Dividing a small number by a big number can seem like a daunting task, but with the right approach, it can be made much simpler. This article will provide a step-by-step guide on how to divide a small number by a big number, breaking down the process into manageable chunks. Whether you’re a student struggling with long division or an adult looking to brush up on your math skills, this article will provide you with the tools you need to confidently tackle this mathematical operation.
The first step in dividing a small number by a big number is to set up the problem correctly. Write the small number as the numerator and the big number as the denominator. For example, if you want to divide 12 by 24, you would write it as 12 ÷ 24. Once you have set up the problem correctly, you can begin the division process. Start by dividing the first digit of the numerator by the first digit of the denominator. In our example, this would be 1 ÷ 2, which equals 0. Write the 0 above the numerator.
Next, multiply the denominator by the quotient you just found and subtract the result from the numerator. In our example, this would be 2 × 0, which equals 0. We then subtract 0 from 12, which gives us 12. Bring down the next digit of the numerator and repeat the process. In our example, this would be 12 ÷ 2, which equals 6. Write the 6 above the numerator. Continue this process until there are no more digits left in the numerator. In our example, this would be 12 ÷ 2, which equals 6. We would then write the 6 above the numerator and the remainder would be 0.
Divide Using Long Division
Long division is a method for dividing large numbers by smaller numbers. It involves repeated subtraction and multiplication to gradually reduce the dividend (the number being divided) until there is no remainder or the remainder is smaller than the divisor (the number dividing into the dividend).
Here are the steps involved in long division:
Step 1: Set Up the Problem
Write the dividend and the divisor as a fraction, with the dividend as the numerator and the divisor as the denominator. If necessary, multiply or divide both numbers by a factor of 10, 100, or 1000 to make the divisor a whole number.
Step 2: Find the First Digit of the Quotient
Divide the first digit of the dividend by the first digit of the divisor to find the first digit of the quotient. Write the quotient above the dividend, directly above the digit being divided.
Step 3: Multiply and Subtract
Multiply the divisor by the quotient digit you just found. Subtract the result from the first part of the dividend. Bring down the next digit of the dividend.
Step 4: Repeat Steps 2-3
Continue dividing, multiplying, and subtracting until there are no more digits in the dividend. If there is a remainder, it should be smaller than the divisor.
Step 5: Check Your Answer
To check your answer, multiply the quotient by the divisor and add the remainder. The result should be the same as the original dividend.
Estimate the Quotient
When dividing a small number by a big number, the quotient (the answer) will be a small number. To estimate the quotient, divide the first digit of the dividend (the number you’re dividing) by the first digit of the divisor (the number you’re dividing by). This will give you an estimate of the quotient.
For example, let’s say we want to divide 12 by 100. The first digit of 12 is 1 and the first digit of 100 is 1. Dividing 1 by 1 gives us 1, so we estimate that the quotient will be around 1.
This estimate can be used to check your answer when you actually perform the division. If your answer is significantly different from the estimate, you may have made a mistake in your division.
Example
Let’s divide 12 by 100 using long division:
| 12 |
|---|
| 100 |
| __ |
| 120 |
| -100 |
| 20 |
| -20 |
| 0 |
As you can see, the quotient is 0.12, which is close to our estimate of 1.
Use Partial Quotients
Partial quotients is a method for long division that can be used to divide a small number by a big number. It is a systematic process that can be broken down into a series of steps.
Step 1: Set up the problem
The first step is to set up the problem. This involves writing the dividend (the number being divided) and the divisor (the number dividing) in a long division format. For example, if we are dividing 12345 by 678, we would write it as follows:
| 12345 | | 678 |
Step 2: Find the first partial quotient
The next step is to find the first partial quotient. This is the largest digit that can be divided evenly into the first digit of the dividend. In our example, the first digit of the dividend is 1, and the largest digit that can be divided evenly into 1 is 0. We therefore write 0 above the long division problem, as follows:
| 12345 | | 678 |
| 0 |
Step 3: Multiply the divisor by the partial quotient and subtract the result from the dividend
The next step is to multiply the divisor by the partial quotient and subtract the result from the dividend. In our example, we would multiply 678 by 0 and subtract the result (which is 0) from the dividend. This leaves us with the following:
| 12345 | | 678 |
| 0 | |
| 12345 |
Step 4: Repeat steps 2 and 3 until the dividend is zero
We then repeat steps 2 and 3 until the dividend is zero. In our example, we would find the next partial quotient, multiply the divisor by the partial quotient, and subtract the result from the dividend. We would then continue this process until the dividend is zero. The final result would be as follows:
| 12345 | | 678 |
| 18 | |
| 0 |
Convert to Fractions
Converting a small number to a fraction with a large denominator is a useful technique for making it easier to divide. To do this, simply add a decimal point to the small number and then add as many zeros as needed to create a denominator of the desired size. For example, to convert 5 to a fraction with a denominator of 100, we would write 5.00. Dividing 5.00 by 100 would then be equivalent to dividing 5 by 100, which is much easier to calculate.
Here is a table showing how to convert small numbers to fractions with different denominators:
| Small Number | Fraction |
|---|---|
| 5 | 5.00/100 |
| 10 | 10.00/100 |
| 15 | 15.00/100 |
| 20 | 20.00/100 |
| 25 | 25.00/100 |
Once you have converted the small number to a fraction, you can then divide it by the large number using the standard division algorithm. For example, to divide 5 by 100, you would:
- Set up the division problem as follows:
- Divide the first digit of the dividend (5) by the divisor (100) and write the result (0) above the dividend.
- Multiply the divisor by the quotient (0) and write the result (0) below the dividend.
- Subtract the result from the dividend to get a remainder of 5.00.
- Bring down the next digit of the dividend (0) and repeat steps 2-4 until there are no more digits to bring down.
- The final quotient is 0.05, which is equivalent to 5/100 or 0.05 in decimal form.
100 | 5.00
100 | 5.00
0
100 | 5.00
0
0
100 | 5.00
0
0
5.00
100 | 5.00
0
0
5.00
500
Use a Calculator
If you have a calculator, dividing a small number by a big number is easy. Simply enter the dividend (the smaller number) and the divisor (the bigger number) into the calculator, and then press the division key. The calculator will display the quotient (the result of the division).
For example, if you want to divide 12 by 3, you would enter 12 into the calculator, then press the division key, then enter 3, and then press the equals key. The calculator would display the answer, which is 4.
You can also use a calculator to divide a decimal number by a whole number. For example, if you want to divide 1.2 by 3, you would enter 1.2 into the calculator, then press the division key, then enter 3, and then press the equals key. The calculator would display the answer, which is 0.4.
If you want to divide a whole number by a decimal number, you can convert the decimal number to a fraction and then divide. For example, if you want to divide 12 by 0.5, you can convert 0.5 to the fraction 1/2. Then, you can divide 12 by 1/2 by multiplying 12 by the reciprocal of 1/2, which is 2. The answer is 24.
| Dividend | Divisor | Quotient |
|---|---|---|
| 12 | 3 | 4 |
| 1.2 | 3 | 0.4 |
| 12 | 0.5 | 24 |
Solve Word Problems
Division word problems typically involve real-world scenarios where you need to divide a quantity into equal parts or find the number of times one quantity is contained within another. To solve these problems, follow these steps:
- Read the problem carefully to identify the information given.
- Determine what you need to find, usually represented by the unknown quantity (e.g., “How many bags?” or “What is the length?”).
- Set up a division equation using the given information and the unknown quantity.
- Solve the equation by dividing the dividend by the divisor to find the unknown quantity.
- Check your answer by substituting it back into the original problem and verifying if it makes sense.
Example 1: Dividing Candy Evenly
Given 24 pieces of candy, how many bags can you fill if each bag can hold 3 candies?
- Unknown: Number of bags
- Division equation: Number of bags = 24 candies / 3 candies per bag
- Solving: 24 / 3 = 8
- Answer: 8 bags
Example 2: Finding the Length of Fence
If you have 120 feet of fence and want to enclose a square area, what is the length of each side of the square?
- Unknown: Side length of square
- Division equation: Perimeter = 4 x Side length, so Side length = Perimeter / 4
- Solving: 120 feet / 4 = 30 feet
- Answer: 30 feet per side
Example 3: Calculating Distance Traveled
A car travels 360 miles in 6 hours. What was the car’s average speed in miles per hour?
- Unknown: Average speed
- Division equation: Average speed = Distance / Time
- Solving: 360 miles / 6 hours = 60 miles per hour
- Answer: 60 miles per hour
Check Your Answer
Once you have found a number that gives you your denominator, multiply that number by your numerator to double check your answer. If the answer matches your dividend, then you have successfully divided the small number by the big number. If not, then you will need to try again.
8. Divide 12 by 19,291
To solve this problem, set up your long division like you would when dividing 12 by 192. Then, to find the first digit of your answer, you multiply 192 by X. As x goes up, so will the result of 192 x. When you get to 192 multiplied by 10, you know that 19200 is too high (19200 > 12), while 192 multiplied by 9 is too low (192 x 9 = 17280 < 12). Therefore, the answer is 192 x 9 = 17280. Subtract 17,280 from 12,000 to get 4800. Bring down the next digit 0, then repeat the process until there are no more digits in your dividend.
Setting this all up in long division format should give you the following:
0.0006278 19,291)12.0000 115746 48240 38582 96580 96455 1250 Common Mistakes to Avoid
1. Avoiding Repeated Subtraction
When dividing a small number by a large number, it’s tempting to use repeated subtraction. This method is highly inefficient and prone to errors. It’s better to use the long division method instead.
2. Misplacing the Decimal Point
Pay close attention to the placement of the decimal point when dividing a decimal by a whole number or another decimal. Misplacing the decimal can lead to incorrect results.
3. Using a Division Sign as a Fraction Bar
The division sign (÷) is not the same as a fraction bar. When dividing a number, write it as a numerator and denominator in fraction form or use the long division method.
4. Forgetting to Include a Remainder
When dividing a small number by a large number, there may be a remainder that is less than the divisor. This remainder should be included in the quotient as a decimal or fraction.
5. Rounding Off Too Early
When dividing a small number by a large number, it’s important to carry out enough decimal places to achieve the desired accuracy. Rounding off too early can lead to loss of precision.
6. Dividing Zero by a Number
Dividing zero by any number (except zero) results in undefined. This is because any number multiplied by zero is zero, so there is no number that can be multiplied by zero to get a non-zero result.
7. Dividing a Positive Number by a Negative Number
Dividing a positive number by a negative number results in a negative quotient. Similarly, dividing a negative number by a positive number results in a positive quotient.
8. Sign Errors in Remainders
When the dividend and divisor have different signs, the sign of the remainder will be the same as the sign of the dividend.
9. Misinterpreting Incomplete Quotients
Incomplete quotients can occur when the divisor is significantly larger than the dividend. In such cases, the quotient should be interpreted as an approximation of the true quotient. To obtain a more accurate quotient, it’s necessary to carry out more decimal places or use alternative methods such as a calculator or computer software.
Mistake Description Example Avoiding Repeated Subtraction Using repeated subtraction instead of long division Dividing 1 by 100 using repeated subtraction: 1 – 0.01 – 0.001 – 0.0001 – … Misplacing the Decimal Point Incorrectly placing the decimal point when dividing decimals Dividing 0.5 by 5 and placing the decimal point after the first digit: 0.10 Using a Division Sign as a Fraction Bar Treating the division sign as a fraction bar Writing 1 ÷ 2 as 1/2, which is a fraction Forgetting to Include a Remainder Omitting the remainder when dividing with a decimal divisor Dividing 1 by 3 and ignoring the remainder of 1: 0.3 Rounding Off Too Early Premature rounding of the quotient Dividing 1 by 7 and rounding to two decimal places: 0.14, instead of 0.1428 Dividing Zero by a Number Attempting to divide zero by a non-zero number Dividing 0 by 5: undefined Dividing a Positive Number by a Negative Number Incorrect sign of the quotient when dividing a positive number by a negative number Dividing 5 by -2: -10, instead of 5 Sign Errors in Remainders Incorrect sign of the remainder when the dividend and divisor have different signs Dividing -5 by 2: -2 remainder 1, instead of -2 remainder -1 Misinterpreting Incomplete Quotients Mistaking an incomplete quotient for the true quotient Dividing 1 by 1000: 0.001, instead of an approximation like 0.00099 Practice Makes Perfect
Dividing small numbers by large numbers can be challenging, but practice makes perfect. Engage in regular practice exercises to improve your skills and increase your efficiency in handling such calculations. Consecutive practice sessions reinforce your understanding and build confidence in your abilities.
10. Division Algorithm and Long Division Process
The division algorithm provides a systematic approach to divide small numbers by large numbers. It involves the following steps:
- Divide the dividend (the small number) by the divisor (the large number) until the quotient (the result) is smaller than the divisor.
- Multiply the divisor by the quotient to get the product.
- Subtract the product from the dividend to get the remainder.
- If the remainder is zero, the division is complete. Otherwise, repeat steps 1-3 until the remainder is zero or the quotient reaches the desired level of precision.
The long division process is a detailed representation of the division algorithm. It involves setting up the dividend and divisor vertically, performing the division steps (dividing, multiplying, subtracting, and bringing down the next digit), and continuing until the desired result is obtained. A step-by-step example of long division is provided below:
Example: Explanation: 1256 ÷ 7 Dividend (1256) and divisor (7) 179 R 3 Quotient (179), remainder (3) How To Divide A Small Number By A Big Number
When dividing a small number by a big number, it’s important to remember that the quotient (the answer) will be a small number as well. To perform this division, you can use the following steps:
- Set up the division problem with the dividend (the small number) on top and the divisor (the big number) on the bottom.
- Divide the first digit of the dividend by the divisor. If the result is a decimal, truncate it to the nearest whole number.
- Multiply the result by the divisor and subtract it from the dividend. Bring down the next digit of the dividend.
- Repeat steps 2 and 3 until you have brought down all the digits of the dividend.
- The quotient is the number you have been writing above the dividend.
For example, to divide 12 by 100, you would set up the problem as follows:
“`
12 ÷ 100
“`Then, you would divide the first digit of the dividend (1) by the divisor (100). The result is 0.01, which you would truncate to 0.
“`
12 ÷ 100 = 0
“`Next, you would multiply the result (0) by the divisor (100) and subtract it from the dividend (12). This gives you 12.
“`
12 – (0 x 100) = 12
“`You would then bring down the next digit of the dividend (2) and repeat steps 2 and 3.
“`
122 ÷ 100 = 0.01
“`
“`
122 – (0 x 100) = 122
“`
“`
1222 ÷ 100 = 0.01
“`
“`
1222 – (0 x 100) = 1222
“`The quotient is 0.012, which you can write as 0.012 or 1.2%.
People also ask
How do you divide a fraction by a whole number?
To divide a fraction by a whole number, you can multiply the fraction by the reciprocal of the whole number. The reciprocal of a number is 1 divided by the number.
How do you divide a mixed number by a whole number?
To divide a mixed number by a whole number, you can first convert the mixed number to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
How do you divide a decimal by a whole number?
To divide a decimal by a whole number, you can move the decimal point in the dividend (the number being divided) to the right by the same number of places as there are zeros in the divisor (the number dividing into the dividend). Then, divide as usual.
