To simplify the expression, we will first simplify the numerator and the denominator separately, then divide the simplified numerator by the simplified denominator.

To simplify the expression, we will first simplify the numerator and the denominator separately, then divide the simplified numerator by the simplified denominator. The expression is: (53)/(4) ÷ 1(1)/(3) - 4(1)/(2) × (2)/(15)(1)/(2) - (7)/(20) Step 1: Convert all mixed numbers to improper fractions. 5(3)/(4) = (5 × 4 + 3)/(4) = (23)/(4) 1(1)/(3) = (1 × 3 + 1)/(3) = (4)/(3) 4(1)/(2) = (4 × 2 + 1)/(2) = (9)/(2) Step 2: Simplify the numerator. The numerator is (23)/(4) ÷ (4)/(3) - (9)/(2) × (2)/(15). First, perform the division: (23)/(4) ÷ (4)/(3) = (23)/(4) × (3)/(4) = (23 × 3)/(4 × 4) = (69)/(16) Next, perform the multiplication: (9)/(2) × (2)/(15) = (9 × 2)/(2 × 15) = (18)/(30) Simplify the fraction (18)/(30) by dividing both numerator and denominator by their greatest common divisor, which is 6: (18 ÷ 6)/(30 ÷ 6) = (3)/(5) Now, perform the subtraction in the numerator: (69)/(16) - (3)/(5) Find a common denominator for 16 and 5, which is 80. (69 × 5)/(16 × 5) - (3 × 16)/(5 × 16) = (345)/(80) - (48)/(80) = (345 - 48)/(80) = (297)/(80) So, the numerator is (297)/(80). Step 3: Simplify the denominator. The denominator is (1)/(2) - (7)/(20). Find a common denominator for 2 and 20, which is 20. (1 × 10)/(2 × 10) - (7)/(20) = (10)/(20) - (7)/(20) = (10 - 7)/(20) = (3)/(20) So, the denominator is (3)/(20). Step 4: Divide the simplified numerator by the simplified denominator. (297)/(80)(3)/(20) = (297)/(80) ÷ (3)/(20) To divide by a fraction, multiply by its reciprocal: (297)/(80) × (20)/(3) Simplify by canceling common factors. 20 divides into 80 four times, and 3 divides into 297 ninety-nine times. (297 ÷ 3)/(80 ÷ 20) = (99)/(4) Convert the improper fraction to a mixed number: (99)/(4) = 24(3)/(4) The simplified expression is 24(3)/(4). What's next?