2 2/3 + 1/2

To solve this expression, we’ll follow the order of operations, which in this case involves adding mixed numbers and fractions. First, let’s convert the mixed number into an improper fraction to make the calculation easier.

The mixed number 2 ²⁄₃ can be converted into an improper fraction as follows: [ 2 \frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} ]

Now, we have: [ \frac{8}{3} + \frac{1}{2} ]

To add these two fractions, we need a common denominator. The least common multiple of 3 and 2 is 6. So, we’ll convert both fractions to have a denominator of 6: [ \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} ] [ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} ]

Now, we can add them: [ \frac{16}{6} + \frac{3}{6} = \frac{16 + 3}{6} = \frac{19}{6} ]

So, the result of ( 2 \frac{2}{3} + \frac{1}{2} ) is ( \frac{19}{6} ).

To convert this improper fraction back into a mixed number: [ \frac{19}{6} = 3 \frac{1}{6} ]

Therefore, ( 2 \frac{2}{3} + \frac{1}{2} = 3 \frac{1}{6} ).

Breaking Down the Solution

Step-by-Step Process

1. Convert the Mixed Number: First, we converted ( 2 \frac{2}{3} ) into an improper fraction, ( \frac{8}{3} ).
2. Find a Common Denominator: We then found a common denominator for ( \frac{8}{3} ) and ( \frac{1}{2} ), which was 6.
3. Add the Fractions: After converting both fractions to have a denominator of 6, we added them together to get ( \frac{19}{6} ).
4. Convert Back to Mixed Number (Optional): Finally, we converted ( \frac{19}{6} ) back into a mixed number for a more familiar representation, getting ( 3 \frac{1}{6} ).

Practical Applications

Understanding how to add mixed numbers and fractions is crucial in many real-world applications, such as: - Cooking and Recipes: Many recipes require adjusting ingredient quantities, which involves adding fractions and mixed numbers. - Construction and DIY Projects: When building or repairing items, being able to calculate lengths and quantities of materials is essential. - Science and Engineering: Fractions and mixed numbers are fundamental in calculating volumes, concentrations, and pressures.

Expert Tip

When dealing with fractions and mixed numbers, it’s essential to simplify your fractions after addition or subtraction to express the answer in its simplest form. This not only makes the answer more understandable but also reduces errors in further calculations.

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