Lesson 9 Section 3 MULTIPLY MENTALLY BY

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
Please "turn" the page and do some Problems.
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