11 = 3. ÷ = ×, or 3. In the division of fractions, change mixed numbers to improper fractions. 17. How many times is 13 yd. contained in 9 yd? 78. Division of Fractions by Integers What is the length of each piece of ribbon when of a yard is cut into 2 equal lengths? When 3 yards is cut into 3 equal lengths? Notice that dividing a number by 2 is the same as multiplying by, and that dividing by 3 is the same as multiplying by 3. 3. A line 71⁄2 inches long is divided into 3 equal lengths. How long is each section? 4. Find the length of each section when a line 3 inches long is divided into 2 sections. When a line 23 inches long is divided into 3 sections. 79. Test and Graded Practice This test is to help you find out and overcome your difficulties in the division of fractions. If you fail to get the right answer to a problem in the test, practice solving the problems in the set below having the same letter, then try the problem again. 1. A 6-inch line is what part of a 12-inch line? A 10-inch line is what part of a 30-inch line? A 12-inch line is what part of a 48-inch line? 2. A package weighing 6 oz. is how many times as heavy as one weighing 3 oz.? A package weighing 16 oz. is how many times as heavy as one weighing 5 oz.? A comparison between two numbers answers one of two questions: What part? or, How many times? (1) What part of 24 oranges are 18 oranges? Since 1 orange is 4 of 24 oranges, 18 oranges are of 24 oranges. † = & (2) How many times 18 oranges are 24 oranges? 24 oranges are, or 13, times 18 oranges. To compare two numbers, express the comparison by writing the numbers as a fraction, and then reduce the fraction to its simplest form. 3. $10 is what part of $15? 4. 18 days are what part of 24 days? 5. 30 miles are what part of 50 miles? 6. A yard is how many times as long as a 24-inch line? 7. A pound is how many times as heavy as 14 ounces? |