Find each product or quotient where possible. -10/17 ÷ (-12/5)

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Identify the problem as a division of two fractions: \(\frac{-10}{17} \div \frac{-12}{5}\).

Recall that dividing by a fraction is the same as multiplying by its reciprocal. So rewrite the expression as \(\frac{-10}{17} \times \frac{5}{-12}\).

Multiply the numerators together and the denominators together: numerator = \(-10 \times 5\), denominator = \(17 \times -12\).

Simplify the product of the numerators and denominators separately, keeping track of the signs.

Reduce the resulting fraction to its simplest form by dividing numerator and denominator by their greatest common divisor (GCD).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Division of Fractions

Dividing fractions involves multiplying the first fraction by the reciprocal of the second. The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, dividing by 3/4 is the same as multiplying by 4/3.

Multiplication of Fractions

To multiply fractions, multiply the numerators together and the denominators together. Simplify the resulting fraction if possible. For example, (a/b) × (c/d) = (a×c)/(b×d).

Simplifying Fractions

After performing operations, fractions should be simplified by dividing numerator and denominator by their greatest common divisor (GCD). This makes the fraction easier to interpret and use in further calculations.

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