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

Verified step by step guidance

1. Identify the expression to simplify: \(\left(\frac{3}{4}r\right)(-12)\).
2. Rewrite the expression by multiplying the fraction and the integer first: \(\frac{3}{4} \times (-12) \times r\).
3. Multiply the numerical coefficients: \(\frac{3}{4} \times (-12)\).
4. Simplify the multiplication of the numbers by dividing 12 by 4 first, then multiply by 3 and apply the negative sign.
5. Combine the simplified numerical result with the variable \(r\) to write the final simplified expression.

Key Concepts

Multiplication of Fractions and Integers

Multiplying a fraction by an integer involves multiplying the numerator by the integer while keeping the denominator the same. For example, (3/4) × (-12) means multiplying 3 by -12 and then dividing by 4.

Multiplication of Variables and Constants

When multiplying a variable by a constant, the constant multiplies the coefficient of the variable. In (3/4)r × (-12), the variable r is multiplied by the product of the constants, affecting the overall expression.

Simplifying Algebraic Expressions

Simplifying involves performing all possible multiplications and divisions to rewrite the expression in its simplest form. This includes reducing fractions and combining like terms to make the expression easier to understand or use.