To write the repeating decimal 0.8333... as a vulgar fraction, we can use algebra. Step 1: Let x equal the repeating decimal. x = 0.8333... Step 2: Multiply x by 10 to move the decimal point one place to the right, so that the repeating part aligns. 10x = 8.3333... Step 3: Subtract the original equation (x = 0.8333...) from the new equation (10x = 8.3333...). 10x = 8.3333... x = 0.8333... ----------------- 9x = 7.5 Step 4: Solve for x by dividing both sides by 9. x = (7.5) / 9 Step 5: To get rid of the decimal in the numerator, multiply both the numerator and the denominator by 10. x = (7.5 × 10) / (9 × 10) x = 75 / 90 Step 6: Simplify the fraction by finding the greatest common divisor (GCD) of 75 and 90. The GCD is 15. Divide both the numerator and the denominator by 15. x = 75 ÷ 15 / 90 ÷ 15 x = 5 / 6 The vulgar fraction for 0.8333... is 5/6.