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When dealing with mathematical expressions like \(-46-3(-12)\), simplifying expressions is all about making the problem more manageable. We begin by following the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In this case, there's a subtraction and a multiplication within the expression.

• First, focus on actions within parentheses. This ensures calculations inside any brackets are done initially.
• Then address any multiplication and division from left to right.
• Lastly, perform addition and subtraction from left to right.

This structured approach helps solve complex expressions accurately step-by-step. Simplifying is like organizing your work on paper so the final problem at hand is as easy as possible.

Mathematical operations convert one number into another through addition, subtraction, multiplication, and division. When tackling a problem, it’s important to know which operation to perform and in what order.
In the expression \(-3(-12)\), the operation between \(-3\) and \(-12\) is multiplication. Interestingly, multiplying two negative numbers results in a positive number. Here:

• Multiplying \(-3\) by \(-12\) gives us \(36\).

It's crucial to multiply and determine sign changes correctly before moving to the next operation in the sequence. Once multiplication is sorted, focus shifts to the addition or subtraction of numbers remaining in the expression. By following the correct sequence of mathematical operations, accurate results are achieved.

Fraction simplification makes a fraction easier to understand by reducing it to its smallest possible terms. For the fraction \(\frac{-10}{40}\), both numbers share a greatest common divisor (GCD), which is \(10\).
To simplify this:

• Divide both the numerator and denominator by their GCD. Therefore, \(-10 \div 10\) equals \(-1\), and \(40 \div 10\) equals \(4\).
• This reduction gives us \(\frac{-1}{4}\).

Simplifying fractions ensures the expression is as clear and concise as possible, making future calculations easier. Look for the largest number that can evenly divide both parts of the fraction to find its GCD, streamlining the fraction to its simplest form.