Math Problem Statement

Simplify: 1/2 + 1/2 ÷ 4/7

Solution

The problem in the image asks you to simplify the expression:

12+12÷47\frac{1}{2} + \frac{1}{2} \div \frac{4}{7}

Step-by-Step Solution:

  1. First, handle the division of fractions: 12÷47=12×74=78\frac{1}{2} \div \frac{4}{7} = \frac{1}{2} \times \frac{7}{4} = \frac{7}{8}

  2. Now, add the two fractions: 12+78\frac{1}{2} + \frac{7}{8}

    To add these fractions, you need a common denominator. The least common denominator of 2 and 8 is 8. So, rewrite 12\frac{1}{2} as 48\frac{4}{8}: 48+78=118\frac{4}{8} + \frac{7}{8} = \frac{11}{8}

Final Answer:

118 or 138\frac{11}{8} \text{ or } 1 \frac{3}{8}

Would you like a more detailed explanation of any step or have additional questions?

Here are some related questions:

  1. How do you divide two fractions in general?
  2. What is the process for adding fractions with different denominators?
  3. Can this result be written as a decimal? What would it be?
  4. What is the importance of finding a common denominator when adding fractions?
  5. How can you convert improper fractions to mixed numbers?

Tip: When dividing fractions, remember that division is equivalent to multiplying by the reciprocal of the second fraction.

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Math Problem Analysis

Mathematical Concepts

Fractions
Division of Fractions
Addition of Fractions

Formulas

Division of Fractions: a/b ÷ c/d = a/b * d/c
Addition of Fractions: a/b + c/d = (ad + bc) / bd

Theorems

Division and Addition of Fractions

Suitable Grade Level

Grade 6-8