How will I solve mathematics, physics and chemistry without calculator how. This is a very good question. However, i have answered it in a separate article. Check it out here How will I solve mathematics,physics and chemistry without calculator how.
Multiplying Numbers up to 10
You don’t need to memorize the multiplication table, just use this way at any time!
We will start by learning how to multiply numbers up to 10. Let’s look how it works:
We’ll take 7 × 8 as an example.
Write this example down in your notebook and draw a circle below each number to be multiplied.
7 × 8 =
( ) ( )
Now go to the first number (7) to be multiplied. How many more do you need to make 10? The answer is 3. Write 3 in the circle below the 7. Now go to the 8. How many more to make 10? The answer is 2. Write this number in the circle below the 8.
It should look like this:
7 × 8 =
Now you have to subtract diagonally. Take either one of the circled numbers (3 or 2) away from the number, not directly above, but diagonally above. In other words, you either take 3 from 8 or 2 from 7. You only subtract one time, so choose the subtraction you find easier. Either way, the answer will be the same 5. This is the first digit of your answer.
8 − 3 = 5 or 7 − 2 = 5
Now multiply the numbers in the circles. Three times 2 is 6. This is the last digit of your answer. The answer is 56.
Multiplying Numbers in the Teens
Let’s see how to apply this method to multiplying numbers in the teens. We will use 10 as our reference number and the following example:
(10) 13 × 14=
Both 13 and 14 are above our reference number, 10, so we put the circles above the multipliers. How much above? 3 and 4. So we write 3 and 4 in the circles above 13 and 14. Thirteen equals 10 plus 3 so we write a plus sign in front of the 3; 14 is 10 plus 4 so we write a plus sign in front of the 4.
(10) 13 × 14=
As in the previous example, we work diagonally. 13+4 or 14+3 is 17. Write this number after the equals sign. Multiply the 17 by the reference number 10 and get 170. This number is our subtotal, so write 170 after the equals sign.
In the last step, we should multiply the numbers in the circles. 3 × 4=12. Add 12 to 170 and we get our finished answer 182.
(10) 13 × 14=170+12=182
Multiplying Numbers Greater Than 10
This method is also working in the case of large numbers.
96 × 97=
What do we take these numbers up to? How many more to make what? 100. So write 4 under 96 and 3 under 97.
96 × 97=
Then subtract diagonally. 96-3 or 97-4 is 93. This is the first part of your answer. Now, multiply the numbers in the circles. 4 × 3=12. This is the last part of the answer. The finished answer is 9,312.
96 × 97=9,312
This method is certainly easier than the method you learned in school! We believe that everything genial is simple, and maintaining simplicity is a hard work.
Multiplying Numbers Above 100
Here, method is the same. We would use 100 as our reference number.
(100) 106 × 104=
The multipliers are higher than the reference number 100. So we draw circles above 106 and 104. How much more than 100? 6 and 4. Write these numbers in the circles. They are positive (plus) numbers because 106 is 100 plus 6 and 104 is 100 plus 4.
(100) 106 × 104=
Add diagonally. 106+4=110. Then, write 110 after the equals sign. Multiply 110 by the reference number 100. How do we multiply by 100? By adding two zeros to the end of the number. That makes our subtotal 11,000.
Now multiply the numbers in the circles 6 × 4=24. Add the result to 11,000 to get 11,024.
Multiplying Using Two Reference Numbers
Previous method for multiplication has worked well for numbers that are close to each other. When the numbers are not close, the method still works but the calculation become more difficult.
It’s possible to multiply two numbers that are not close to each other by using two reference numbers.
8 × 27=
Eight is close to 10, so we will use 10 as our first reference number. 27 is close to 30, so we use 30 as our second reference number. From the two reference numbers, we choose the easiest number to multiply by. It is 10. This becomes our base reference number. The second reference number must be a multiple of the base reference number. 30 is 3 times the base reference number 10. Instead of using a circle, write the two reference numbers to the left of the problem in brackets.
(10 × 3) 8 × 27=
Both the numbers in the example are lower than their reference numbers, so draw the circles below.
How much are 8 and 27 lower than their reference numbers (remember the 3 represents 30)? 2 and 3. Write these numbers in the circles.
(10 × 3) 8 × 27=
Now multiply the 2 below the 8 by the multiplication factor 3 in the parentheses.
2 × 3=6
Write 6 in the bottom circle below the 2. Then take this bottom circled number 6, diagonally away from 27.
Multiply 21 by the base reference number 10.
21 × 10=210
210 is our subtotal. To get the last part of the answer, multiply two numbers in the top circles, 2 and 3, to get 6. Add 6 to our subtotal of 210 and get our finished answer of 216.
When we write prices, we use a decimal point to separate the dollars from the cents. For example, $1.25 represents one dollar, and 25 hundredths of a dollar. The first digit after the decimal point represents tenths of a dollar. The second digit after the decimal point represents hundredths of a dollar.
Multiplying decimals is no more complicated than multiplying any other numbers. Let’s see an example:
1.3 × 1.4=
We write down the problem as it is, but ignore the decimal points.
(10) 1.3 × 1.4=
Although we write 1.3 × 1.4, we treat the problem as:
13 × 14=
Ignore the decimal point in the calculation and say 13+4=17, 17 × 10= 170, 3 × 4=12, 170+12=182. Our work isn’t finished yet, we have to place a decimal point in the answer. To find where we put the decimal point we look at the problem and count the number of digits after the decimal points, the 3 in 1.3 and the 4 in 1.4. Because there are two digits after the decimal points in the problem there must be two digits after the decimal point in the answer. We count two places backwards and put the decimal point between the 1 and the 8, leaving two digits after it. So, the answer is 1.82.
Let’s try another problem.
9.6 × 97=
We write the problem down as it is, but call the numbers 96 and 97.
(100) 9.6 × 97=
93 × 100 (reference number)=9,300
4 × 3=12
Answer is 931.2
Calculating Square Roots
There is an easy method for calculating the exact answer for square roots. It involves a process called cross multiplication.
To cross multiply a single digit, you square it.
3²=3 × 3=9
If you have two digits in a number, you multiply them and double the answer. For example:
34=3 × 4=12
12 × 2=24
With three digits, multiply the first and third digits, double the answer, and add this to the square of the middle digit. For example, 345 cross multiplied is:
3 × 5=15
15 × 2=30
It’s hard to believe, but now squaring big numbers without a calculator is possible! Learn fast techniques of mental math below here that will help you to perform like a genious.
To square a number simply means to multiply it by yourself. A good way to visualize this is, if you have a square brick section in your garden and you want to know the total number of bricks making up the square, you count the bricks on one side and multiply the number by itself to get the answer.
13² = 13 × 13 =169
We can easily calculate this using some methods for multiplying numbers in the teens. In fact, the method of multiplication with circles is easy to apply to square numbers, because it is easiest to use when the numbers are close to each other. In fact, all of the strategies taught here make use of the general strategy for multiplication.
Method of Using a Reference Number
(10) 7×8 =
The 10 to the left of the problem is our reference number. It is a number we take our multipliers away from.
Write the reference number to the left of the problem and then ask yourself, are the numbers you are multiplying above (higher than) or below (lower than) the reference number? In this case the answer is lower (below) each time. So we put the circles below the multipliers. How much below? 3 and 2. We write 3 and 2 in the circles. Seven is 10 minus 3, so we put a minus sign in front of the 3. Eight is 10 minus 2, so we put a minus sign in front of the 2.
(10) 7×8 =
We now work diagonally. Seven minus 2 or 8 minus 3 is 5. We write 5 after the equals sign. Now, multiply the 5 by the reference number, 10. Five times 10 is 50, so write a 0 after the 5. (To multiply any number by 10 we affix a zero.) 50 is our subtotal.
Now multiply the numbers in the circles. Three times 2 is 6. Add this to the subtotal of 50 for the final answer of 56.
(10) 7×8 = 50
-(3) -(2) +6
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This is a very good question. However, i have answered it in a separate article. Check it out here How will I solve mathematics,physics and chemistry without calculator how