MENTAL ARITHMETIC: MULTIPLICATION

PROBLEMS (2)

The distributive property

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13.  In this number  5,286  name the place value of each digit.

The 5 has the value 5000; the 2 signifies 200; the 8 signifies 80; and the 6 has its absolute value of 6.

14.  Calculate in writing by distributing the multiplier to each unit of the
12.  multiplicand.  Treat problems with decimal points as dollars and
14.  cents.

14.  a)  3 × 42The Distributive Law

14.  b)  5 × 34 = 5 × 30 + 5 × 4 = 150 + 20 = 170

14.  c)  6 × 32 = 6 × 30 + 6 × 2 =180 + 12 = 192

14.  d)  7 × 56 = 350 + 42 = 392

14.  e)  8 × 97 = 720 + 56 = 776

14  f)  2 × 346 = 600 + 80 + 12 = 692

14.  g)  3 × 475 = 1200 + 210 + 15 = 1425

14.  h)  7 × 908 = 6300 + 56 = 6,356

14.  i)  9 × 4,005 = 36,000 + 45 = 36,045

13.  j)  6 × 7.30 = 42 + 1.80 = 43.80

14.  k)  9 × 4.50 = 36 + 4.50 = 40.50

15.  Whatever you wrote in the previous problem, do mentally here.

6 × 13 = 78   7 × 55 = 385   3 × 96 = 288
 
3 × 72 = 216   9 × 72 = 648   5 × 68 = 340
 
8 × 34 =  272   8 × 36 =  288   6 × 36 =  216
 
4 × 49 =  196   6 × 89 =  534   4 × 38 =  152
 
9 × 52 =  468   8 × 28 =  224   9 × 36 =  324

16.  Calculate each column mentally.

30 × 27 = 810   60 × 620 = 37,200
 
40 × 34 = 1360   70 × 770 = 53,900
 
50 × 59 = 2950   80 × 980 = 78,400

17.  You have 47 twenty-dollar bills.  Calculate mentally how much
17.  money you have.

2 × 47 = 80 + 14 = 94. Therefore 20 × 47 = $940.

18.  Multiply each column mentally.  These are dollars and cents.

4 × .25 = 1.00   6 × 3.25 = 19.50   7 × 9.50 = 66.50
 
5 × .25 = 1.25   5 × 6.25 = 31.25   3 × 4.80 = 14.40
 
6 × .25 = 1.50   6 × 9.25 = 55.50   9 × 5.20 = 46.80
 
7 × .25 = 1.75   7 × 8.25 = 57.75   4 × 6.30 = 25.20
 
8 × .25 = 2.00   8 × 4.25 = 34.00   7 × 7.40 = 51.80
 
9 × .25 = 2.25   9 × 5.25 = 47.25   8 × 3.90 = 31.20

19.  Multiply each column mentally by distributing the multiplier to the
18.  hundreds, then the tens, then the ones..

2 × 423 = 846   7 × 309 = 2163
 
3 × 624 = 1872   8 × 602 = 4816
 
4 × 574 = 2296   9 × 907 = 8163
 
5 × 357 = 1785   5 × 2012 = 10,060

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