At first, dividing by a decimal number might seem a little difficult. After all, nobody learns the multiplication tables of "0, 7", for example. The key is to change the division problem to a format that only uses integers. After rewriting the problem in this way, it becomes a normal long division exercise.
Part 1 of 2: Rephrasing the problem as a common division problem
Step 1. Assemble the division problem
Use a pencil as you may want to proofread the work.
how much is it 3 ÷ 1, 2?
Step 2. Write the whole number in decimal form
Place a decimal separator (comma sign) after the integer, and write zeros after the separator. Do this until both numbers have the same number of places to the right of the decimal point. This does not change the integer value.
in question 3 ÷ 1, 2, the integer is 3. Since 1, 2 has a place to the right of the decimal point, rewrite 3 as 3, 0 so that it also has a place after the decimal point. Now the equation has changed to 3, 0 ÷ 1, 2.
- Warning: do not add zeros to the left of the decimal separator! The number 3 is the same as 3, 0, but not the same as 30 or 300.
Step 3. Move the decimal separators to the right until you have whole numbers
In division problems, you can move the comma, but only if you move the same amount in both numbers. This converts numbers to whole numbers.
to change 3, 0 ÷ 1, 2 to whole numbers, move the decimal separators one place to the right. The number 3, 0 will become 30, and the number 1, 2 will become 12. Now the equation has changed to 30 ÷ 12.
Step 4. Write the problem using long division
Place the dividend (usually the largest number) below the division symbol. Put the divider out of it. Now you have a common long division problem with whole numbers. If you want to remind how to do long division, read the next section.
Part 2 of 2: Solving Long Division Problem
Step 1. Find the first digit of the answer
Start solving as you normally would, comparing the divisor to the first digit of the dividend. Calculate the number of times the divisor "fits" within that digit and write that number above it.
we're trying to fit the number 12 into the number 30. Compare the 12 to the first digit of the divisor, 3. Since the 12 is greater than the number 3, it fits 0 times. Write 0 above the 3, in the line of the answer.
Step 2. Multiply this digit by the divisor
Write the product (the answer to the multiplication problem) below the dividend. Place it directly below the first digit of the dividend, as it is the digit used previously.
as 0 x 12 = 0, write 0 below 3.
Step 3. Subtract to find the rest
Subtract the product you just found by the digit directly above it. Write your answer on a new line below.
3 - 0 = 3, are write
Step 3. directly below 0.
Step 4. Lower the next digit
Put down the next digit of the dividend next to the number you just typed.
the dividend is 30. We've already used the number 3, so the next digit to go down is 0. Put it down next to the 3 to make the number
Step 5. Try to fit the divider inside the new number
Now repeat Step 1 of this section to find the second digit of the answer. This time, compare the divisor to the number you wrote on the last line.
how many times does the number 12 fit within the number 30? The closest we can get is 2, since 12 x 2 = 24. Write
Step 2. in the second square of the answer line.
- If you're not sure what the answer is, try doing some multiplication until you find the biggest answer that fits the dividend. For example, if you think the answer is 3, multiply 12 x 3 and you get 36. This answer is too big since we're trying to fit it into the number 30. Try one less number, 12 x 2 = 24. This answer fits, so 2 is the right answer.
Step 6. Repeat the Steps above to find the next number
This is the same long division process used above, and can be used for any other long division problem:
- Multiply the new digit of the answer line by the divisor: 2 x 12 = 24.
- Write the product on a new line below the dividend: write 24 directly below the number 30.
- Subtract the lowest line from the line above it: 30 - 24 = 6, then write the number 6 on a new line below.
Step 7. Continue until you reach the end of the answer line
If there are still any digits left in the dividend, lower it and continue to solve the problem in the same way. If you've reached the end of the answer line, go to the next Step.
we just wrote the number
Step 2. at the end of the answer line. Go to the next step.
Step 8. Add a decimal to increase the dividend if necessary
If the numbers divide evenly, the last subtraction will have the number "0" in the answer. This means that you are done and that an integer is the answer to the problem. However, if you reach the answer line and still have more numbers to divide, you'll need to increase the dividend by adding a decimal separator followed by the digit 0. Remember that this doesn't change the value of the integer.
we are at the end of the answer line, but the answer to the last subtraction is "6". Increase the number "30" under the long division sign by adding ",0" to the end. Write the decimal separator also in the same place on the same line as the answer, but don't write anything after that for now.
Step 9. Repeat the same steps to find the next digit
The only difference here is that you must lower the decimal point of the same place on the answer line. After doing this, finding the remaining digits of the answer can be done in exactly the same way.
drop the new digit 0 to the last line to form the number "60". As the 12 fits into the number 60 exactly 5 times, write
Step 5. as the last digit in the answer line. Don't forget to put a decimal separator on the answer line, then 2, 5 is the final answer to the problem.
- You can write this as the remainder (so the answer for 3 ÷ 1, 2 is "2 with remainder 6"). Now that you're working with decimal numbers, your teacher will probably expect you to solve the decimal part of the answer as well.
- By following the long division methods correctly, you will always end up with the decimal separator in the right place or no decimal separator if the division is exact. Don't try to guess where to put them; it usually differs with respect to the decimal separator of starting numbers.
- If the long division problem is too big, you can stop at some point and round the number. For example, to solve for 17 ÷ 4, 20, just calculate down to 4, 047… and round the answer to "approximately 4, 05."
- Remember to use these terms:
- The dividend is the number that will be divided by the divisor.
- The divisor is the number that the dividend will be divided by.
- The quotient is the result of the mathematical problem.
- All together: dividend ÷ divisor = quotient