STEPS TO GENERAL RULE. 1. Both expressions, 3 x 4 and 4 × 3, =? 2. What principle do you find established on page 37? 3. How much is × 6? × 18? 4. How much is 6 × 1? 18 × 1? 5. How much is of 6?of 18? 6. "Of" between a fraction and a following number is equivalent to what sign? 7. Express 27 × by using "of.” 8. In how many ways can you indicate the product of 16 1. Fractions, as factors, may be used in any convenient order. 2. A fractional multiplier may be used as expressing the part of the multiplicand to be taken. EXERCISES. 1. Multiply by 3. Process. Explanation. {x}=} of {, Principle 2. of = { } of } 5 8 X 3 Write the integers and mixed numbers in fractional form; cancel common factors, and find the product of the remaining factors of the numerators for a new numerator, and of the denominators for a new denominator. of of 15? 2. of 1 of 8 X 3. 31 × × 4 × 3 of 7? 4. 5 times 18 × § of 3 times of 4? 6. 1 of 34 of 34 × 7 of 49? 7. 18 of 18 × 28 of 118? 8. 19 of 102 × 144 of 273 of 1898? Required the cost of: 1728 PROBLEMS. 1. 45 pairs of shoes at $14 per pair. 2. of a yard of cloth at $5 a yard. 3. 120 yards of ribbon at 163 cents a yard. 4. 44 tons of hay at $167 per ton. 5. 465 Rochester lamps at $73 apiece. 6. 250 tons of coal at $63 a ton. 7. 127 cords of wood at $53 a cord. 8. If 16 feet make a rod, how many feet are there in 51 rods? 9. There are 24 many cubic feet in 5 cubic feet in a perch of stone. How perches? 10. Mr. Lipmann bought a lot of crockery, of which the retail price was $5763, but he got a reduction of for wholesale and for cash. What amount did he pay? DIVISION OF FRACTIONS. INDUCTIVE STEPS. 1. 1 divided by 1 equals what? 4 divided by 1 equals what? 2. If ÷ 1 = , equals how many times ? 3. If ÷ = 3 times, } } } ÷ } = } × } 8 = times. Hence, 4. Divide in like manner by and by . What principles on page 68 did you apply? become X, and has become, i.e., has become inverted. |