Find each product or quotient where possible. See Example 2. -10⁄17 ÷ ( -12⁄5 )

Verified step by step guidance

1. Convert the division of fractions into multiplication by taking the reciprocal of the second fraction: $-\frac{10}{17}\times (-\frac{5}{12})$.
2. Multiply the numerators: $-10\times -5$.
3. Multiply the denominators: $17\times 12$.
4. Simplify the resulting fraction if possible by finding the greatest common divisor (GCD) of the numerator and the denominator.
5. Express the simplified fraction as the final answer.

Key Concepts

Division of Fractions

Dividing fractions involves multiplying by the reciprocal of the divisor. For example, to divide -10/17 by -12/5, you would multiply -10/17 by the reciprocal of -12/5, which is -5/12. This process simplifies the operation and allows for easier calculation.

Negative Numbers in Fractions

When dealing with negative fractions, it's important to remember that the division of two negative numbers results in a positive number. In the given problem, both -10/17 and -12/5 are negative, so their division will yield a positive result, affecting the final outcome of the calculation.

Simplifying Fractions

After performing the division, the resulting fraction may need to be simplified. This involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by this number. Simplifying fractions makes them easier to understand and work with in further calculations.