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Negative numbers can seem tricky, but they're just as straightforward as positive numbers once you get the hang of them. A negative number is any number less than zero and is usually represented with a minus sign (-). For example, -3 is a negative number.

When it comes to division with negative numbers, there's a simple rule to remember:

• Dividing two negative numbers results in a positive outcome.
• Dividing a negative number by a positive number (or vice versa) results in a negative outcome.

In this exercise, we divided -145 by -5. According to our rule, dividing two negatives gives us a positive number. Thus, \[-145 \div -5 = \frac{145}{5} = 29\]. Understanding how negative numbers interact during division makes simplifying the signs in Step 2 straightforward.

Fraction simplification is the process of reducing a fraction to its simplest form. A fraction is simplified when the numerator (top number) and the denominator (bottom number) are as small as possible while still maintaining the same value.

In the context of the problem, we started with the fraction \[-145/-5\]. Since both the numerator and the denominator are negative, they cancel each other out, turning the fraction positive. This makes \[-145/-5\] equivalent to \[-(-145)/-(-5) = 145/5\].

Simplifying involves performing the actual division to get the simplest form. Here, dividing 145 by 5 gives us 29. So, \[-145/-5 = 29\]. This step eliminates the negative signs and reduces the fraction to its simplest form.

Verification of division is a crucial step to ensure the accuracy of your work. It involves checking the result by reversing the operation. In division, we use multiplication for verification.

In our exercise, we reached the quotient of 29 from the division \[-145/-5\]. To verify:

• We multiply the quotient (29) by the divisor (5).
• If the product equals the original numerator, the division was performed correctly.

This looks like: \29 \times 5 = 145\. Since 145 matches the original numerator, the division is verified, confirming our result.

Always remember to check your work. This step not only confirms your accuracy but deepens your understanding of the concepts involved.