Math Problem Statement

Which model represents 1/2 + 1/6?

Solution

To solve the problem of determining which model represents 12+16\frac{1}{2} + \frac{1}{6}, we will break it down:

Step 1: Find a common denominator.

  • The denominators in 12\frac{1}{2} and 16\frac{1}{6} are 2 and 6, respectively.
  • The least common denominator (LCD) is 6.

Step 2: Rewrite the fractions with the same denominator.

  • 12\frac{1}{2} can be rewritten as 36\frac{3}{6} (since 12=36\frac{1}{2} = \frac{3}{6}).
  • 16\frac{1}{6} remains as 16\frac{1}{6}.

Step 3: Add the fractions.

  • Now we can add 36+16=46\frac{3}{6} + \frac{1}{6} = \frac{4}{6}.
  • Simplify 46\frac{4}{6} to 23\frac{2}{3}.

Step 4: Analyze the models.

The correct model should represent 23\frac{2}{3}.

  • A) Shows 4 out of 6 shaded, which represents 46\frac{4}{6}, or 23\frac{2}{3}. This is the correct model.
  • B) Shows fewer parts shaded and doesn’t represent 12+16\frac{1}{2} + \frac{1}{6}.
  • C) Shows more parts shaded, which would be incorrect for this sum.
  • D) Shows 12\frac{1}{2}, but no additional shading for 16\frac{1}{6}.

Conclusion:

The correct answer is A).

Would you like more details or have any questions?

Here are 5 related questions to think about:

  1. What is the least common denominator of 25\frac{2}{5} and 34\frac{3}{4}?
  2. How do you convert improper fractions to mixed numbers?
  3. What visual model would represent 34+12\frac{3}{4} + \frac{1}{2}?
  4. How do you subtract fractions with different denominators?
  5. What is the visual difference between adding fractions and multiplying them?

Tip: Always simplify fractions after adding or subtracting to make calculations easier.

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Math Problem Analysis

Mathematical Concepts

Fractions
Addition of fractions
Least common denominator

Formulas

1/2 + 1/6 = (3/6 + 1/6) = 4/6 = 2/3

Theorems

Fraction addition with different denominators

Suitable Grade Level

Grades 4-6