This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Okay, Alexino. I'll solve Question 1 from the image you sent. Question 1a: A woman spent (1)/(4) of her salary on drugs and (1)/(8) on rent, what fraction of her salary is left? Step 1: Find the total fraction of salary spent. To do this, we add the fractions spent on drugs and rent. Total spent = (1)/(4) + (1)/(8) To add these fractions, find a common denominator, which is 8. Total spent = (1 × 2)/(4 × 2) + (1)/(8) = (2)/(8) + (1)/(8) = (2+1)/(8) = (3)/(8) Step 2: Calculate the fraction of salary left. The total salary can be represented as 1 (or (8)/(8)). To find the fraction left, subtract the total fraction spent from 1. Fraction left = 1 - (3)/(8) Fraction left = (8)/(8) - (3)/(8) = (8-3)/(8) = (5)/(8) The fraction of her salary left is (5)/(8). Question 1b: Simplify 2 (2)/(3) × 1 (1)/(2) - 4 (4)/(5) Step 1: Convert all mixed numbers to improper fractions. 2 (2)/(3) = ((2 × 3) + 2)/(3) = (6+2)/(3) = (8)/(3) 1 (1)/(2) = ((1 × 2) + 1)/(2) = (2+1)/(2) = (3)/(2) 4 (4)/(5) = ((4 × 5) + 4)/(5) = (20+4)/(5) = (24)/(5) Step 2: Perform the multiplication. (8)/(3) × (3)/(2) We can cancel out the 3s and simplify the 8 and 2. (8)/(3) × 32 = (8)/(2) = 4 Step 3: Perform the subtraction. Now we have 4 - (24)/(5). To subtract, find a common denominator, which is 5. 4 - (24)/(5) = (4 × 5)/(5) - (24)/(5) = (20)/(5) - (24)/(5) = (20 - 24)/(5) = (-4)/(5) The simplified expression is -(4)/(5). That's 2 down. 3 left today — send the next one.