Thursday, August 27, 2009
Short Cut in Multiplying by 11
How do we multiply by eleven easily?
First we will try this by writing the answer backwards.
So, when always multiplying a large number by 11, the last number will always be the last number of the sum we are multiplying.
Let me explain.
176 is the number we are multiplying.
So the last number in out answer will be 6. If the sum was 143 the last number in our answer would be 3… get it? So now what? Easy, just add the next number to the last number, 7 + 6 = 13 So the next last number will be 3, carry the 1. Add the 7 and 1 together, giving 8, then add the carried 1, 9 then write that number as our next part of the answer, 936 Then, the last number will be the first number in our sum, in this case 1. So the answer is 1936. Try 278Last number is 8 7 + 8 = 15 Second last number is 5, carry the 1 7 + 2 = 9 add the carried 1, 10 Third last number is 0, carry the 1 Add the carried 1 to the first number in the sum, 2 giving: 2 + 1 = 3 So the answer is 3058! Alternatively, you could always just add a zero to the number you are multiplying and then add the original number to it again… 156 X 11 try it this way: Add a zero to the end 1560 Add 156 to this 1560 + 156 = 1716 Whatever method works best, stick to it!
Thursday, August 20, 2009
Top 9 TRICKS
Multiplication involving certain numbers can be computed using methods other than just standard multiplication. Sound confusing? Check out these nine tricks and see what I mean.
1. To multiply any number of two figures by 11: Write the sum of the figures between them. Thus, 34 x 11 = 374. (3 + 4 = 7; place the seven between the 3 and 4) When the sum is of the figures is more than 9, increase the left-hand number by the 1 to carry. Thus, 98 x 11 = 1078 (9 + 8=17; add 1 to 9 to get 10; place the seven between the 10 and 8)
2. To square any number of 9s immediately without multiplying: set down as many 9s less one (beginning at the left) as there are 9s in the given number, an 8, as many 0s as you do 9s, and a 1. Example: 999 x 999: put down 2 9s: 99. Then an 8: 998. then 2 0s (because you have 2 9s): 99800. The append a 1: 998001. That's it!
3. To square any number ending in 5: Omit the 5, and multiply the number as it will then stand, by the next higher number, and append 25 to the product. Example: 35 x 35. Omit the 5: 3. Next multiply 3 by the next higher number, 4: 3 x 4 = 12. Finally, append 25: 1225. That's the answer: 1225.
4. To square any compound fraction containing 1/2, like 5 1/2 for instance, Multiply the whole number by the next higher whole number and append 1/4 to the product. Thus, 5 1/2 x 5 1/2 = 30 1/4. (5 x (5+1) = 30; tag on 1/4 to get 30 1/4.)
5. To multiply any two like numbers with fractions that sum to 1 (for instance, 4 3/4 x 4 1/4), multiply the whole number by the next highest number (4 x 5) and append the product of the fractions (3/4 x 1/4). In the case of 4 3/4 x 4 1/4, 4 x 5 = 20. Then append the product of 3/4 x 1/4, 3/16. Thus, 20 3/16.
6. To multiply any two numbers whose ones digits sum to 10 and with like remaining numbers (for instance, 106 x 104) multiply the upper tens numbers by the next higher number (in this case, 10 x 11) and multiply the ones digits that sum to 10 (6 x 4) and then set the products next to one another successively (11024). Another example is 57 x 53. 5 x 6 = 30; 7 x 3 = 21; answer is 3021.
7. To multiply any number by any number of 9's (for instance, 28 x 99), append as many 0's to the multiplicand as there 9's in the multiplier (2800), and from this number subtract the multiplicand (2800 - 28 = 2772). The remainder is the answer. (2772)
8. Cross multiplication is a method of multiplying large numbers in a single line. Take the example 18 x 76. First multiply 8 x 6, set down the 8, and carry the 4. Next multiply 1 x 6, 7 x 8, add the products and add the carried 4 to give 66. Set down the 6, multiply 1 x 7, and add 6 to the product to give 13 which you set down to conclude the problem and yield the answer, 1368. (To learn this, work a few examples on paper.)
9. Here's a rather complicated trick for calculating any two 2-digit numbers:
Note: To do this trick, you need to know the squares of numbers up to 100 in advance.
1. Calculate the average of the two numbers.
2. Square your answer (here's where you need to know the squares of numbers through 100)
3. Subtract the largest of your original two numbers from the average
4. Square the answer
5. Subtract it from your answer in step 2 for the final answer
Example: 27 * 15First, calculate the average (42 / 2 = 21)Then square it (212 = 441)Now subtract largest number from the average (27 - 21 = 6)Square your answer (62 = 36)Subtract the square from the first square (441 - 36 = 405). And there's your answer: 405This works every time, but as the average and differences can end in .5, you have to know these squares as well.By the way, this trick works because (x + y)(x - y) = x * x - y * y
1. To multiply any number of two figures by 11: Write the sum of the figures between them. Thus, 34 x 11 = 374. (3 + 4 = 7; place the seven between the 3 and 4) When the sum is of the figures is more than 9, increase the left-hand number by the 1 to carry. Thus, 98 x 11 = 1078 (9 + 8=17; add 1 to 9 to get 10; place the seven between the 10 and 8)
2. To square any number of 9s immediately without multiplying: set down as many 9s less one (beginning at the left) as there are 9s in the given number, an 8, as many 0s as you do 9s, and a 1. Example: 999 x 999: put down 2 9s: 99. Then an 8: 998. then 2 0s (because you have 2 9s): 99800. The append a 1: 998001. That's it!
3. To square any number ending in 5: Omit the 5, and multiply the number as it will then stand, by the next higher number, and append 25 to the product. Example: 35 x 35. Omit the 5: 3. Next multiply 3 by the next higher number, 4: 3 x 4 = 12. Finally, append 25: 1225. That's the answer: 1225.
4. To square any compound fraction containing 1/2, like 5 1/2 for instance, Multiply the whole number by the next higher whole number and append 1/4 to the product. Thus, 5 1/2 x 5 1/2 = 30 1/4. (5 x (5+1) = 30; tag on 1/4 to get 30 1/4.)
5. To multiply any two like numbers with fractions that sum to 1 (for instance, 4 3/4 x 4 1/4), multiply the whole number by the next highest number (4 x 5) and append the product of the fractions (3/4 x 1/4). In the case of 4 3/4 x 4 1/4, 4 x 5 = 20. Then append the product of 3/4 x 1/4, 3/16. Thus, 20 3/16.
6. To multiply any two numbers whose ones digits sum to 10 and with like remaining numbers (for instance, 106 x 104) multiply the upper tens numbers by the next higher number (in this case, 10 x 11) and multiply the ones digits that sum to 10 (6 x 4) and then set the products next to one another successively (11024). Another example is 57 x 53. 5 x 6 = 30; 7 x 3 = 21; answer is 3021.
7. To multiply any number by any number of 9's (for instance, 28 x 99), append as many 0's to the multiplicand as there 9's in the multiplier (2800), and from this number subtract the multiplicand (2800 - 28 = 2772). The remainder is the answer. (2772)
8. Cross multiplication is a method of multiplying large numbers in a single line. Take the example 18 x 76. First multiply 8 x 6, set down the 8, and carry the 4. Next multiply 1 x 6, 7 x 8, add the products and add the carried 4 to give 66. Set down the 6, multiply 1 x 7, and add 6 to the product to give 13 which you set down to conclude the problem and yield the answer, 1368. (To learn this, work a few examples on paper.)
9. Here's a rather complicated trick for calculating any two 2-digit numbers:
Note: To do this trick, you need to know the squares of numbers up to 100 in advance.
1. Calculate the average of the two numbers.
2. Square your answer (here's where you need to know the squares of numbers through 100)
3. Subtract the largest of your original two numbers from the average
4. Square the answer
5. Subtract it from your answer in step 2 for the final answer
Example: 27 * 15First, calculate the average (42 / 2 = 21)Then square it (212 = 441)Now subtract largest number from the average (27 - 21 = 6)Square your answer (62 = 36)Subtract the square from the first square (441 - 36 = 405). And there's your answer: 405This works every time, but as the average and differences can end in .5, you have to know these squares as well.By the way, this trick works because (x + y)(x - y) = x * x - y * y
Wednesday, August 19, 2009
The Importance of Math in our Lives...
Like sand through the hour glass, so is the maths of our lives. There are more grains of sand on Earth than there are stars in sky, or so the saying goes. 
As what we know, you can think of almost everything as a math problem. Actions like getting dressed, eating breakfast, catching the school bus, eating in the cafeteria, English, P.E., geography and just about everything else is related to math. How are these "problems" solved? We might here comments like ....
As what we know, you can think of almost everything as a math problem. Actions like getting dressed, eating breakfast, catching the school bus, eating in the cafeteria, English, P.E., geography and just about everything else is related to math. How are these "problems" solved? We might here comments like ...."Math has contributed greatly to science and other fields of knowledge. "
"Mathematics is very interesting to me, and I enjoy math courses."
"My mind goes blank, and I am unable to think clearly when working math."
"Mathematics is dull and boring because it leaves no room for personal opinion."
It's a Math World is a WebQuest in which students are asked to create a book that answers this question.
What Good is Math? is a site for students that attempts to answer this oft-asked question.
Mathletics looks specifically at the mathematics of sports. (Mathletics=Math +athletics--get it?)
Math in Daily Life examines how we use math to get things done, from cooking to decorating to playing games.
Get Real: Math in Everyday Life provides some examples of real world connections to math and suggests links to explore these ideas.
When a sixth grade class talked about math in everyday life, their teacher put their ideas together in Math is Everywhere!MathPulse.com has a series of articles about how we use math every day
Tuesday, August 4, 2009
Me and teaching World
My teaching world which guided with the principle that Teacher as a role model who can institute change and bring an authentic learning experience into the new frontiers in teaching.
5 major questions which I encountered during my HCT interview which I think summarizes my teaching roles and guiding principle as a math teacher.
1. Describe what major contribution you feel you could make to Higher Education in the United Arab Emirates.
A. For a teacher like me who loves to teach mathematics and be part in one of the largest, most progressive and innovative places of higher learning in the UAE would be a dream come true. My dream is basically about on how to arouse my student’s interest in mathematics and to help them master the basic foundation of all mathematical concept. Help maintain the highest quality in the math department and enhance students learning by new skills and techniques. The mastery of my subject areas will be of great help to become one of the dedicated professionals not only to teach but also to support and encourage students to reach as high a standard as possible so that students may develop the skills and attributes they need to succeed in their chosen occupational sectors and jobs. Lastly, be a part of AUE history in building a workforce with young Emirate who is capable of operating effectively in today's global business environment.
2. What is your greatest achievement to date and why do you regard it as such?
A. For the past 13 years, I realized that being a qualified teacher is not enough but the passion to teach "math" matters most. I am proud to note the following achievement: Establishment of the CLRC (Classroom Resource Learning Center) which generated almost ½ of school income for Remedial and advanced math learning; Developed and enriched the Math Curriculum thus put me as a faculty Awardee of the year ; Excellent ratings & high recommendation from my UAE students once again proved the awards that I garnered in the Philippines moved me to strive more to empart the skills & abilities especially if given a chance to be part in reaching the HCT goals.
3. Describe yourself in the words of an imaginary, fair and impartial critic.
A. A dynamic, self motivated and goal oriented person. I've got extensive experience in field of mathematics for the past 13 years in the Philippines and UAE and have the specific skills you are looking for. I'm a fast learner who adapts quickly to change and will hit the ground running. I'm dedicated and enthusiastic about helping your school to meet its goals, and will provide top-quality results with minimal oversite. I'm an outstanding performer who takes pride in my work.
4. Why are you interested in a position with the Higher Colleges of Technology? (If you are an overseas applicant, why are you considering a career move to the Middle East, and to the United Arab Emirates in particular?)
A. HCT is the right place for me being as one of the largest, most progressive and innovative places of higher learning in the UAE. I have always wanted this opportunity to work with an environment that will help expands my knowledge that provides a vital public service, leads industry to innovative and mold students to be prepared and equipped in the globalised workplace in the future.
5. What are your hobbies and interests?
A. love reading especially books related to success in life, solving complicated problems, I love teaching the slowest student in class in fact it’s one my greatest challenge to let them understand the hardest lesson, I like activities which requires organizational skills, prioritization and time management. It is my passion to teach students not only to learn math but to LOVE math to its truest sense.
5 major questions which I encountered during my HCT interview which I think summarizes my teaching roles and guiding principle as a math teacher.
1. Describe what major contribution you feel you could make to Higher Education in the United Arab Emirates.
A. For a teacher like me who loves to teach mathematics and be part in one of the largest, most progressive and innovative places of higher learning in the UAE would be a dream come true. My dream is basically about on how to arouse my student’s interest in mathematics and to help them master the basic foundation of all mathematical concept. Help maintain the highest quality in the math department and enhance students learning by new skills and techniques. The mastery of my subject areas will be of great help to become one of the dedicated professionals not only to teach but also to support and encourage students to reach as high a standard as possible so that students may develop the skills and attributes they need to succeed in their chosen occupational sectors and jobs. Lastly, be a part of AUE history in building a workforce with young Emirate who is capable of operating effectively in today's global business environment.
2. What is your greatest achievement to date and why do you regard it as such?
A. For the past 13 years, I realized that being a qualified teacher is not enough but the passion to teach "math" matters most. I am proud to note the following achievement: Establishment of the CLRC (Classroom Resource Learning Center) which generated almost ½ of school income for Remedial and advanced math learning; Developed and enriched the Math Curriculum thus put me as a faculty Awardee of the year ; Excellent ratings & high recommendation from my UAE students once again proved the awards that I garnered in the Philippines moved me to strive more to empart the skills & abilities especially if given a chance to be part in reaching the HCT goals.
3. Describe yourself in the words of an imaginary, fair and impartial critic.
A. A dynamic, self motivated and goal oriented person. I've got extensive experience in field of mathematics for the past 13 years in the Philippines and UAE and have the specific skills you are looking for. I'm a fast learner who adapts quickly to change and will hit the ground running. I'm dedicated and enthusiastic about helping your school to meet its goals, and will provide top-quality results with minimal oversite. I'm an outstanding performer who takes pride in my work.
4. Why are you interested in a position with the Higher Colleges of Technology? (If you are an overseas applicant, why are you considering a career move to the Middle East, and to the United Arab Emirates in particular?)
A. HCT is the right place for me being as one of the largest, most progressive and innovative places of higher learning in the UAE. I have always wanted this opportunity to work with an environment that will help expands my knowledge that provides a vital public service, leads industry to innovative and mold students to be prepared and equipped in the globalised workplace in the future.
5. What are your hobbies and interests?
A. love reading especially books related to success in life, solving complicated problems, I love teaching the slowest student in class in fact it’s one my greatest challenge to let them understand the hardest lesson, I like activities which requires organizational skills, prioritization and time management. It is my passion to teach students not only to learn math but to LOVE math to its truest sense.
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