To solve this expression, follow the order of operations (also known as PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) step by step.
Simplify the division inside the parentheses: (25/16) / (5/2) To divide fractions, multiply the first fraction by the reciprocal of the second fraction: (25/16) * (2/5) Multiply the numerators and denominators: (25 * 2) / (16 * 5) Simplify: 50 / 80 Reduce the fraction: 5/8
Multiply the result from step 1 by the second part of the expression: (5/8) + 0.375 * (1/3) Multiply: (0.375 * 1) / 3 Simplify: 0.375/3 = 0.125
Add the two parts of the expression: (5/8) + 0.125 Find a common denominator between 8 and 1 (the denominator of 0.125): Multiply the denominators: 8 * 1 = 8 Multiply numerator and denominator of 0.125 by 8 to have the same denominator: (5/8) + (0.125 * 8)/8 = 5/8 + 1/8 = 6/8
Simplify the fraction: The numerator and denominator have a common factor of 2, so divide them both by 2: 6/8 = 3/4
Therefore, ((25/16)/(5/2) + 0.375 * (1/3)) equals 3/4 or 0.75.
