Art. 9. To multiply a number by 25: Multiply of the (i) Find the sum of the twelve products. Art. 10. To multiply a number by 26: number, to which add the number itself. 25 times 36 = 900 Take 25 times the Why? 90036936 36 × 26 (j) Find the sum of the twelve products. Art. 11. To multiply a number by 27: number, to which add twice the number. Take 25 times the Why? 900+72 972 = 92574999 (k) Find the sum of the twelve products. Art. 12. To multiply a number by 24: Take 25 times the number, from which subtract the number itself. Why? (1) Find the sum of the twelve products. Art. 13. To multiply a number by 20: Multiply of the How may a number be multiplied by 21? number by 100. (m) Find the sum of the twelve products. Art. 14. To multiply a number by 163: Multiply of the number by 100. How may a number be multiplied by 17? (n) Find the sum of the twelve products. Art. 15. To multiply a number by 121: Multiply of the number by 100. How may a number be multiplied by 131? by 141? by 111? (0) Find the sum of the twelve products. Art. 16. To multiply a number by 125: Multiply of the number by 1000. How may a number be multiplied by 126? by 127? by 124? 96 × 126. 125 times 96 = 12000 12000 + 96 = 12096 (p) Find the sum of the nine products. Art. 17. To multiply a number by 250: Multiply 1 of the number by 1000. How may a number be multiplied by 251? by 252? by 249? 48 x 250 of 48 × 1000 = 12000 250 times 48 = 12000 12000 + 48 = 12048 48 × 251 (q) Find the sum of the nine products. Art. 18. To square 21, 31, 41, etc.: Multiply the integer by the integer plus 1, and add to the product. 21 × 21 = 2 times 2 + 2 times 1 + 1 of 2 + 1 of 1 But 2 times + of 2=1 time 2; and 1 of 1 = 1 (r) Find the sum of the nine products. Multiply the tens' Art. 19. To square 25, 35, 45, etc.: figure* by the tens' figure increased by 1; regard the product as hundreds, to which add 25. To explain this rule, think of 25 as 2 tens and of a ten, and apply the explanation given under Art. 18. 25 x 252 x 3 hundred and 25 = 625 35 x 35 = 3 × 4 hundred and 25 = 1225 45 × 45 = 4 × 5 hundred and 25 = 2025 *The author is aware that the expressions "Multiply the tens' figure" and "the tens' figure increased by 1," are tabooed by the hypercritical. But it is believed that neither obscurity nor misconception will arise from this use of the word figure. The word as here used clearly means the form value of the figure-the number which the figure by virtue of its shape represents. Art. 20. To multiply 24 by 2, 31 by 34, etc.: Multiply the integer by the integer plus 1, and to the product add the product of the fractions. Observe that this rule will apply only when the integer of the multiplicand and the integer of the multiplier are the same, and the sum or the fractions is 1. 24 by 23 = 2 times 2+2 times + § of 2 + 3 of 1 But 2 times of 2 = 1 time 2, and 3 of 4 = √ Hence 21 × 23 = 2 × 3 + 2 of 4 = 61% (t) Find the sum of the six products. Art. 21. To multiply 24 by 26, 33 by 37, etc.: Multiply the tens' figure by the tens' figure increased by 1; regard the product as hundreds, to which add the product of the units' figures. Observe that this rule will apply only when the tens' figure of the multiplicand and the tens' figure of the multiplier are alike, and the sum of the units' figures is 10. 22 × 28 = 2 × 3 hundred and 16 = 616 44 × 46 = 4 × 5 hundred and 24 = 2024 x (u) Find the sum of the nine products. |