How Does Division Work as Repeated Subtraction?
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction. The technique of repeatedly subtracting one number from another until the final result is zero is known as division. This method is frequently used and seen when dividing numbers and is an effective technique to teach division to younger grades. To further understand the concept, let's study more about repeated subtraction, how to divide using repeated subtraction, and how to solve a few problems.
Division is a Process of Repeated Subtraction
Division is the Process of Repeated Subtraction
The act of repeatedly subtracting the same number from a large number until the final result, or remainder, is zero or less, is referred to as repeated subtraction. Another name for this procedure is division. In other words, repeated subtraction is the process of subtracting the same number from the other number until the remainder is zero or until it is smaller than the original number. This operation can also be written in the form of division. As in an illustration \[12 - 3 = 9,9 - 3 = 6,6 - 3 = 3,3 - 3 = 0\] . This indicates that the number has been deducted five times, and the division form is\[12 \div 3 = 4\]. Thus Repeated Subtraction is Called Division.
Dividing 1 Digit Number
Take the dividend's first digit starting from the left in step one. Verify that this digit exceeds or is equal to the divisor.
Next, divide it by the divisor, and write the result as the quotient on top.
Subtract the outcome from the digit, and then write the difference below.
Decrease the dividend's subsequent digit (if present).
Carry out Step 4 again.
From the given image, we can understand how to divide 1 Digit Number.
Example of How to divide 1 Digit Number
Division by Repeated Subtraction
Similar to how repeated addition is used to solve multiplication problems, repeated subtraction can be used to address difficulties with division. Dividend, divisor, quotient, and remainder are the four components of division that are taken into account when dividing any integer.
The procedures for division by iterative subtraction are as follows:
Take note of the dividend and divisor. Dividend and divisor both refer to an amount that must be divided; the dividend is the amount that the divisor divides.
Subtract the divisor once again using that number after obtaining the difference.
If you don't get a result that is less than the divisor or zero, keep trying to subtract.
The quantity of times the subtraction procedure is finished is referred to as Quotient.
The remainder is the amount that remains after subtracting a number.
Examples for Dividing 1 Digit Number
Example 1: Use the repeated subtraction method to divide 120 by 15.
120 divided by 15 is the dividend.
Repeatedly subtract 15 from 120.
\[\begin{array}{l}120 - 15 = 105\\105 - 15 = 90\\90 - 15 = 75\\75 - 15 = 60\\60 - 15 = 45\\45 - 15 = 30\\30 - 15 = 15\\15 - 15 = 0\end{array}\]
Here, 15 is removed eight times from 120, leaving 0 as the remainder. Thus, the quotient is \[120 \div 15 = 8\] , which is 8.
Example 2: Bella needs to provide 8 apples to each of her friends out of the 48 she has on hand. How many buddies can you divide 48 apples equally among?
Given that Dividend = 48 and Divisor = 8,
Using the method of repeated subtraction,
\[\begin{array}{l}48 - 8 = 40\\40 - 8 = 32\\32 - 8 = 24\\24 - 8 = 16\\16 - 8 = 8\\8 - 8 = 0\end{array}\]
Therefore, 48 is taken away six times from 8, leaving behind 0.
Bella can therefore distribute 48 apples among her six buddies.
Example 3: Divide 60 by 10 by the process of Repeated Subtraction.
For \[60 \div 10\],
\[\begin{array}{l}60 - 10 = 50\\50 - 10 = 40\\40 - 10 = 30\\30 - 10 = 20\\20 - 10 = 10\\10 - 10 = 0\end{array}\]
Thus, \[60 \div 10 = 6\].
FAQs on Division is Repeated Subtraction: Explained with Examples
1. How does repeated subtraction work for division?
Repeated subtraction is a method to understand division by continuously subtracting the divisor (the number you are dividing by) from the dividend (the total amount) until you reach zero. The total number of times you subtract the divisor gives you the quotient, which is the answer to the division problem.
2. Can you explain how to solve 18 ÷ 6 using the repeated subtraction method?
Yes. To solve 18 ÷ 6, you must repeatedly subtract 6 from 18 until you get 0. Here are the steps:
- Step 1: 18 - 6 = 12 (1st subtraction)
- Step 2: 12 - 6 = 6 (2nd subtraction)
- Step 3: 6 - 6 = 0 (3rd subtraction)
3. Why is it important for students to learn division as repeated subtraction?
Learning division as repeated subtraction is important because it builds a strong foundational understanding of what division means. It connects the new concept of division to subtraction, an operation students are already familiar with. This method makes the idea of 'sharing equally' more concrete and visual, preparing students for more complex division methods later on.
4. What happens in repeated subtraction if you can't reach exactly zero?
If you cannot subtract until you reach exactly zero, the final number left over is called the remainder. This happens when the dividend is not a perfect multiple of the divisor. For example, to solve 14 ÷ 4, you subtract 4 three times (14 → 10 → 6 → 2). You cannot subtract 4 from 2, so the answer is a quotient of 3 with a remainder of 2.
5. How are repeated subtraction and multiplication related?
Repeated subtraction and multiplication are inverse (or opposite) operations that describe the same concept of grouping. For example:
- Repeated Subtraction (Division): How many times can you subtract 5 from 15? The answer is 3. (15 ÷ 5 = 3)
- Repeated Addition (Multiplication): What do you get when you add 5 three times? The answer is 15. (5 x 3 = 15)
6. In the problem 20 ÷ 5 = 4, which numbers are the dividend, divisor, and quotient?
When using repeated subtraction for the problem 20 ÷ 5 = 4, the terms are:
- Dividend: 20, the initial number you are dividing.
- Divisor: 5, the number you repeatedly subtract.
- Quotient: 4, the number of times you subtracted the divisor.
