MULTIPLYING BY 2½
Rule: Starting from the first digit of the given number, double each digit and add one-half the given digit. Ignore any fractions. Add any tens digits to the previous answer digit. Add 5 if the preceding digit of the given number is odd. Affix ½to the answer if the given number is odd.
Use this short cut when the given number is an integer or a decimal number. Mixed numbers and fractions are difficult to handle with this method.
This short cut will be used in the example:
517,849 x 2½
Double the 5 and add one-half of itself to obtain the first answer digit.
5 + 5 = 10; 10 + ½ (5) = 10 + 2 = 12
(The fraction i is ignored.)
Record 12 as the first two answer digits. Double 1. One-half of 1 is ½, which is Ignored. But since the preceding given digit is odd, add 5 to the result of this step.
1 + 1 = 2; 2 + ½ (1) = 2 + 0 = 2 2 + 5 = 7
Record the 7 as the next answer digit.
127
The next given digit is 7.
7 + 7= 14; 14 + ½ (7) = 14 + 3 = 17
The previous given digit, 1, is odd; therefore add 5.
17 + 5 = 22
Record the units digit, 2, as an answer digit. Carry the tens digit, also 2, and add it to the previous answer digit. The answer thus far is
1292 Continue this process with the balance of the given digits.
8 + 8 – 16; 16 + 4 = 20; 20 + 5 = 25
Record 5; add the 2 to the previous answer digit. The answer at this point is
12945
