**Adding Fractions: 1 3/4 plus 2/3**

In this article, we will learn how to add two fractions, 1 3/4 and 2/3, and express the result as a single fraction.

**Step 1: Convert Mixed Numbers to Improper Fractions**

To add these fractions, we need to convert the mixed number 1 3/4 to an improper fraction. An improper fraction is a fraction where the numerator is greater than the denominator.

**1 3/4 = ?**

To convert 1 3/4 to an improper fraction, we multiply the whole number part (1) by the denominator (4) and then add the numerator (3).

1 × 4 = 4 4 + 3 = 7

So, 1 3/4 is equal to the improper fraction 7/4.

**Step 2: Add the Fractions**

Now that we have converted 1 3/4 to an improper fraction, we can add the two fractions:

**7/4 + 2/3**

To add these fractions, we need to find the least common multiple (LCM) of the denominators, which are 4 and 3.

The LCM of 4 and 3 is 12. So, we need to convert both fractions to have a denominator of 12:

**7/4 = 21/12**
**2/3 = 8/12**

Now we can add the fractions:

**21/12 + 8/12 = 29/12**

**Step 3: Simplify the Fraction**

The result of the addition is 29/12. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 29 and 12 is 1, so the fraction is already in its simplest form.

**Result**

Therefore, 1 3/4 plus 2/3 is equal to **29/12** as a fraction.

I hope this helps! Let me know if you have any questions.