Super Fast and Easy: Two-Digits Multiplication

Multiplying Two-Digit Numbers: The Other Way

While some of our kids or students easily give the answer in the above multiplication, others still  find it difficult to multiply such in a small amount of time. This post may help them to do such. With proper guidance of the teacher or the parent, they can do it.

Let us first recall one topic in Algebra which is the Product of Two Binomials

(a +b)² = a² + b² + 2ab

(a-b) ²  = a² + b² - 2ab

(a + b)  (c + d) = ac + ad + bc + bd.

(a + b)  ( c - d) = ac - ad + bc - bd.

(a-b) (c+ d) = ac + ad -bc -bd.

(a-b) (c-d) = ac - ad - bc + bd.

Let us rewrite a number k as a sum or difference of two numbers in the form

(a +b) or (a-b)

where a is equal to the nearest multiple of 10 less than or just greater than the number K.

For examples:

63 would be rewritten as (60 + 3) and 68 would be rewritten as (70 - 2).

73 would be rewritten as 70 + 3 and 79 would be rewritten as 80 - 1.

Let us first calculate 47 * 47

Let us use the formula

(a-b) * (a-b) = a * a - 2 * a * b + b *b where a = 50 and b = 3.

So 47 * 47 = 2500 - 300 + 9 = 2209.

Let us calculate 73 * 73

Let us use these formula (a+b) * (a + b) = a*a + 2 * a * b + b*b

73 * 73 = (70 + 3) ( 70 + 3 ) = 4900 + 420 + 9 = 5329.

26 * 26 = ( 30 - 4)(30 - 4) = 900 - 240 + 16 = 676.

Use (a +b)(c +d) to calculate 93 * 57 as

(90 + 3) * ( 50 + 7 )

= 4500 + 630 + 150 + 21,                                           Simplify this further by writing this as,

4500 + 600 + 30+100 + 50 + 20 + 1, 4500 + 700 + 101        which can be easily calculated as

5301

Let us similarly calculate 47 * 69 using the expression for (a-b) (c-d).

Let us rewrite the product as

=(50-3) (70-1).                        Expanding the individual terms as

=3500 - 50 - 210 + 3,              rewriting this as

=3500 - 200 - 60 + 3;              rewriting this as

=3500 - 200 - 60 + 3;              So

=3243.

Using the expression (a-b)(c+d) let us calculate 43 * 88,

Rewrite the original expression as

(40 +3)*(90 - 2). Compute individual sums as

= 3600 - 80 + 270 - 6

= 3870 - 86

= 3870 - 70 - 16

= 3800 - 16

= 3784.

Let us use the expression (a-b) (c-d) = ac - ad -bc + bd to calculate 57 * 79 quickly.

Rewriting this as

(60 - 3) * (80 -1)

= 4800 - 60 - 240 + 3

= 4800 - 300 + 3

= 4503.

This can be extended to 3 digit numbers, where the sums of products can be easily formulated using distributive laws of addition and multiplication respectively.

Let us try to calculate 153 * 94 quickly, by rewriting 153 as 100 + 50 +3 and 94 as 90 + 4.

Let us write the original product as

(100+ 50 + 3) (90 + 4);                                   the sum of individual terms is

9000 + 400 + 4500 + 200 + 270 + 12.            Sort is by thousands, hundredths and Units place.

13000 + 1000 + 300 + 82;                              quickly calculate the sum as

14382.

How to "NOT to Fail" Math Tests

Do anxiety levels hit all-time highs when a math test is around the corner? Are studies and preparations inevitably accompanied by nervous tension and anticipation? For many kids, math tests spell long nights, confusion, repeated practice, and frustration. All that can change with the right approach to practicing and preparing for a math test. You will be surprised at how a calm mind, focus, dedicated efforts, and planning ahead can change your reactions to a test.

The academic world is becoming tougher by the day and students have exams, homework, assignments, project and a variety of other co-curricular and extracurricular activities to worry about. Even though a student may be well prepared for an exam, he/she may not score well and this is perhaps due to improper planning.

Here are some important hints and tips to help you get ready for that much-dreaded math test. Read on, follow the steps, and watch those grades go up!

1.    Complete all the learning and memorizing much before the exam.
While you need to use your logical skills when it comes to math, and you cannot memorize all the different kinds of problems, there are some formulas and concepts that you need to know by heart. Finish the first steps of understanding and knowing all the important facts well before your exam. Cramming and learning all of it at the last minute will leave you with little time to actually practice math problems and concepts, leaving you confused and frustrated.

2.    Make quick notes of all the important points.
From the different formulas to simple tips and pointers to notes on aspects that you find difficult to remember, make notes. This will serve two very important purposes. One, writing it all down is one way of remembering and practicing. Another reason is that these notes will prove to be rather helpful in the last few minutes before the test. A quick glance over these highlights before the exam will help you remember all the important points before you begin. Simple flash cards also can be of great help.

3.    Practice, practice, practice.
Math is not a theory subject. Many kids believe that as they read through certain problems and their solutions, if they understand it, they will be able to do it. When it comes to math, you have to solve each problem. When you sit down and begin, you might realize that you draw a blank or do not even know where to begin. Practice will help you identify what your weak

areas are and what you should focus more on. Take old homework problems and solve them again. There is no alternative to practice when it comes to math.

4.    Review and revise.
Once you have covered all the topics and concepts that you will be tested on, mix up problems from different topics and solve them. Have a study partner or friend prepare a list of math problems and sample test paper for you. Reviewing what you have learned will ensure that you remember everything better and are more confident.

5.    Take adequate breaks.
Yes, while you are bound to be nervous and may want to spend all your time pouring over your books, it is important to take breaks as well. Spend some time doing what you enjoy and stop thinking about math. But be sure to time your breaks. Don’t let your breaks get too long, you will lose interest and will not get back to studying. Short breaks every couple of hours will help you study longer without tiring of it. The night before the exam, make sure you get enough sleep and are not tense.