MENTAL ARITHMETIC:  MULTIPLICATION

PROBLEMS

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1.  a)  3 × 4 cm.  What does that mean?  4 cm + 4 cm + 4 cm.

1.  a)  What is 3 called?  The multiplier.

1.  a)  What is 4 cm called?  The multiplicand.

1.  b)  4 × 3 cm.  What does that mean?  3 cm + 3 cm + 3 cm + 3 cm.

1.  b)  Which is the multiplicand?  3 cm.

1. b)   What is 4 called?  The multiplier.

2.  a)  Five 7's are what multiplication?  5 × 7

2.  b)  Six eights are what multiplication?  6 × 8

3.  According to the order property of multiplication:

Nine 6's =  Six 9's.

4.  The order of factors.  Multiply mentally.

4.  a)  2 × 9 × 6 × 5 = 10 × 54 = 540

4.  b)  7 × 25 × 8 × 4 = 100 × 56 = 5600

4.  c)  2 × 2 × 2 × 3 × 5 × 5 × 7 = (2 × 2 × 5 × 5) × 2 × 3 × 7 =

100 × 42 = 4200

5.  When numbers are repeatedly added, we obtain their multiples.  Write
5.  the first six multiples of the following.

5.  a)   25.   25, 50, 75, 100, 125, 150.

5.  b)   12.   (To go to the next multiple of 12, you could add 10 and then
5.  b)   12.    add 2.  24 + 12 = 24 + 10 + 2 = 34 + 2 = 36.)
5.  b)   12.   12, 24, 36, 48, 60, 72.

5.  c)   18.   (To go to the next multiple of 18, you could add 20 and then
5.  b)   12.    subtract 2.  18 + 18 = 18 + 20 − 2 = 38 − 2 = 36.)
5.  b)   12.   18, 36, 54, 72, 90, 108.

5.  d)   35.   35, 70, 105, 140, 175, 210.

5.  e)   75.   75, 150, 225, 300, 375, 450.

6.  Whole numbers that end in 0's.  Calculate mentally.

6.  a)  3 × 60 = 180               b)  30 × 600 = 18,000

6.  c)  300 × 6000 = 1,800,000

5.  d)  9 × 50 = 450                 e)  40 × 7 = 280              f)  60 × 8 = 480

5.  g)  250 × 300 = 75,000           h)  2000 × 1200 = 2,400,000

5.  i)  700 × 700 = 490,000          j)  3,000 × 15,000 = 45,000,000

7.  Calculate mentally.

7.  a)  6 × $.40 = $2.40       b)  7 × $.30 = $2.10      c)  8 × $.60 = $4.80

6.  d)  9 × $.70 = $6.30      e)  5 × $.80 = $4.00      f)  4 × $.50  = $2.00

8.  Decomposing the multiplier.  Calculate in writing by decomposing
7.  the multiplier into its tens and ones.

8.  a)  15 × 3.  (10 threes + 5 threes) = 30 + 15 = 45.

8.  b)  14 × 7 = Ten 7's + Four 7's = 70 + 28 = 98.

8.  c)  17 × 9 = Ten 9's + Seven 9's = 90 + 63 = 153.

8.  d)  32 × 6 = 180 + 12 = 192.

8.  e)  11 × 53 = 530 + 53 = 583.

  9.   Calculate mentally.  That is, whatever you wrote in the previous problem, do mentally here.
 
  a)  12 × 9 = 90 + 18 = 108.   b)  14 × 4 = 40 + 16 = 56.
 
  c)  16 × 3 = 30 + 18 = 48.   d)  18 × 5 = 50 + 40 = 90.
 
  e)  16 × 9 = 90 + 54 = 144.   f)  12 × 6 = 60 + 12 = 72.
 
  g)  13 × 12 = 120 + 36 = 156.   h)  15 × 7 = 70 + 35 = 105.
  10.   Multiplication by 11.  Calculate mentally.
 
  a)  11 × 15 = 150 + 15 = 165.   b)  11 × 24 = 240 + 24 = 264.
 
  c)  11 × 36 = 360 + 36 = 396.   d)  11 × 49 = 490 + 49 = 539.

11.  Calculate mentally.

10.  a)   27 × 3 = 60 + 21 = 81.

10.  b)   32 × 6 = 180 + 12 = 192.

10.  c)   45 × 5 = 200 + 25 = 225.

10.  d)   64 × 9 = 540 + 36 = 576.

12.    Zero
 
  a)   0 × 312 = 0.   b)   9 × 0 = 0.

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