then add the numerators and place their sum over the common denominator. Simplify this result, if possible. (Sec. 21.) 17. To subtract fractions, first reduce them to their L.C.D., then subtract their numerators and place the result over the common denominator. Simplify, if possible. (Sec. 22.) 3911 17. (a) Change 18" to a mixed number. (b) Change 93" to an improper fraction. 18. Which is greater, 12" or }''? 19. Reduce the following fractions to their lowest terms: 18 12 8 16, 32, 12. 2911 32 20. Change the following fractions to their L.C.D.: 38", H", 3", 1" 21. Add the following fractions: ", 1", 1" and ". , 16 171 22. From }" take 18". 3 16 32 711 23. Fig. 8 shows a panel for a door. What is the thickness of the panel? 24. The door stile shown in Fig. 8. is to be 13" thick. If the veneers are each ji" thick, how thick must the core be? 25. A drawing board is built of three plies; one is 3" thick, one is it" thi and one is 3" thick. What is the total thickness of the board? 26. A dressed board is required fl" thick. How much must be planed off from a rough board 1" thick to give the required thickness? 27. A floor is laid by first putting down the rough sheathing which is }" thick. On this are placed furring strips }" thick and then the top or finish floor is laid which consists of boards 13" thick. What is the total thickness of this floor? 28. Fig. 9 shows a board grooved for splines. If a 1"X}" spline is to be used, what will be the width of the projection A on each side of the groove? 29. Fig. 10 shows 1X4 partition material in section. Give the missing dimensions indicated by the letters A, B, C and D. 30. Flooring 11" nominal size is worked to 132" in the mill. How much is it scant? 31. Fig. 11 shows a mortise and tenon joint for a table leg. How far back from the face of the leg must the outside edge of the mortise be? In other words, what is the distance A? 32. What is the missing dimension on the dovetail drawer joint indicated by the letter A in Fig. 12? 33. What must be the size of the square key used for the dovetail mortise joint shown in Fig. 13? 34. A lumber dealer has in stock 2000 bundles of shingles. Of these 400 bundles are graded Extra Clear and 1600 are Extra Each grade is what fractional part of the whole stock? Give the fractions in their lowest terms. *A*. CHAPTER III MIXED NUMBERS. ADDITION, SUBTRACTION AND MULTIPLICATION OF MIXED NUMBERS. CAN- 23. Working with Mixed Numbers. In performing operations with mixed numbers, there are two possible methods of procedure; either the whole numbers and the fractions may each be handled separately or the mixed numbers may be reduced to improper fractions and the operations performed as though working directly with fractions. In general, the first method is used when adding or subtracting mixed numbers and the second method is used when multiplying or dividing them. 24. Adding Mixed Numbers. It is often necessary to add mixed numbers. Although this operation is somewhat long it is not at all difficult. To add mixed numbers we first add the whole numbers and then the fractions, reducing the final result to its lowest terms. Example. What is the sum of the following dimensions: 67'', 316", 916”, 61" and 4,3"? 28 63" (Reduce fractions to L.C.D.) 32 32 316" 6 32 22 32 911" а Explanation. The first step is to write the numbers in a vertical column for adding. It is then necessary to reduce the fractions to a common denominator before we can add them. The common denominator in this case is easily seen to be 32. We must, then, multiply both the numerator and denominator of each fraction by such a number as will make the denominator of the new fraction 32. After this has been done we add the numerators and place their sum over the common denominator, finally reducing the resulting improper fraction to a mixed number, which is 237". We next add the whole numbers together to get 28 and to this we add the number obtained by adding the fractions. This gives 3032" as the final result. 25. Subtracting Mixed Numbers. To subtract mixed numbers we treat the whole numbers and the fractions separately, just as we did in adding them. We subtract the fractions and the whole numbers separately and reduce the resulting expression to its lowest terms. Example. How much more is 913" than 75"? 91" (Reduce fractions to L.C.D.) =918" 16 511 =718" 216'' 3 11 Ans. -2'64" 511 2'8" Expianation. The first step, just as in adding fractions, is to write the figures in a vertical column. We must then reduce the fractions to a common denominator before we can subtract them. The L.C.D. in this case is 16. We do not have to do anything with the 13" but we do have to change " to sixteenths. Multiplying both the numerator and the denominator of this fraction by 2 gives 18. We can now subtract both the fractions and the whole numbers to get the result, 21”, which tells how many inches longer is a stick which measures 91/" than a stick which measures 75". Sometimes in subtracting mixed numbers we find that the fraction in the subtrahend (the number to be taken away) is larger than the fraction in the minuend (the number from which we subtract). In this case we may borrow one whole unit or 1 from the whole number of the minuend and add it to the fraction of the minuend after it has been reduced to the same denominator. This makes an improper fraction out of it and we can then subtract the other fraction from it. Example. How much wider is a board =57" Ans. 711 5711 |