Lesson 4 MULTIPLYING AND DIVIDING




Doing that is an example of skill in arithmetic, which is to be able to do a problem as quickly and as easily as possible. Traditional multiplication would eventually give the right answer (we hope). But it is not skillful, and it does not take advantage of positional numeration. The student should let go of that written method immediately. 



Examples.
Problem. If 5 pounds of sugar cost $2.79, how much will 50 pounds cost? Answer. Since 50 pounds are ten times 5 pounds, they will cost ten times more. Move the decimal point one place right: $27.90. Since money has two decimal digits, we added on a 0. (Lesson 3, Question 8) 



These example illustrate that, whenever we multiply or divide by a power of 10, the digits do not change We simply move the decimal point or add on 0's. Finally, we must see how to divide a whole number by a power of 10. Now in Lesson 2 we saw that when a whole number ends in 0's, we simply take off 0's. (Lesson 2, Question 10) 265,000 ÷ 100 = 2,650 But when a whole number does not end in 0's  as 265  then there are no 0's to chop off We will see that we must place a decimal point to separate digits on the right. 



When we divide a whole number by a power of 10, the answer will have as many decimal digits are there are 0's. 8 ÷ 100 = .08 Two 0's. Two decimal digits. Again, as in Lesson 2, consider this array: As we move up the list  as we push the digits one place right  the number has been divided by 10 because each place to the right is worth 10 times less. (As we move from 26.58 to 2.658, we go from 2 tens to 2 ones.) It appears, though, as if the decimal point has shifted one place left, or, with the whole number 26580, that a 0 has been taken off. As we move down the list  as we push the digits to the left through the decimal point  each number has been multiplied by 10. And so we can easily multiply or divide by a power of 10 because of our system of positional numeration. Each place belongs to the next power of 10. At this point, please "turn" the page and do some Problems. or Continue on to the Section 2: The meaning of percent Introduction  Home  Table of Contents Please make a donation to keep TheMathPage online. Copyright © 2016 Lawrence Spector Questions or comments? Email: themathpage@yandex.com 