Dividing by a whole number involves splitting a quantity into equal groups where the size of each group is determined by the whole number divisor.
Here's a breakdown of the process, covering both basic understanding and methods:
Understanding Division
- Dividend: The number being divided (the total quantity).
- Divisor: The whole number you are dividing by (the number of groups you want to create).
- Quotient: The result of the division (the size of each group).
- Remainder: The amount left over if the dividend cannot be divided equally into the divisor.
The relationship can be represented as: Dividend ÷ Divisor = Quotient + Remainder (if any)
Methods for Dividing by a Whole Number
1. Basic Division/Short Division
This method is suited for smaller divisors.
- Example: 15 ÷ 3
- Ask yourself: "How many times does 3 go into 15?"
- Answer: 5 (because 3 x 5 = 15)
- Therefore, 15 ÷ 3 = 5
2. Long Division
This method is typically used for larger divisors or dividends, or when dealing with remainders or decimals. It involves a structured process:
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Set up: Write the dividend under the division symbol (the "house") and the divisor to the left.
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Divide: Determine how many times the divisor goes into the first digit(s) of the dividend. Write this number (the quotient) above the division symbol.
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Multiply: Multiply the quotient by the divisor. Write the result below the corresponding digits of the dividend.
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Subtract: Subtract the product from the corresponding digits of the dividend.
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Bring Down: Bring down the next digit of the dividend next to the result of the subtraction.
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Repeat: Repeat steps 2-5 until all digits of the dividend have been used.
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Remainder (if any): If there's a number left after the last subtraction, it's the remainder.
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Example: 147 ÷ 4
- 4 goes into 14 three times (3 x 4 = 12). Write "3" above the "4" in 147.
- Subtract 12 from 14, which leaves 2.
- Bring down the 7, making it 27.
- 4 goes into 27 six times (6 x 4 = 24). Write "6" above the "7" in 147.
- Subtract 24 from 27, which leaves 3.
- The remainder is 3.
Therefore, 147 ÷ 4 = 36 with a remainder of 3 (or 36 R3). You can also express the remainder as a fraction (36 3/4) or a decimal (36.75).
3. Using Multiplication Facts
A strong understanding of multiplication tables makes division easier. If you know that 7 x 8 = 56, then you also know that 56 ÷ 7 = 8 and 56 ÷ 8 = 7.
4. Estimation and Approximation
Before dividing, estimate the answer. This helps you check if your final answer is reasonable. For example, if you are dividing 215 by 5, you might estimate that 200 ÷ 5 = 40, so the answer should be around 40.
Key Considerations
- Remainders: Be mindful of how to handle remainders. Depending on the context, you might need to express them as fractions, decimals, or simply state the remainder.
- Zero: Dividing zero by any non-zero whole number always results in zero (0 ÷ 5 = 0). Dividing any number by zero is undefined.
In summary, dividing by a whole number is the process of splitting a quantity into equal groups determined by the whole number divisor, often accomplished through methods like short division, long division, or the utilization of multiplication facts.
