Division facts using repeated subtraction demonstrate how many times one number (the divisor) can be taken away from another number (the dividend) until you reach zero or a remainder. The number of times you subtract is the quotient.
Here's a breakdown:
- Concept: Repeated subtraction is a method of division where you repeatedly subtract the divisor from the dividend until you reach zero or a number smaller than the divisor (the remainder).
- Quotient: The number of times you successfully subtract the divisor is the quotient (the answer to the division problem).
- Remainder: If you can't subtract the divisor anymore without going into negative numbers, the remaining number is the remainder.
Example:
Let's divide 15 by 3 using repeated subtraction:
- 15 - 3 = 12
- 12 - 3 = 9
- 9 - 3 = 6
- 6 - 3 = 3
- 3 - 3 = 0
We subtracted 3 a total of 5 times. Therefore, 15 ÷ 3 = 5 (with no remainder).
Another Example with a Remainder:
Let's divide 17 by 3 using repeated subtraction:
- 17 - 3 = 14
- 14 - 3 = 11
- 11 - 3 = 8
- 8 - 3 = 5
- 5 - 3 = 2
We subtracted 3 a total of 5 times, and we are left with 2. Therefore, 17 ÷ 3 = 5 with a remainder of 2.
Connection to Division Facts:
Repeated subtraction illustrates the core concept of division. Each subtraction represents a group of the divisor being taken out of the dividend. The final count of these groups is the quotient, representing how many "divisors" fit into the "dividend." By visualizing division as repeated subtraction, the division facts become more intuitive.
In essence, division facts through repeated subtraction reveal the underlying mechanism of division, reinforcing the understanding of quotient and remainder through iterative removal of equal groups.
