Dividing by a Unit Fraction. How many thirds of an inch in 1 in.? Then 1+ is how many? What can you say about the values of 1+1 and 3x1? In the same way, what can you say about the values of 3 and 2 × 3? + + What can you say about the values of ÷ 1 and 3 × & ? To divide a number by a unit fraction, multiply the number by the denominator of the fraction. USING WHAT YOU HAVE LEARNED 1. If a sheet of veneer is in. thick, how many sheets pressed together will have a thickness of in.? 16 2. If a sheet of veneer is in. thick, how many sheets pressed together will have a thickness of 21 in. ? 3. If a sheet of blotting paper is in. thick, how many sheets are there in a pile that is 127 in. thick? 4. If a wagon wheel makes of a revolution in going 1 ft., how many feet will it go in making 144 revolutions? DIVIDING BY A FRACTION All work oral 1. Suppose that you have a room 18 ft. wide and wish to find how many strips of carpet & yd. wide will be needed to run lengthwise in the room. First you must find how many yards there are in 18 ft. How many yards are there? 2. If you have to divide 6 yd. by & yd., you may think of the 6 yd. as fourths of a yard. Express 6 as fourths. 3. If now you have to divide 24 by &, you may think of the results in the cases of 24¢÷3¢ and 24 in. 3 in. What are the results? 4. Then how much is 24? How many strips of carpet will you need to carpet the room? 5. Divide by . Multiply g by 5. 6. Show that ÷ gives the same result as §×₺. It should now be clear to the pupil that division by a fraction is a case of multiplication; that is, we divide by multiplying by the fraction inverted. Since the multiplier is always placed first, this practice should be continued, as in the examples above, in order to avoid learning a new order of the factors for this special case. 16 8. How many paper pads, each in. thick, will it take to make a package 18 in., or & in., thick? Dividing by a Fraction or a Mixed Number. If the terms of a fraction are interchanged, the resulting fraction is called the reciprocal of the fraction. The reciprocal of is g. On page 96 we found that we often need to divide by a fraction. We also found how to do this. We know that when we divide by we may multiply by 3, and when we multiply a divisor by 2 we divide the quotient by 2. Therefore, to divide any number by a fraction, multiply the number by the reciprocal of that fraction. Illustrative Problems. 1. Divide by §. we may cancel as here shown, and the This plan is usually less liable to error than 용 the plan of considering the fractional form and P multiplying both terms by 6 × 8, or even by 24. 516 0100 3815 в ။ 9 20 3 8100+ number and the result is found to be 13, as shown above. Further Illustrative Problems. 1. Divide 3 by 23. Instead of reducing 2 to an improper fraction, the more mature pupils may proceed as on page 92, thus: Think of the fractional form and multiply both terms by 3. 3 22 3 × 2+2 6+2 2. Divide 7 by 41. Multiply by 3 × 5 both terms of the fractional form we have In Exs. 1-16 first divide as indicated and then divide the second 17. How many strips of ribbon, each 23 yd. long, can be cut from a piece of ribbon that is 133 yd. long? USING WHAT YOU HAVE LEARNED 1. How many half-yard pieces can be made by cutting 9 yd. of ribbon? by cutting 15 yd. of ribbon ? 2. If your recipe for making cake calls for lb. of sugar, 71 lb. of sugar is enough for how many times as much cake? 3. How many mats, each yd. long, can be made from a strip of carpet 12 yd. long? 4. How many towels, each requiring § yd. of toweling, can be made from a strip 117 yd. long? 5. How many strips of cloth, each 5ğ yd. long, can we get from a strip 48 yd. long? 6. How many city lots, each with 313 ft. frontage, can a man get from a piece of land having 1583 ft. frontage? 7. How many yards of cloth at 663¢ a yard can be bought for $8? for $17? for $36? 8. How many books, each in. thick, will it take to make a pile 23ğ in. high? 9. How many strips of wood, each in. thick, will it take to make a pile 1911 in. high? 19. How many sheets of bookbinding board, each in. thick, will it take to make a pile 93 in. high? 11. If the product of two numbers is 58, and one of the numbers is 3ğ, what is the other number? |