Multiplication
To Multiply Any Number by 11
Write the first right-hand figure, add the first and second, the second and third, and so on; then write the left-hand figure. Carry when necessary.
219434 × 11 = 2413774
Put down the right-hand figure 4. Then say, 4 and 3 are 7; then, 3 and 4 are 7; then, 4 and 9 are 13, put down 3 and carry 1; then, 9 and 1 and 1 are 11, put down the 1 and carry 1; then, 1 and 2 and 1 are 4; then write the left-hand figure 2. In multiplying small numbers, such as 24 by 11, write the sum of the two figures between the two figures, making 264, the required product.
To Multiply by 101, 1001, etc.
To multiply by 101, add two ciphers to the multiplicand, and add to this the multiplicand.
2341 × 101 = 234100 + 2341
To multiply by 1001, add three ciphers to the multiplicand, and add to this the multiplicand.
To Multiply by 5, 25, 125
To multiply by 5, add a cipher and divide by 2.
To multiply by 25, add two ciphers and divide by 4.
To multiply by 125, add three ciphers and divide by 8.
Another Easy Way to Multiply
82
54
4428
To multiply two figures by two figures, proceed as follows: Multiply units by units for the first figure.
Carry and multiply tens by units and units by tens, (adding) for the second figure. Carry and multiply tens by tens for the remaining figure or figures. In this example proceed as follows:
2 × 4 = 8 = 1st figure.
(4 × 8) + (5 × 2) = 42. Therefore 2 = 2d figure.
(5 × 8) + 4 carried = 44 = 3d and 4th figures.
By a little practice any one may become as familiar with this rule and as ready in its application as with the ordinary method.
To multiply any number by 2 1/2, add one cipher, and divide by 4.
To multiply any number by 3 1/3, add one cipher, and divide by 3.
To multiply by 33 1/3, add two ciphers, and divide by 3.
To multiply any number by 1 3/7, add one cipher, and divide by 7.
To multiply by 16 2/3, add two ciphers, and divide by 6.
To multiply by 14 2/7, add two ciphers, and divide by 7.
To multiply by 875, add three ciphers, and divide by 8.
To divide by 25, multiply by 4, and cut off two figures.
To divide by 125, multiply by 8, and cut off three figures.
To multiply by 12 1/2, add two ciphers, and divide by 8.
To find the value of any number of articles at 75 cents each, deduct one-quarter of the number from itself and call the remainder dollars.
To Subtract Any Number Consisting of Two Figures From 100
Take the first figure from 9, and the second from 10. For example: in subtracting 73 from 100, or in taking 73 cents change out of a dollar, say 7 from 9 and 2, and 3 from 10 and 7, or 27 cents. Practice this rule. It is simple, and will be found particularly helpful in making change.
Divisions
A number is divisible by 2 when the last digit is even.
A number is divisible by 4 when the last two digits are divisible by 4.
To divide by 12 1/2, multiply by 8, and cut off two figures.
Simple Discount Rule
This simple rule is in use in many houses where several discounts are allowed from list prices. Suppose the list price of a piano to be $500, and you allow an agent 25, 20 and 10 off.
| 100 | 100 | 100 | ||||
| 25 | 20 | 10 | ||||
| 75 | × | 80 | × | 90 | = | .540000 |
Subtract each from 100 and multiply and you get.54. $500 ×.54 = $270, the agent’s price.
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Percentage
The name percentage is applied to certain arithmetical exercises in which 100 is used as the basis of computation. Per cent. is an abbreviation of the Latin per centum, meaning by the hundred. This sign % is used for the words per cent. Thus, 10% of a number equals 10/100, or 1/10 of the number; 50% equals 50/100, or 1/2, etc.
FRACTIONAL EQUIVALENTS.
| 50 | % | = | .50 | = | 1/2. |
| 33 1/3 | % | = | .33 1/3 | = | 1/3. |
| 25 | % | = | .25 | = | 1/4. |
| 20 | % | = | .20 | = | 1/5. |
| 16 2/3 | % | = | .16 2/3 | = | 1/6. |
| 12 1/2 | % | = | .12 1/2 | = | 1/8. |
| 10 | % | = | .10 | = | 1/10. |
| 8 1/3 | % | = | .08 1/3 | = | 1/12. |
| 6 1/4 | % | = | .06 1/4 | = | 1/16. |
| 5 | % | = | .05 | = | 1/20. |
| 2 1/2 | % | = | .02 1/2 | = | 1/40. |