by Ike Prudente

There are parents who are allergic to Math and  who say MATH is an acronym for

Mental Abuse THumans

They conclude that just because they are allergic to math and are certified math-haters, they cannot teach math to their children.  And I’d tell them the first and most important MATH lesson you can teach your child is “Mathitude.”

Mathitude is the term I use to refer to the attitude to use in approaching Math (and many everyday) problems. Among the more important things that I taught my children are:

• Most problems can be solved.
Complex problems can usually be broken down into simpler parts which are more easily solved.
• Problems can have different solutions.
Obvious solutions may not be the best.
• You can develop shortcuts in problem solving, but do not take shortcut in education.
One must not only learn, but also master, the basic concepts. Each succeeding math course builds upon the previous courses. If they find the current lesson hard to understand, then they must review the previous lessons.
• The cliché “practice makes perfect” is especially true in Math.
Math is learned not just by reading but by also doing. I ask my children to solve every available exercise or problem about the current lesson.
• Teaching helps learning.
I ask them to teach their classmates or younger kids. You cannot teach what you don’t know.
• Try to solve problems first before asking for help.
Study lessons before they are discussed in class. This helps the children develop self-reliance. But don’t be afraid to ask questions if needed.
• Understand and not just memorize.
Math is best learned by understanding the basic concepts and not just memorizing the math facts and solution steps.

Ike Prudente is a Math Advocate, creator of the Math-Inic system, and the best-selling author of the book
“25 Math Short Cuts.”

Subscribe to the free “There’s a Math Teacher in the House” newsletter at http://events.math-inic.org/TMaTH/

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

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

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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If the sum of adjacent digits is 10 or more, the procedure (see Math Tip #1) will have to be modified.
Example: 39 x 11

Step 1: Split the two digits: 3 __ 9

Step 2: Add the two digits, 3 + 9 = 12. The result is a two digit number but only one digit can be placed in between 3 and 9.

3 (12) 9 –> 3 2 9

Step 3: Carry over the 1 from the 12 and add it to the 3 giving a final answer of 429.

(3+1) 2 9 –> 4 2 9

So 39 x 11 = 429.

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