Math Problem Statement

Evaluate the expression: (3/5 - 1/5) ÷ 1/4 - 1/2

Solution

The image asks to evaluate the expression:

(3515)÷1412\left( \frac{3}{5} - \frac{1}{5} \right) \div \frac{1}{4} - \frac{1}{2}

Let's proceed to solve this step by step:

  1. First, evaluate inside the parentheses: 3515=25\frac{3}{5} - \frac{1}{5} = \frac{2}{5}

  2. Then, divide this result by 14\frac{1}{4}: 25÷14=25×41=85\frac{2}{5} \div \frac{1}{4} = \frac{2}{5} \times \frac{4}{1} = \frac{8}{5}

  3. Now subtract 12\frac{1}{2} from this result: 8512\frac{8}{5} - \frac{1}{2}

    To subtract, we need a common denominator: 85=1610,12=510\frac{8}{5} = \frac{16}{10}, \quad \frac{1}{2} = \frac{5}{10}

    So, 1610510=1110\frac{16}{10} - \frac{5}{10} = \frac{11}{10}

Thus, the final result is 1110\frac{11}{10} or 1.1.

Do you need more details or have any questions?

Here are some related questions for further practice:

  1. How do you divide two fractions in general?
  2. What is the process for finding a common denominator?
  3. How can we convert an improper fraction to a decimal?
  4. What are some other methods for simplifying expressions with fractions?
  5. How would this expression change if it were multiplication instead of division?

Tip: When dividing fractions, always multiply by the reciprocal of the divisor.

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Math Problem Analysis

Mathematical Concepts

Fractions
Order of Operations
Division and Subtraction of Fractions

Formulas

Division of Fractions: a/b ÷ c/d = a/b * d/c
Subtraction of Fractions: a/b - c/d requires a common denominator

Theorems

Order of Operations (PEMDAS/BODMAS)

Suitable Grade Level

Grades 6-8