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00:00


Ask a friend to pick any three-digit number. Tell him or her to multiply the number by 7, then 11, and then 13 on a calculator. Before they have a result, you already will know the answer.



Let’s see how this works. Imagine your friend picks 123. You can instantly say the final result is 123,123. Or if your friend picks 479, you know the answer is 479,479.


The pattern is very simple so you can only do this trick once. The trick is that a number ABC multiplied by 7, then 11, then 13 will be ABC, ABC as a six-digit number.



Proof
Note that 7 x 11 x 13 = 1001. When you multiply ABC by 1001, that is the same as multiplying by (1000 + 1). Multiplying by 1000 shifts the number ABC by three spots to get ABC, 000. Then we multiply by 1 and add the result, which means adding ABC to the number again. The final result is ABCABC as a six-digit number.


EXERCISE
Attempt these simple questions   
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00:00

This week, we’ll be considering how to multiply two digits numbers from 11 to 20. This trick makes multiplying numbers between 11 and 20 an extension of the times from 1 to 10. This trick will help you figure out the times' table from 11 to 20 by extending the times table up to 10. 


Can you multiply 12 by 14 easily? Problems up to 10 are often memorized when we learn the times' table up to 10.

There are four main steps. First, add the unit’s digits of the second number to the first number. second, multiply the result by 10. third, multiply the unit’s digits of both numbers. And finally, add the results from the second and third steps.    



Let’s do an example of 12 x14.the number 14 has the unit’s digits of 4. We add the unit’s digit 4 to the number 12 to get 16. Then we multiply that by 10 to get 160. Third, we multiply the unit’s digits of 2 and 4 to get 8. finally, we add 160 and 8 to get 168.



Let’s do another example of 15 by 18. We add 8 to 15 to get 23, and then we multiply that by 10 to get 230. We then multiply the unit’s digits of 5 and 8 to get 40. Adding that to 230 get’s an answer of 270.



Notice we would get the same answer even if we did 18 times 15. In this problem, we would add 5 to 18 to get 23, which e multiply by 10 to get 230 then we multiply the unit’s digits of 8 and 5to get 40. Adding 230 and 40 once again results in the answer of 270.


EXERCISE

CLICK HERETO ATTEMPT SOME SIMPLE QUESTIONS

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00:00



In America, a full-time job typically means 40 hours per week for about 50 weeks, which means translates into 40 x 50 = 2,000 hours in a year. So, you can find your hourly wage by dividing your annual salary by 2,000.


Take a look at this example!

Let’s say you earn $60,000 in a full-time job. What is your hourly wage?

A good estimate is to divide your compensation by 2,000. This can be done expediently by halving your compensation and then dividing by 1,000 (moving the decimal 3 spots to the left).

So, let’s divide $50,000 by 2,000. We half $60,000 to get $30,000, and then we divide by 1,000 to get $30 per hour.


ACTIVITIES


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00:00


This week, we will be considering the rules of 72


  •   You invest #1,000 at a guaranteed 4% interest rate annually. How long will it take your money to double to #2,000?

We can solve the problem by computing compound interest. In the first year, you earn 4% on #1,000 which is #40. In other words, your investment grows to #1,000(1.04) = #1040. In the next year, you earn another 4% on top of #1040, which means your investment grows to #1040(1.04) = #1081.6 which is #1040(1.04)2.  Note the pattern, we can see that in X years your investment will grow to #1000(1.04) x.  We can set this equal to #2000 and solve (using logarithms) that x is about 17.67 years. In other words, it takes about 18 years for your investment to double.


The rule for 72 is a shortcut to estimate this answer very quickly. You divide 72 by the interest rate, expressed as a percentage, to get the doubling time.


For example, to calculate the doubling time with a fixed 4% interest rate, we divide 72 by the interest rate of 4%. Since 72/4 = 18, that means the investment will double in roughly 18 years. This is pretty close to the exact answer of 17.67!


Similarly, we can solve an investment with 6% interest will double in roughly 72/6 = 12 years, an investment with 8% interest will double in roughly 72/8 = 9 years, and an investment 12% interest will double in roughly 72/12 = 6 years. These are all very close to the exact answers and the rule avoid having to compute compound interest.


There are two important caveats when using the rule of 72.

First, the rule is a good approximation but it is not an exact answer. When you are working with investments, you may want to check an exact answer with a calculator or spreadsheet.


Secondly, the rule of 72 works only if the interest rate is fixed. When you invest in the stock market, the rate of return varies over time, and so you cannot use the rule of 72 with the same accuracy as you could for an investment with a fixed and guaranteed return.

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01:57

PERCENTAGES
This week, we will be considering how to calculate percentages.
While you can use a calculator to figure out percentages, there is a simple method you can use to solve them in your head. The best part is you probably are familiar with the basic skills for calculating percentages, which are calculating 10% and 50%.


Calculating 10%. Calculating 10 percent of a number is the same as dividing the number by 10. The procedure to divide a number by 10 is to move the decimal point one spot to the left. For example, to calculate 10% of 123 is the same as dividing the number by 10. This is accomplished by moving the decimal point over 1 spot to the left, which means that 12.3 is 10% of 123. Similarly, 10% of 56 is 5.6 and 10% of 4987.56 is 498.756.

Calculating 50%. calculating 50 percent of a number is the same as dividing the number by 2, which means to half the number. For example, to calculate 50% of 123 is the same as halving 123. So, 50% of 123 is 61.5. similarly, 50% of 56 is 28 and 50% of 5000 is 2500.

Calculating other percentages. You can calculate most percentages in your head if you can calculate 10% and 50%! The reason is that many percentages can be found as a combination of 10% and 50%.
Let’s do an example of calculating 15% of 63. Note that 15% is equal to 10% plus 5%. To do this, you can calculate 10% and then half of 10% (which is 5%) to half itself. So, we can calculate 10% of 63 is equal to 6.3. then we calculate 5% as half of that, which is 3.15. so, we add these together to get 9.45. which is 15% of 63.
Let’s do another example of 25% of 84. Note that 25% is equal to half of 50%. So, we can calculate 25% of 84 by finding 50% and then halving the result. We can readily calculate that 50% of 84 is equal to 42, and then we need to take half of that number to get 21. Therefore, we have 25% of 84 is equal to 21.
Here is some short guide.
5% = half of 10%
10% = divide by 10
15% = add 10% and half of 10%
20% = find 10% and then double it
25% = find 50% and then half it
30% = find 10% and then triple it
40% = find 10% and 50%. Subtract 10% value from 50% value
50% = divide in half
60% = find 10% and 50%. Add 10% value to 50% value
75% = find 50% and 25% and add together
80% = find 20% (double 10%) and subtract from the whole.
90% = find 10% and subtract from the whole.
Note that there can be more than one way to calculate a given percentage. For example, you can also calculate 60% by finding 10% and then multiplying that value by 6. You can do the same thing for 20, 30, 40, 60, 70, 80, and 90.



Exercise
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09:55 1
MENTAL MATH

What is mental math?

Mental math has a mixed reputation. Some consider it useless because they felt is not necessary to get good grades in mathematics or to pursue a professional math carrier. So, what is the point of learning mental math?
There are many benefits of learning mental math. First, math skills are needed for regular tasks like calculating the tip in a restaurant or comparison shopping to find the best deal. Secondly, mental math is one of the few times people enjoy talking about math. Third, mental math methods can help students build confidence in maths and numbers.
Mental math is fun to share. Imagine your friend asks you to multiply 93 and 97, and before they can type it into a calculator, you can figure out the answer in your head. Or imagine your friend asks you to divide 17 by 91, you can calculate out the exact decimal answer in your head. Mental mat is impressive to see and they can be exciting to learn.
Mental math reduces the chore of simple math, build confidence in math skills, and serve as educational entertainment at parties and pubs. Each week has some mental math calculations that require extensive memorization and lots of practice to learn.
Each week explains a math trick, and then has practice problems with complete solutions to illustrate the method. Every method is accompanied with a mathematical proof to justify why the trick works.

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