Mental Calculations and Estimation of Products

Mental Calculations

Computative numbers and substitution/distributive property (numbers that are easy to calculate).

Compatible Numbers
Rearrangement of numbers.
                         1.         5 x 346 x 2 = 5 x 2 x 346 = 10 x 346 = 3460
              
                         2.         2 x 25 x 5 x 2 = 2 x 2 x 25 x 5 = 100 x 5 = 500
                                          
Substitutions

Distributive property is useful for mental calculations of products.

Example:

               14 x 102 = 14 x (100 + 2) = 1400 + 28 = 1428

                                            Distributive property

Equal Products

This method is based on the fact that the product of two numbers is unchanged when one of the numbers is divided by a given number and the other number is multiplied by the same number.

Example:

              12 x 52 =

                          12/2 x (52 x 2 ) = 

                                                   6 x 104 = 624 

Estimation of Products

Rounding

Products can be estimated by rounding one or both numbers. 
  
                         1.      71 x 58 » 70 x 60 = 4200

                               

                         2.      205 x 29 »  200 x 30 = 6000

                                          or » 210 x 30 = 6300

Compatible Numbers

Estimation of products combined with mental calculations become a useful tool when using compatible numbers. For example, to estimate 4 x 237 x 26, we might replace 26 by 25 and use a different ordering of the numbers.

                4 x 237 x 26 » 4 x 25 x 237 = 100 x 237 = 23,700

Front-End Estimation
Is related to rounding. keep the leading digit and everything else becomes a zero. For example, to estimate 62 x 83, keep the leading digits 60 x 80 so the estimated product is 4800.

Example:
               62 x 83 » 60 x 80 = 4800
Kids Olr  is a good website to collect information about math.             
Most of the information on this blog was taken from the text book: Mathematics for Elementary Teachers and from other sources.