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Lesson 9  Section 3

MULTIPLY MENTALLY BY
ROUNDING OFF

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Example 1.   Multiply 3 × 98  by rounding off 98 to 100.

   Solution. 3 × 98  =  3 × 100  −  3 × 2
 
   =  300 − 6
 
   =  294.

We added 2 to 98 to round it off.  Therefore we must subtract 2 -- three times. We must subtract 3 × 2.  For, we added 100 three times: Lesson 5.


 6.   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 2.   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 3.   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.)


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