Question

Use the distributive property to rewrite the expression without parentheses. $$ -\frac{2}{3}(t-24) $$

Short answer

The expression \(-\frac{2}{3}(t-24)\) without parentheses is \(-\frac{2}{3}t + 16\).

Step-by-step solution

Identify the distributive property

The distributive property of multiplication over subtraction is: \(a * (b - c) = a * b - a * c\). Here \(a = -\frac{2}{3}\), \(b = t\) and \(c = 24\). The task is to apply this property to the given expression.

Apply the distributive property

Apply the distributive property: \(-\frac{2}{3} * t - (-\frac{2}{3} * 24)\). This involves multiplying -2/3 with 't' and -2/3 with '24' separately.

Simplify the expression

After multiplication, the expression becomes: \(-\frac{2}{3}t + 16\). The negative sign before 2/3 has changed to positive when multiplied with 24 because the multiplication of two negative numbers gives a positive result.