Math Problem Statement

What is the sum of 2/3 and 5/6? Complete the equation and simplify the result.

Solution

The image shows the equation:

23+56=_+_=_\frac{2}{3} + \frac{5}{6} = \_ + \_ = \_

To solve this, we need to add the fractions 23\frac{2}{3} and 56\frac{5}{6}. Here's the step-by-step solution:

Step 1: Find a common denominator.

The least common denominator (LCD) of 3 and 6 is 6. We need to convert 23\frac{2}{3} to a fraction with a denominator of 6.

23=2×23×2=46\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}

Step 2: Add the fractions.

Now we can add 46\frac{4}{6} and 56\frac{5}{6}:

46+56=4+56=96\frac{4}{6} + \frac{5}{6} = \frac{4+5}{6} = \frac{9}{6}

Step 3: Simplify the result.

96\frac{9}{6} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

96=9÷36÷3=32\frac{9}{6} = \frac{9 \div 3}{6 \div 3} = \frac{3}{2}

So the final answer is 32\frac{3}{2}, or 1121 \frac{1}{2} if written as a mixed number.

Complete equation:

23+56=46+56=96=32\frac{2}{3} + \frac{5}{6} = \frac{4}{6} + \frac{5}{6} = \frac{9}{6} = \frac{3}{2}

Do you have any questions or would you like more details?


Here are 5 related questions to expand your understanding:

  1. How do you find the least common denominator between two fractions?
  2. Why is it necessary to convert fractions to a common denominator before adding them?
  3. How can you check if a fraction can be simplified?
  4. How would the approach change if you had three fractions to add instead of two?
  5. How do you convert an improper fraction to a mixed number?

Tip: Always simplify fractions at the end of your calculations for a cleaner final answer!

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Math Problem Analysis

Mathematical Concepts

Fractions
Addition of Fractions
Simplifying Fractions

Formulas

Common denominator for addition of fractions
Simplifying fractions by greatest common divisor (GCD)

Theorems

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Suitable Grade Level

Grade 5-6