Long division is an operation used to divide huge numbers. It includes numerous steps that must be completed in a specific order. The dividend is divided by the divisor in the same way that conventional division problems are split, yielding the quotient and, in some cases, a remainder. This article provides you with an overview of the long division method, including steps and examples.
How to do long division
You can execute long division or short division if one of the integers is a single digit but first, you must understand how to do long division, as it is the foundation of the entire process of dividing.
The division symbol (厂) resembles an ending parenthesis attached to a horizontal line that crosses the number string beneath it. Outside the long division bar, you should write the divisor, the number you’ll be dividing, and inside the long division bar, you should write the dividend, the number you’ll be dividing into.
Instead of writing 65 / 5 or 65 ÷ 5, we can place the 5 outside the division bar and the 65 underneath it:
____
5 ) 65
What is the long division method?
Step 1
Divide the dividend’s first digit by the divisor. To put it another way, figure out how many times the divisor (the number outside the division bar) enters the dividend’s first digit. Place the entire number result directly above the divisor’s first digit, above the division line.
Step 2
Divide the divisor by the digit above the division bar. Multiply the number you just drew above the division bar by the divisor (the number to the left of the division bar). Write the result in a new row below the dividend, aligned with the dividend’s first digit.
Step 3
Subtract the dividend’s first digit from the multiplication result. To put it another way, subtract the digit in the dividend directly above it from the number you just placed in the new row below it. In a new row, write the result in the same order as the digits from the subtraction problem. Carry the dividend’s second digit down. Add the dividend’s second digit to the new bottom row, just to the right of the subtraction result you just got.
Step 4
Repeat the process of long division. Use the dividend (the number to the left of the division bar) and the new bottom-row number this time (the result of your first round of calculations and the digit you carried down). To get your result, divide, multiply, and then subtract.
Step 5
Repeat the process of long division. Begin by dividing, then multiplying, and finally subtracting. Get the rest by doing another round of long division. Take note that there is a leftover when you finish this problem. This residual will be placed next to your full number solution.
Parts of a long division equation
A lengthy division equation has different elements so make sure that you understand what they mean and how to recognize them:
- The dividend is the number under the line on the right side of the calculation. It is the amount that is being divided.
- The number on the left is the divisor. It is the one who divides.
- The quotient is the highest number. When the equation is finished, it indicates the answer or the number of units in each place value.
- The number on the upper right is the remainder. It indicates the units that are left after the quotient has been evenly split.
5 online educative resources to discover
How do you divide step by step?
Long division is the most efficient method for dividing integers. It is especially useful for converting fractions and mixed numbers to decimals. Consider the following division 3 ÷ 4. To do this without a calculator, you’ll have to use long division
- Step 1: Place the denominator outside the division bracket (to the left) and the numerator inside the division bracket to begin the long division equation (to the right). This is depicted in black on the diagram below.
- Step 2: Your result will be less than 1 when working with fractions where the numerator (3) is smaller than the denominator (4). As a result, place a 0 over the 3 as illustrated in the red diagram below.
- Step 3: Things get a little complicated because we can’t divide 3 by 4. You can carry the 3 over and omit the decimal point once step 2 is completed. To put it another way, the 3.0 can be interpreted as 30. 7 x 4 = 28, and 28 is the closest whole divisible by 4 to 30. Write 7 above the first 0 (tenths) and 28 beneath the 3.0, as shown in blue on the diagram below.
- Step 4: You could be thinking, “But 28 isn’t 30.” What are we going to do with the other two? The next 0 (hundredths) can be considered as 20 (shown on the diagram below in green). As 4 x 5 =20, 20 is divisible by four. As a result, put 5 above the second 0 (hundredths). The long division operation is complete because 20 is divisible and there is no remainder.
0.75
4) 3.00
– 2 8
2 0
0
As such, 3 ÷ 4 = 0.75
Long division examples
Divide 75 by 3 using long division
Using the methods listed, this is what it should look like:
25
3) 75
– 6
15
– 15
0
As such, 75 divided by 3 is 25.
Divide 4000 by 25 using long division
160
25) 4000
– 25
150
-150
00
As such, 4000 divided by 25 is 160.
Divide 75 by 4 using long division
18
4) 75
– 4
35
– 32
3
As such, 75 divided by 4 is 18 with a remainder of 3.
Maths tutoring services
Many kids struggle with mathematical operations, and it’s difficult to catch up once you’ve fallen behind. Thankfully, tutors are here to help. Students in elementary school, middle school, high school, and even university benefit from Tutorax’s in-home and online tutoring services. Tutoring is available in maths as well as other subjects. Tutorax helps students with homework, exam preparation, and classroom support, among other things.