2016 June

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

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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

MATH-Inic San Pablo City – June 2016 Schedule

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Please take note of our new schedule:
Leveling Up Ceremony & MATH-Inic Challenge National Finals Awarding (San Pablo City Delegates) – June 18, 2016
Start of Saturday Classes – June 25, 2016

For inquiries, please contact us at 543 5351, 562 6006, 0917 853 5069, 0939 939 9702 or 0922 854 3244. Thank you!

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MATH-Inic Congressional Ave. Ext., QC – June 2016 Classes

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Enroll your children in our 20-hour modules designed to make Math fun, fast, and easy!

MATH-Inic classes are now being offered on weekdays starting June 13. Saturday classes will resume on July 2. Weekday tutorials are also accepted.

Reserve now thru 0917 5004796 or 0922 8004796.

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MATH-Inic Better Living, Parañaque – Saturday Classes Start on June 25

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Saturday classes start on June 25 at the Fruit of the Spirit Academy at 39 Saudi Arabia St. Better Living Subd. Parañaque.

For inquiries: 370-7616 / 0999-883-1098

https://www.facebook.com/MATHInicBetterLivingParanaque

Find the MATH-Inic Center near you!

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Enroll in MATH-Inic: Math made Fun, Fast, and Easy!

We turn Math haters to Math lovers,

and Math lovers to Math masters!

MATH-Inic Centers in Metro Manila,

Luzon, Visayas, and Mindanao:

MATH-Inic Centers

 

MATH-Inic Bacolod City

Puzzles Learning Center, G/F University Courtyard, La Salle

Avenue, Bacolod City, Negros Occidental

(034) 703 3088   (0905) 488 6882   (0942) 388 6775

MATH-Inic Better Living, Parañaque City

Fruit of the Spirit Academy, 39 Saudi Arabia Street,

Better Living Subdivision, Parañaque City

(02) 721 1088   (0999) 883 0185

 MATH-Inic Catholic Filipino Academy

8F Obispado de Cubao, 41 Lantana Street, Cubao, Quezon City

(02) 721 1088   (0999) 883 0185

MATH-Inic Congressional Avenue, Quezon City

2/F Balai Lakbay, 2 Alondras St. corner Congressional Avenue

Extention, Mira-Nila Homes, Quezon City

(0917) 500 4796   (0922) 800 4796

MATH-Inic Cotabato City

Lord of Peace Learning Center, 6 Bougainvillea Street, Gutierrez

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MATH-Inic Ednas School of Alaminos

Magsaysay Drive, Alaminos City, Pangasinan

(075) 551 2466

 MATH-Inic Ednas School

Tapuac District, Dagupan City, Pangasinan

(075) 552 2440

MATH-Inic Ednas of San Carlos

Roxas Boulevard, San Carlos City, Pangasinan

(075) 532 2385   (0922) 808 2972

MATH-Inic Iloilo

Tiny Green Island Interactive Playschool, San Nicolas, Oton, Iloilo

(0917) 878 4184

 MATH-Inic Puerto Princesa City

Palawan State University – Laboratory Elementary School,

Valencia Street, Puerto Princesa City, Palawan

(048) 433 2158   (0928) 977 2965 

MATH-Inic San Carlos City

Hide and Seek Kiddie Corner, Palaris Street,

San Carlos City, Pangasinan

(075) 532 5704   (0922) 808 2972

MATH-Inic San Pablo City

MSC Institute of Technology, Inc. – Junior and Senior High School

Sitio IX, Barangay San Gabriel, San Pablo City, Laguna

(049) 562 6006   (049) 543 5351

(0917) 853 5069   (0922) 854 3244   (0939) 939 9702

 MATH-Inic Silang, Cavite

Fablearn Academic Center, 109 J.P. Rizal Street, Silang, Cavite

(0908) 204 3843 or (0939) 925 4032

 

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You may also learn our fun, fast and easy methods

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8 1/ 2 Squared

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8mental math.

What is 8 1/2 x 8 1/2 ?

Traditional solution:

Convert to improper fractions:

8 ½ x 8 ½  = 17/2 x 17/2

Perform the multiplication:

17/2 x 17/2  = (17 x 17) /(2 x 2)

= 289/ 4

Convert to Mixed number: 72  1/ 4

MATH-Inic Mental solution:

This is an extension of the technique of squaring numbers ending in 5 where the answer is composed of two parts. The first part is obtained by using the Vedic Math Sutra “ By one more than the one before” and the second part is always 25.  For example 25 x 25 is 2 x (2+1)| 5 x 5 = 625.

Here the answer is simply 8 x (8 + 1)|1/2 x 1/ 2 = 72|1/4 = 72 1/4

Algebraic proof:

Use (a + b)2 = a2 + 2(a)(b) + b2

        (a + 1/2)2 = a2 + 2(a)(1/2) + (1/2)2

= a2 + a + (½)2

= a(a+1)+ ¼

For further explanations and more examples see MSC #15 Squaring numbers ending in 5, p 53, 25 Math Short Cuts

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