Question

1. \two - thirds of a number is negative 20.\

Explanation:

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the sentence into an equation

"Two - thirds of a number" can be written as \( \frac{2}{3}x \), and "is negative 20" means \( \frac{2}{3}x=-20 \).

Step3: Solve for \( x \)

Multiply both sides of the equation \( \frac{2}{3}x = - 20\) by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \). So \( x=-20\times\frac{3}{2}\).
Calculate \( - 20\times\frac{3}{2}\): \( -20\div2=-10 \), \( -10\times3 = - 30 \). So \( x=-30 \).

Answer:

The number is \(-30\)