📚 Topic Summary
Solving division equations involves finding the missing number that, when multiplied by the divisor, equals the dividend. In simpler terms, you're undoing division using multiplication. For example, in the equation $x \div 3 = 5$, you need to find the value of 'x'. To do this, you multiply both sides of the equation by 3, giving you $x = 5 \times 3$, which simplifies to $x = 15$. This means 15 divided by 3 equals 5.
Another way to look at it is recognizing the inverse relationship between multiplication and division. If you have an equation like $y \div 7 = 2$, you're essentially asking, "What number, when divided by 7, equals 2?" Multiplying 2 by 7 ($2 \times 7 = 14$) gives you the answer: y = 14. Mastering this inverse relationship is key to solving division equations efficiently.
🧮 Part A: Vocabulary
Match the term with its definition:
- Term: Dividend
- Term: Divisor
- Term: Quotient
- Term: Equation
- Term: Variable
- Definition: A symbol (usually a letter) that represents an unknown number.
- Definition: The number being divided.
- Definition: A statement that two expressions are equal.
- Definition: The number by which another number is divided.
- Definition: The result of division.
| Term |
Matching Definition Number |
| Dividend |
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| Divisor |
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| Quotient |
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| Equation |
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| Variable |
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✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct words.
In a division equation, the ______ is the number being divided, and the ______ is the number by which it is divided. The answer is called the ______. To solve for a variable in a division equation, you can use the inverse operation, which is ______. For example, if you have $x \div 4 = 9$, you multiply both sides by ______ to find $x = ______$.
🤔 Part C: Critical Thinking
Explain in your own words why multiplication is the inverse operation of division. Provide an example to support your explanation.