PROBLEMS Before working the following problems record the data on suitable blanks. 1. A. D. Price had a balance in the bank, made deposits, and drew checks as follows: May 2d, balance $2480.35; deposits $295.60; checks $24.70, $39.20, $10, $62.50. May 3d, deposits $328.25; checks $16.35, $1480.00, $4.25. May 4th, deposits $395.10; checks $12.50. May 5th, deposits $247.20; checks $21.40, $50, $7.15, $4.80, $18.65, $21.45, $34.75. May 6th, deposits $435.90; checks $16.40, $25.00, $31.20. May 7th, deposits $527.35; checks $20, $20, $20, $25, $25, $35. Enter the daily balances and check as on page 28. 2. On a certain day the collection department of a bank showed the following items: A's paper, face $3600; discount $41.60; Com. & Exch. $1.50 1.20; E's paper, face 420; discount 6.30; Com. & Exch. 1.20 4.60; Com. & Exch. 2.50 Com. & Exch. 5.60 Com. & Exch. 2.75 = 3. From a large farm wheat was hauled to the elevator as indicated below. Each load was weighed on the wagon (Gross Weight), and after unloading, the wagon was weighed (Tare). Find the net weight of the wheat and the number of bushels. (60 lb. 1 bushel.) Gross Weight 3760, Tare 1460; Gr. Wt. 4420, T. 1480; Gr. Wt. 4540, T. 1470; Gr. Wt. 4390, T. 1510; Gr. Wt. 4360, T. 1500; Gr. Wt. 4520, T. 1480; Gr. Wt. 4510, T. 1460; Gr. Wt. 4490, T. 1420; Gr. Wt. 4520, T. 1450; Gr. Wt. 4320, T. 1490; Gr. Wt. 4610, T. 1520; Gr. Wt. 4620, T. 1500; Gr. Wt. 4160, T. 1420. CHAPTER IV MULTIPLICATION 37. Definition of Multiplication. — Multiplication is the process of taking one number, called the multiplicand, as many times as the number one is contained in another number, called the multiplier. 38. Uses of Multiplication. In business multiplication is in constant use and must be mastered thoroughly by anyone who wishes to become an accountant or even a clerk. Practically all bills made out involve multiplication. 39. Multiplication Table. - All multiplication is based on the following table, which should be memorized perfectly. Sometimes the table is given to 12 × 12, but the table to 10 × 20 is much more useful. 40. Product, Factors. The result obtained by multiplication is called the product. The multiplier and multiplicand are called the factors of the product. Thus 6 × 8 is read "6 times 8" and indicates that the product of 6 and 8 is to be found. The sign X placed between two numbers indicates that one of the numbers is to be multiplied by the other. 41. Multiplying by 10, 100, etc. It follows directly from the principles of the decimal notation that annexing a zero at the right of a number multiplies it by 10, since this moves each figure into the place of the next higher order. Similarly, annexing two zeros at the right multiplies the number by 100, annexing three zeros multiplies it by 1000, and so on. 42. Multiplying by a Product. The following example illustrates an important principle in multiplication : = To multiply 8 by 15 we may multiply 8 by 3 and the product by 5, obtaining 3 × 8 24 and 5 X 24 product by 3, obtaining 5 × 8 = = 120. Or we may multiply 8 by 5 and the 40 and 3 X 40 120. Hence we have the = Rule: To multiply by the product of two numbers we may multiply by one of the factors and the product so found by the other factor. This principle is used when multiplying by such numbers as 60, 700, 8000, 340, and so on. Thus to multiply by 60 we first multiply by 6 and then multiply the product by 10 by annexing a zero to the right. To multiply by 700 we first multiply by 7 and then multiply the product by 100 by annexing 2 zeros to the right. Similarly to multiply by 8000 we first multiply by 8 and then multiply by 1000 by annexing three zeros to the right. 43. Multiplying a Sum. The following example illustrates another principle in multiplication: To multiply the sum of two numbers as 6 and 8 by 4 we may multiply 6 and 8 by 4 separately, and then add the products. Hence we have the Rule: To multiply the sum of two numbers we may multiply each number separately and then add the products. This principle is used when multiplying a number having two or more figures. 44. General Process of Multiplication. The general process of multiplication is a direct result of the two principles in §§ 42, 43. Example. Multiply 3894 by 378. In the above example how do we multiply by 70? How do we multiply by 300? What zeros are omitted in writing down the work? WRITTEN EXERCISES Multiply each of the following. Check by repeating the work. Remember that a result is useless until you know it is correct. 45. Multiplication of Numbers Containing Zeros. Example 1. Multiply 374 by 208. 374 2992 748 77792 To multiply by 208 we multiply by 8 and by 200. Explain how the multiplication by 200 is effected. Example 2. Multiply 4700 by 830. 4700 830 141 376 To multiply 4700 by 830 multiply 47 by 83 and then multiply the product by 1000 by annexing three zeros. We notice that multiplying either factor by a number multiplies the product by that number. That is, annexing one zero to one of the factors requires us to annex a zero to the product. Hence, omit all zeros to the right and multiply the remaining numbers. Annex to the result as many zeros as were omitted in both factors. 3901000 Remark. In finding the product of two numbers use that one as a multiplier which has the smaller number of figures other than zero. Thus, in 4007 X 241 use 4007 as the multiplier. |