Overview
If division were limited to single-digit divisors and math facts, it would be comparatively easy. Long division is more difficult to visualize and tie to real-world manipulative objects. Paradigms exist for long division, and there are tips and tricks for dealing with other problems.
Divisibility
Sometimes it is easier to tell if a dividend is evenly divisible by a divisor before working the problem out on paper. If a number in the units digit is divisible by 2 or 5, the entire number will be divisible by 2 or 5. For example, 385 is divisible by 5. Similarly, if the sum of the digits in a number is divisible by 3 or 9, the number is divisible by 3. If the sum of the last 2 digits is divisible by 4, the number will be divisible by 4. If a number is divisible by both 2 and 3, it will be evenly divisible by 6.
Long Division by Repeated Subtraction
The steps for division include directions for repeated subtraction. This paradigm can be used for one-digit divisors as well as long division. It involves subtracting multiples of the divisor, adding the results up, and continuing until the leftover amount is less than the divisor. Suppose the number is 124/32. Then subtract 124 – 32 = 92 – 32 = 60 – 32 = 28. This method does not use place value, and makes it easier to see the concept.
Long Division by Place Value
One of the ways to look more carefully at division is to color-code both the dividend and the divisor using the color-coding that is available for chip-trading, such as red, thousands place, green, hundreds place, blue, tens place, and yellow, units place. Suppose the division problem is 4800/25. That would result in 4 red chips and 8 green chips. The 4 red chips cannot be evenly divided by 25, but they could be traded in for 40 green chips. The 40 green chips can be added to the 8 green chips that are already there to leave 48 green chips. The 48 green chips can then be divided by 25, which will leave 23 green chips. The 1 goes above the green. The 23 green chips become 230 blue chips. 225 of them (25*9) can be eliminated, and the 9 can go above the blue. The remaining 50 is evenly divisible by 25, so the solution is 100 + 90 + 2 = 192.
Why Dividing by Zero Is Undefined
Normally, any number divided by itself is 1. What happens when zero is divided by itself? The answer is not 1, it is not determined. If any other number is divided by zero, the answer cannot be determined either. Dividing by zero is not allowed, because it doesn’t make any sense.
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