S k i l l
 i n
A R I T H M E T I C

Table of Contents | Home | Introduction


MENTAL ARITHMETIC
MULTIPLICATION

Lesson 8  Section 3

Distributing over a difference:  Rounding Off

Here is an example of distributing over a difference:

3 × 98 = 3 × (100 − 2)  =  3 × 100  −  3 × 2
 
   =  300 − 6
 
   =  294.

What we have done is to multiply  3 × 98  by rounding off to 100.  We then compensated by subtracting 3 × 2.


 5.   How do we multiply mentally by rounding off?
 
3 × 98 = 3 × 100  −  3 × 2
 
  Add to the multiplicand to make it a whole number or a multiple of 10.  To compensate, as many times as you multiplied, subtract from your answer whatever you added to the multiplicand.

Example 1.   You buy four pairs of stockings at $6.95 each.  How much do you pay?

Technique.  Round off $6.95 to $7.00.  Then

4 × $7.00 = $28.00

Now, to round off, we added 5¢.  And we added 5¢ four times because we multiplied by 4.  Therefore we must subtract 5¢ four times -- we must subtract 20¢.

$28.00 − $.20 = $27.80

That is,

4 × 6.95  =  4 × (7.00 − .05) = 4 × 7.00  −  4 × .05
 
  4 is distributed to 7.00 and to .05.

Example 2.   What is the price of 8 items that cost $12.99 each?  What is the price of 80 such items?

Solution.  Add 1¢ and round off to $13.00.  Then

8 × 13 = 80 + 24 = $104

-- minus 8 cents is $103.92.

We must subtract 8¢, because we multiplied by 8; that is, we added  1¢ eight times.

This is the price of 8 items.   As for 80 items, they will cost 10 times more.  Move the decimal point one place right:

10 × 103.92 = 1039.2 = $1,039.20

(Lesson 3, Question 2.)


Please "turn" the page and do some Problems.

or


Introduction | Home | Table of Contents

Please make a donation to keep TheMathPage online.
Even $1 will help.

Copyright © 2001-2007 Lawrence Spector

Questions or comments?

E-mail:  themathpage@nyc.rr.com