Multiplying Strategies

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This section has numerous methods and strategies for multiplying, squaring, and manipulating numbers.  By using these strategies you should be able to calculate complex operations in you head with relative ease.

            * = easy                    should be learned by Elementary level students

            ** = medium              should be learned by Junior High level students

            *** = difficult             should be learned by High School level students

Many of these methods are overlapping.  In other words, you can use several methods for one question.  For example, you can use the squaring numbers rule for 692 or you can use the method for squaring a number that ends in a 9.  You must decide what method is best in different situations.

Note:  Unless stated otherwise, all the steps will ask you to write the answer down reading from right to left.  In other words, you will write down the one’s digit to the answer first, followed by the ten’s digit, followed by the hundred’s digit, and so on.

(*)    FOIL method  (*PDF*)

(*)    Double and half method  (*PDF*)

(*)    Squaring a 2-digit number  (*PDF*)

(*)    Squaring a number ending in 5  (*PDF*)

(**)  Squaring a number ending in 6  (*PDF*)

(**)  Squaring a number ending in 7  (*PDF*)

(**)  Squaring a number ending in 8  (*PDF*)

(**)  Squaring a number ending in 9  (*PDF*)

(*)    Squaring a number in the range: 40 - 49  (*PDF*)

(*)    Squaring a number in the range: 50 - 59  (*PDF*)

(*)    Squaring a number in the range: 90 - 99  (*PDF*)

(**)  Difference of 2 squares  (*PDF*)

(**)  Multiplying 2 numbers that end in 5  (*PDF*)

(**)  Multiplying 2 numbers whose tens digit is the same and whose one's digit adds to 5  (*PDF*)

(*)    Multiplying 2 numbers whose tens digit is the same and whose one's digit adds to 10  (*PDF*)

(**)  Multiplying 2 numbers whose tens digit is the same  (*PDF*)

(**)  Multiplying 2 numbers whose ones digit is the same and whose tens digit adds to 10  (*PDF*)

(*)    Multiplying numbers less than 100 but close to 100  (*PDF*)

(*)    Multiplying numbers more than 100 but close to 100  (*PDF*)

(**)  Multiplying one number more than 100 by a number less than 100  (*PDF*)

(*)    Multiplying and adding numbers in the form:  ab + bc  (*PDF*)

(**)  Adding squared numbers in the form: a2 + (2a)2  (*PDF*)

(**)  Adding squared numbers in the form: a2 + (3a)2  (*PDF*)

(**)  Adding squared numbers in the form: a2 + (7a)2  (*PDF*)

(**)  Adding squared numbers in the form: a2 + (10a)2  (*PDF*)

(**)  Multiplying numbers less than 1000 but close to 1000  (*PDF*)

(**)  Multiplying numbers more than 1000 but close to 1000  (*PDF*)

(***) Adding squared numbers in the form:  (10a + b)2 + [10(b-1) + (10-a)]2  (*PDF*)

(**)  Product of 4 consecutive integers plus 1  (*PDF*)

(***)  Adding 2 consecutive squared numbers  (*PDF*)

(***)  Squaring numbers in the form: (101a)2  (*PDF*)

(***)  Adding squared numbers in the form: a2 + b2 - (a - b)2  (*PDF*)