Question

1. \four fifths more than a number is one third.

Explanation:

Step1: Define the variable

Let the number be \( x \). "Four fifths more than a number" means \( x+\frac{4}{5} \).

Step2: Set up the equation

According to the problem, \( x + \frac{4}{5}=\frac{1}{3} \).

Step3: Solve for \( x \)

Subtract \( \frac{4}{5} \) from both sides: \( x=\frac{1}{3}-\frac{4}{5} \).
Find a common denominator (15) for the fractions: \( x = \frac{5}{15}-\frac{12}{15} \).
Simplify the right - hand side: \( x=\frac{5 - 12}{15}=\frac{-7}{15} \).

Step4: Check the solution

Substitute \( x =-\frac{7}{15} \) into the left - hand side of the original equation: \( -\frac{7}{15}+\frac{4}{5}=-\frac{7}{15}+\frac{12}{15}=\frac{-7 + 12}{15}=\frac{5}{15}=\frac{1}{3} \), which is equal to the right - hand side.

Answer:

The number is \( \boldsymbol{-\frac{7}{15}} \)