VIDEO: Divide in writing with decimal numbers

Dividing fractions in writing

The actual written To divide is usually not a problem, but when it comes to floating point numbers, most people ponder. Is 1.25: 0.5 now 2.5, 25 or even 250?

• Floating numbers are also called decimal fractions because they are fractions. In these denominators there is always a power of 10. The exponent of the power corresponds to the number of places after the decimal point. 1.25 is as 125/10² and 0.5 = 5/10¹.
• Fractions are divided by multiplying by the inverted fraction. So 1.25 becomes:, 05 = (125/10²)*(10/5).
• Fractions are multiplied by multiplying the numerators and denominators together. So you get (125 * 10) / 5 * 10²). You can also write it like this: 125/5 * 10/10².
• You can see that you can divide the digits as normal in writing, converting them to 125: 5, which results in 25. But the result still has to be 10/10² be multiplied. 10/10² is 1/10. So you have to divide the result by 10 and get 2.5.


Calculate in writing divided - this is how it works

How did that work again? Calculate in writing divided, that came in the ...

Abbreviated method of division with decimal numbers

Based on this knowledge, you can shorten the procedure. You can derive it like this:

1. So it is easily possible from 1.25: 0.5 = 125/10² * Make 10/5. Now it makes sense if in the 2nd Fraction in the numerator there is a 1. If you want a 1 in the second fraction in the numerator, you need to reduce the entire expression by 10. You get 125 * 10/10² * 10/5*10 = 125*10/10²: 5*10/10.
2. Calculate the expression back again. You will receive it 125 * 10/10²: 5*10/10 = 125/10: 5 = 12,5:5. As you can see, the same thing comes out if you simply shift both commas the same number of places to the right until the second number, i.e. the divisor, is no longer a decimal point.
3. If you now divide in writing, you just have to make sure that you put a comma in the result when you edit the first decimal place. So 12 divided by 5 is 2 remainder 2, the remainder is supplemented with the 5 after the decimal point, you you have to put a comma after the result 2, and then continue calculating as usual, you get 2.5 out.

Example for the written division of decimal numbers

1. 6.7581: 0.027: The divisor has 3 decimal places -> the decimal point must be used for both Counting shifted 3 places to the right.
2. You get 6758.1: 27. Do the usual written division. The 27 goes into the 67 twice, leaving a remainder of 13.
3. Attach the next position (5) to the rest. The 27 goes five times to the 135, there is nothing left.
4. Add the next digit to it, the 27 goes zero times into the 8, the remainder is 8. So you now have the digits 250.
5. Since you are now adding 8 to 81 by taking the decimal place, you now have to put the comma. The 27 goes into the 81 three times. You get 250.3 as a result.

In case you forget what shifting commas is like when dividing decimal numbers in writing, remember that you Decimal numbers can also write as fractions. Then you can easily deduce that yourself.