Question
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22. \( \frac{2}{a b} ; \frac{a-b}{b^{2} c} \)

Ask by Johnston Turnbull. in the United States
Jan 24,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The ratio of \( \frac{2}{ab} \) to \( \frac{a - b}{b^{2}c} \) is \( \frac{2bc}{a(a - b)} \).

Solution

It appears you're presenting two expressions, possibly for comparison, simplification, or to form a ratio. Let's interpret the problem as finding the ratio of the two expressions: Given: 1. \( \frac{2}{ab} \) 2. \( \frac{a - b}{b^{2}c} \) **Finding the Ratio:** The ratio of the first expression to the second is: \[ \frac{\frac{2}{ab}}{\frac{a - b}{b^{2}c}} = \frac{2}{ab} \times \frac{b^{2}c}{a - b} \] **Simplifying the Expression:** 1. Multiply the numerators and the denominators: \[ = \frac{2 \times b^{2}c}{ab \times (a - b)} \] 2. Simplify by canceling common terms (\(b\)): \[ = \frac{2 \times b \times c}{a \times (a - b)} \] 3. Final simplified form: \[ = \frac{2bc}{a(a - b)} \] **Final Answer:** \[ \frac{2}{ab} : \frac{a - b}{b^{2}c} = \frac{2bc}{\,a(a - b)\,} \]

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Mind Expander

In the grand tapestry of mathematics, fractions play a role much like letters in a story—each one contributing to the overall meaning. When simplifying the expression \( \frac{2}{ab} \) and \( \frac{a-b}{b^2c} \), one must keep in mind the importance of finding a common denominator. This process not only clarifies relationships between variables but also helps in taunting pesky errors hiding in your calculations. Now, on to the real-world application! Imagine you're baking cookies and need to adjust a recipe. You find a fraction that describes the amount needed for one ingredient, but plan to make several batches. Understanding how to manipulate and simplify fractions helps you convert measurements accurately—ensuring that your cookies come out perfectly delicious each time!

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