Simplify each expression. (3/4r)(-12)

Verified step by step guidance

1. Identify the expression to simplify: \( \frac{3}{4}r \times (-12) \).
2. Apply the associative property of multiplication to rearrange the terms: \( \left( \frac{3}{4} \times (-12) \right) \times r \).
3. Multiply the fractions: \( \frac{3}{4} \times (-12) \).
4. Simplify the multiplication: \( \frac{3 \times (-12)}{4} \).
5. Simplify the fraction by performing the multiplication and division.

Key Concepts

Multiplication of Fractions

When multiplying fractions, you multiply the numerators together and the denominators together. In this case, the fraction 3/4 is multiplied by -12, which can be expressed as -12/1. Thus, the multiplication involves (3 * -12) / (4 * 1), simplifying the expression effectively.

Simplifying Expressions

Simplifying an expression involves reducing it to its simplest form. This can include combining like terms, reducing fractions, or performing arithmetic operations. In this problem, after multiplying, you would simplify the resulting fraction if possible, ensuring the expression is presented in its most concise form.

Negative Numbers in Multiplication

When multiplying a positive number by a negative number, the result is negative. This concept is crucial in this problem, as the multiplication of 3/4 by -12 will yield a negative result. Understanding how to handle negative signs is essential for accurately simplifying the expression.