Whole Numbers Operations

Multiply by a two digit number.
1.  Multiply the ones.
2.  Multiply the tens place, using zero as a place holder.
3.  Add the partial products for the final product.
4.  Is your answer reasonable?

A cube shaped cage measures 5 units on each side.  To find the amount of space the  cage occupies (volume)  find the cube of the measure of one side of the bird cage.  Express the amount of space occupied by the cage as a power.  Then find the amount in cubic units.

Volume - length x width x height

Volume  =  5         x    5      x  5
Express the cube of the measure of one side.

5³

Find the amount in cubic units.

5 x 5 x 5  = 125 cubic units

 



cube - each side measures 5 units

 

Whole Numbers Operations

Finding Products Mentally
Example # 1
Find the procuct mentally.  40 x 7,000
1.  Find the basic multiplication fact   4 x 7 = 28
2.  Count the number of zeros in each factor.
     40 - one zero
     7,000 - three zeros   Total of 4 zeros
3.  Write the zeros to the right of the product in step 1.
     280,000
Answer 280,000

Example #2
Find the product mentally 21 x 10²
1.   Write 10² without exponents   10² = 100 The exponent tells you the number of zeros in the power of 10.
2.  Find the basic multiplication fact.  21 x 1 = 21
3.  Count the number of zeroes  in the factors - total of 2 zeros
4.  Write the zeroes to the right of the product 2,100
Short cut - Look at the exponent.  In this case it is 2.  This tells you the number of zeros in the power of 10.  You are multiplying 21 by a power of 10 with 2 zeros.

Vocabulary
10² This number is read as 10 to the power of 2 or 10 squared.
10 is the base.  The exponent indicates how many times the base is used as a factor.
10² = 10 x 10
10³ = 10 x10 x 10