Math Problem Statement

Solve the expression: 2 - (5/4) * (8/15 + 2/5) - (1/2)^2

Solution

The expression in the image is:

254(815+25)(12)22 - \frac{5}{4} \left( \frac{8}{15} + \frac{2}{5} \right) - \left( \frac{1}{2} \right)^2

Let's solve it step by step.

Step 1: Simplify the inner fraction

The fractions 815\frac{8}{15} and 25\frac{2}{5} need a common denominator for addition. The common denominator between 15 and 5 is 15.

815+25=815+615=1415\frac{8}{15} + \frac{2}{5} = \frac{8}{15} + \frac{6}{15} = \frac{14}{15}

Step 2: Multiply by 54\frac{5}{4}

54×1415=5×144×15=7060=76\frac{5}{4} \times \frac{14}{15} = \frac{5 \times 14}{4 \times 15} = \frac{70}{60} = \frac{7}{6}

Step 3: Square the fraction

[ \left( \frac{1}{2

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Math Problem Analysis

Mathematical Concepts

Fractions
Multiplication of Fractions
Squaring Fractions
Basic Arithmetic

Formulas

a/b + c/d = (ad + bc) / bd
(a/b) * (c/d) = ac/bd
(a/b)^2 = a^2 / b^2

Theorems

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Suitable Grade Level

Grades 6-8