MULTIPLICATION. 64. A person spends seven shillings daily. How much will he spend in six days? Since in one day he spends 7 shillings, in two days his expenses will be 7+7 shillings, in three days 7+7+7 shillings, &c.; therefore, it is evident that we have to repeat as many times as there are days, or as many times as there are units in 6. Then the expenses are 6 times 7 or 42 shillings, which is thus expressed, 6 x7=42. The same result would have been obtained had we added 7 shillings 6 times to itself, as follows: 7+7+7+ 7+7+7=42. To repeat a number several times is to multiply it. 65. Therefore, to multiply is to repeat a number called multiplicand as many times as there are units in another, called multiplier. The result of a multiplication is called product. In the previous question, which is the multiplicand, which the multiplier, and which the product? 66. The multiplier and multiplicand are also named terms or factors. This The learner will construct the following table, called Multiplication Table, or Pythagoras' Table, from its inventor. he may do several times, in order to get very perfect in its contents. Let him write down the first horizontal and vertical lines, then repeating every figure in the horizontal line by the figures in the vertical one, the results will be the several horizontal lines. 1 2 4 2 MULTIPLICATION TABLE. 3 4 5 6 7 81 9 10 11 12 6 8 10 12 14 16 18 20 22 24 3 6 9 12 15 18 21 24 27 30 33| 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72 7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 72 81 90 99108 80 9 18 27 36 45 54 63 12 24 36 48 60 72 84 96 68. What is the product of 4 and 5? Therefore, 4 and 5 are factors of 20. 90 100 110 120| 99110121 132 108 120132144 Answer, 20. Of what number are 6 and 8 the factors? 8 9 What are the factors of 8, 12, 15, &c. ? 69. Such numbers as 5, 7, 19, &c., which have no factors, but unity and themselves, are named prime numbers; the others are called multiples. 70. The following table is very useful, and may be made by the student : 60=2×30, 3× 20, 4x 15, 5 x 12, 6 x 10. 84 2×42, 3×28, 4×21, 6x14, 7 x 12. 85=5 X 17. 86=2×43. 87=3× 29. 88 2× 44, 4×22, 8x 11. 90=2×45, 3 x30, 5 x 18, 6x 15, 9x 10. 91=7X13. 92=2×46, 4× 23. 93=3×31. 94=2×47. 95=5X19. 96=2×48, 3× 32, 4×24, 6x16, 8x 12. 108 2×54, 3×36, 4×27, 6x 18, 9 x 12. 110=2× 55, 5 × 22, 10×11. 111=3x37. 112=2×56, 4×28, 7 x 16, 8x14. 114=2x57, 3 x 38, 6x 19. 115=5 x 23. 116=2×58, 4×29. 117=3×39, 9×13, 118=2×59, 119=7x17. 120 2x60, 3x40, 4x 30, 5 x 24, 6x 20, 8x 15, 10 x 12. 121 11 x 11. 122=2×61. 123=3x41. 124 2×62, 4×31. 125=5 × 25. 126=2×63, 3×42, 6×21, 7×18, 9×14. 128 2×64, 4x32, 8x16. 129 3 x 43. 130=2×65, 5 × 26, 10 × 13. 132 2×66, 3×44, 4×33, 6×22, 11 x 12. 1337x19. 140=2× 70, 4×35, 5 × 28, 7×20, 10× 14. 141=3×47. 142=2×71. 143 11 x 13. 144 = 2×72, 3 x 48, 4x 36, 6x24, 8x 18, 9×16, 12 x 12. 71. A man gains £2347 yearly. How many pounds does he gain in six years? The answer to this question might be found in adding six numbers equal to 2347, as it is done below:: 2347+2347+2347+2347+2347+2347=14082. But we notice that we have taken 6 times the 7 units of the multiplicand, 6 times the four tens, &c. Therefore, we are led |