Head Start Public School

Simplify calculating percentage

2012-02-04T01:52:00.000-08:00

In your head, you may find it difficult to compute 18% of 25. Instead, try solving for 25% of 18.

25% is just half of half of any number. Half of 18 is 9, and half of 9 is 4.5.

Since 25% of 18 is 4.5, it is also true that 18% of 25 is 4.5.

Multiply Up to 20 X 20 In Your Head

2012-02-04T01:50:00.000-08:00

Lets try 15 x 13.

1. Always place the larger number of the two on top in your mind.

2. Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.

3. Now add 15 + 3 = 18

4. Add a zero behind it (i.e., multiply by 10) to get 180.

5. Multiply the covered lower 3 by the single digit above it, in this case the "5" (3 x 5 = 15)

6. Add the products from steps 5 and 6 to get your answer. 180 + 15 = 195.

That's it! Wasn't that easy? Practice it on paper first!

Multiplying 3 digits or more by 11

2012-02-04T01:48:00.000-08:00

Take for example the number 51236 X 11.
First, write down the number with a zero in front of it.
051236

The zero is necessary so that the rules are simpler.

Draw a line under the number.
Bear with me on this one. It is simple if you work through it slowly. To do this, all you have to do this is "Add the neighbor". Look at the 6 in the "units" position of the number. Since there is no number to the right of it, you can't add to its "neighbor" so just write down 6 below the 6 in the units col.
For the "tens" place, add the 3 to the its "neighbor" (the 6). Write the answer: 9 below the 3.
For the "hundreds" place, add the 2 to the its "neighbor" (the 3). Write the answer: 5 below the 2.
For the "thousands" place, add the 1 to the its "neighbor" (the 2). Write the answer: 3 below the 1.
For the "ten-thousands" place, add the 5 to the its "neighbor" (the 1). Write the answer: 6 below the 5.
For the "hundred-thousands" place, add the 0 to the its "neighbor" (the 5). Write the answer: 5 below the 0.
That's it ... 11 X 051236 = 563596

Sum of digits of a Cube

2012-02-04T01:44:00.000-08:00

The sum of any cube when reduced to a single digit will always be either 1, 8, or 9.

For Example:

5³ = 125 = 1+2+5 =8
9³ = 729 = 7+2+9 = 18=1+8=9
17³ = 4913=4+9+1+3=17=1+7=8
4³=64=6+4=10=1+0=1

Also, they follow a cycle. The numbers 1 ,8, and 9 appear in order:

1 - sum of the digits of cube of 1 would be 1
2 - would be 8
3 - would be 9
4 - would be 1 (4³ = 64 = 6+4 = 10= 1+0 = 1)
5 - would be 8 (5³ = 125 = 1+2+5 = 8)
6 - would be 9 (6³ = 216 = 2+1+6 = 9)

so on and so forth.

Multiplication Sheets – 2 Digits x 11

2011-12-06T04:14:00.000-08:00

Here is an opportunity to practice your math tricks skills by multiplying 2 digit numbers by 11. Remember – add the two digits in the number being multiplied by 11, then insert the sum in between the two digits. Don’t forget to carry over if it is required.

These multiplication sheets are meant to be solved in your head. One trick is to speak out loud as you solve the problems; this will help you to remember the partial answers better – especially when you have to carry numbers. With just a little practice, you will soon be able to solve these types of problems very quickly.

The answers to these multiplication problems are at the bottom of the page; just scroll down to check your answers.

Squaring Two-Digit Numbers Quickly

2011-12-06T03:43:00.000-08:00

Using this math trick, you will be able to square any two digit number very quickly. With a little practice you can do it in your head, or you can do it on paper and still impress others with your math skills. This method of squaring is very easy, and I will be using as an example squaring the number 23.

First, determine the closest number to your number that ends in a zero. In this example, the number is 20. Next, determine the difference between your number and the closest number with the zero. In this case, it will be (23 – 20) = 3. Add the result to your number (23 + 3 = 26). Now, multiply the number with the zero by the sum of your number and the difference you determined:

20 x 26 = 520

Now square the difference you determined before, and add it to the result above:

(3 x 3) + 520 = 529

Presto! There is the square of your number!

Here are some more examples:

The Square of 25

Closest zero number: 20 (note – 30 will also work in this example)

Difference: 25 – 20 = 5

Sum: 25 + 5 = 30

Answer: (5 x 5) + (20 x 30) = 25 + 600 = 625

The Square of 37

Closest zero number: 40

Difference: 37 – 40 = -3

Sum: 37 + -3 = 34

Answer: (-3 x -3) + (40 x 34) = 9 + 1360 = 1369

The Square of 81

Closest zero number: 80

Difference: 81 – 80 = 1

Sum: 81 + 1 = 82

Answer: (1 x 1) + (80 x 82) = 1 + 6400 + 160 = 6561

Noticed how I broke down the (80 x 82) into (80 x 80) + (2 x 80)!

The Square of 12

Closest zero number: 10

Difference: 12 – 10 = 2

Sum: 12 + 2 = 14

Answer: (2 x 2) + (14 x 10) = 4 + 140 = 144

Multiplying by 5, 25, or 125

2011-12-05T05:24:00.001-08:00

Multiplying by 5 is just multiplying by 10 and then dividing by 2. Note: To multiply by 10 just add a 0 to the end of the number.

12x5 = (12x10)/2 = 120/2 = 60.

Another example: 64x5 = 640/2 = 320.

And, 4286x5 = 42860/2 = 21430.

To multiply by 25 you multiply by 100 (just add two 0's to the end of the number) then divide by 4, since 100 = 25x4. Note: to divide by 4 your can just divide by 2 twice, since 2x2 = 4.

64x25 = 6400/4 = 3200/2 = 1600.

58x25 = 5800/4 = 2900/2 = 1450.

To multiply by 125, you multipy by 1000 then divide by 8 since 8x125 = 1000. Notice that 8 = 2x2x2. So, to divide by 1000 add three 0's to the number and divide by 2 three times.

32x125 = 32000/8 = 16000/4 = 8000/2 = 4000.

48x125 = 48000/8 = 24000/4 = 12000/2 = 6000.

Multiplying by 9, or 99, or 999

2011-12-05T05:22:00.000-08:00

Multiplying by 9 is really multiplying by 10-1.
So, 9x9 is just 9x(10-1) which is 9x10-9 which is 90-9 or 81.

Let's try a harder example: 46x9 = 46x10-46 = 460-46 = 414.

One more example: 68x9 = 680-68 = 612.

To multiply by 99, you multiply by 100-1.
So, 46x99 = 46x(100-1) = 4600-46 = 4554.

Multiplying by 999 is similar to multiplying by 9 and by 99.
38x999 = 38x(1000-1) = 38000-38 = 37962.

Multiplication Trick _ Multiplying by 11

2011-12-05T01:38:00.000-08:00

One of the easiest multiplication tricks that I know of is also one of the most impressive. It is the multiplication of two-digit numbers, and, like many othermath tricks, there is an easy rule that you can use to solve problems of this sort very quickly in your head.

An Example:

44 x 11

The technique for quickly solving multiplication problems involving any two-digit number by 11 is easy to remember. Simply add the two digits and insert the result in between the two digit number.

In our example:

44 x 11

4 + 4 = 8, so simply insert “8” between “4” and “4”:

484

So then we have quickly found that
44 x 11 = 484

Birthday Trick

2011-12-04T11:35:00.000-08:00

Birthday Trick

Add 18 to your birth month
Multiply by 25
Subtract 333
Multiply by 8
Subtract 554
Divide by 2
Add your birth date
Multiply by 5
Add 692
Multiply by 20
Add only the last two digits of your birth year
Subtract 32940 to get your birthday!

The answer's format is: month/day/year. For example, an answer of 123199 means that you were born on December 31, 1999.

2011-12-04T11:24:00.001-08:00

Squaring a 2-digit number ending in 1

Take a 2-digit number ending in 1.
Subtract 1 from the number.
Square the difference.
Add the difference twice to its square.
Add 1.

Example:

If the number is 61, subtract 1: 61 - 1 = 60.
60 × 60 = 3600 (square the difference).
3600 + 60 + 60 = 3720 (add the difference twice to its square).
3720 + 1 = 3721 (add 1).
So 61 × 61 = 3721.

Pretty Cool Huh? Mental math shortcuts can benefit students in elementary, middle, high school and beyond!

Here's another:

1. For 81 × 81, subtract 1: 81 - 1 = 80. 2. 80 × 80 = 6400 (square the difference). 3. 6400 + 80 + 80 = 6560 (add the difference twice to its square). 4. 6560 + 1 = 6561 (add 1) 5. So 81 × 81 = 6561.

Mystery Math

2009-09-22T11:05:00.000-07:00

To do this trick, you have to know two things:

- How to take a number's Digital Root

- The number 9

Digital Roots

A number's Digital Root is found by adding all of a number's digits together. If the sum is larger than 9, add up the digits in the answer. Keep doing this until you have a single digit number. This number is the number's Digital Root.

For example:

- Let's say your number is 89783.

- Add up all of the digits in your number → 8 + 9 + 7 + 8 + 3 = 35

- The answer has more than one digit, so add up all of the digits in the answer → 3 + 5 = 8

- This answer has only one digit, so we're done!

- The Digital Root of 89783 is 8.

The Number 9

The number 9 is important because whenever you take a number, scramble its digits to make a new number and then subtract the two numbers, the Digital Root of the answer is always 9! Try this with the example problem:

For example:

- The original number was 30198

- The scrambled number was 13089

- The subtraction problem was 30198 - 13089 = 17109

- The Digital Root of 17109 is 1 + 7 + 1 + 0 + 9 = 18 → 1 + 8 = 9

The computer knows that the Digital Root of your complete answer is 9. You removed one digit and gave the rest to the computer. The computer took the Digital Root of the numbers you gave it and then figured out how much it had to add to get to 9. The amount it had to add was the number you crossed out! Let's look at the example again:

For example:

- The subtraction problem was 30198 - 13089 = 17109

- Cross out the 7

- Tell the computer all of the numbers that are left in the answer → 1109

- The computer computes the Digital Root of 1109 → 1 + 1 + 0 + 9 = 11 → 1 + 1 = 2

- The computer computes how much it needs to get to 9 → 9 - 2 = 7

- The computer knows that you crossed out a 7!

Danger:

The computer (and you!) can't tell the difference between someone crossing out a 9 and someone crossing out a 0. That's why the computer sometimes guesses those wrong. Let's look at the example again:

For example:

- The subtraction problem was 30198 - 13089 = 17109

- Cross out the 9

- Tell the computer all of the numbers that are left in the answer → 1710

- The computer computes the Digital Root of 1710 → 1 + 7 + 1 + 0 = 9

- The computer computes how much it needs to get to 9 → 9 - 9 = 0

- The computer knows that you crossed out a 0! → Not correct!

- The subtraction problem was 30198 - 13089 = 17109

- Cross out the 0

- Tell the computer all of the numbers that are left in the answer → 1719

- The computer computes the Digital Root of 1710 → 1 + 7 + 1 + 9 = 18 → 1 + 8 = 9

- The computer computes how much it needs to get to 9 → 9 - 9 = 0

- The computer knows that you crossed out a 0! → Right! But, it's the same answer as crossing out a 9. If someone crosses out a 0, it looks just like they crossed out a 9. Bummer!