What is 9 2/7 x 9 5/7?

by | June 21, 2016 | Math Made Easy! | No Comments

Complementary numbers

Traditional Solution:

Convert to improper fractions:

65/7  x 68/7 =

Perform the multiplication: (May require pen and paper or calculator)

65/7 x 68/7 = 4420 /49

Convert result to mixed fraction: (May require pen and paper or calculator)

4420 /49 =  90 10/49

MATH-Inic Mental Solution:

The factors 9 2/7 and 9 5/7 are “complementary” in the sense that they have the same whole number part and their fractional parts 2/7 and 5/7 total to 1.

Apply the Vedic Math Sutra “By one more than the one before“:

a)Multiply the whole number part by the next higher number to get the whole number part of the answer

b) Multply the fractional parts to get the fractional part of the answer.

9 x (9 + 1) | 2/7 x 5/7 = 90 | 10/49 = 90 10/49

The solution can be better understood if we use the distributive laws:

9 2/7  x 9 5/7 = (9 + 2/7) x ( 9 5/7)

= 9(9) + 9(5/7) + 2/7(9) + 2/7(5/7)

= 9(9)  + 9(5/7+ 2/7) + (2/7)(5/7)

= 9(9) + 9(1) + 10/49

= 9(9 +1) + 10/49

90 10/49

This solution is similar to that of our previous post “8 1/2 squared“,which is shown below.

For more examples and exercises, please see MSC # 16 -Multiplying Complementary Numbers, pp 57-59, 25 Math Short Cuts

8 1/ 2 Squared

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