**Mixed Fractions:**

A mixed fraction, also known as a mixed number, is a combination of a whole number and a proper fraction. It is written in the form of a whole number followed by a fraction. For example, 2 and 2/3 is a mixed fraction, where 2 is the whole number and 2/3 is the fraction.

**Converting Improper Fractions to Mixed Fractions:**

To convert an improper fraction to a mixed fraction, follow these steps:

1. Divide the numerator (the number on the top) by the denominator (the number on the bottom).
2. Write down the whole number quotient.
3. The remainder becomes the numerator of the fraction part.
4. The denominator remains the same.

For example, let's convert the improper fraction 7/4 into a mixed fraction:

1. Divide 7 by 4: 7 ÷ 4 = 1 remainder 3.
2. The whole number quotient is 1.
3. The remainder, which is 3, becomes the numerator of the fraction part.
4. The denominator remains 4.

Therefore, 7/4 as a mixed fraction is 1 and 3/4.

**Simplifying Mixed Fractions:**

To simplify a mixed fraction, follow these steps:

1. Multiply the whole number by the denominator.
2. Add the product to the numerator.
3. Write the sum over the denominator.

For example, let's simplify the mixed fraction 3 and 2/5:

1. Multiply 3 (the whole number) by 5 (the denominator): 3 × 5 = 15.
2. Add the product to the numerator, which is 2: 15 + 2 = 17.
3. Write the sum, 17, over the denominator, which is 5.

Therefore, 3 and 2/5 can be simplified to 17/5.

**Using Mixed Fractions in Arithmetic Operations:**

Mixed fractions can be used in addition, subtraction, multiplication, and division, just like regular fractions. However, it is often easier to convert them into improper fractions before performing the operations.

For example, let's add 2 and 2/3 to 1 and 1/4:

1. Convert both mixed fractions into improper fractions:
- 2 and 2/3 = (2 × 3 + 2)/3 = 8/3
- 1 and 1/4 = (1 × 4 + 1)/4 = 5/4
2. Now we can add the improper fractions: 8/3 + 5/4.
- Find a common denominator: The common denominator of 3 and 4 is 12.
- Convert both fractions to have a denominator of 12:
- 8/3 = (8 × 4)/ (3 × 4) = 32/12
- 5/4 = (5 × 3)/ (4 × 3) = 15/12
- Add the fractions: 32/12 + 15/12 = 47/12
3. Simplify the resulting fraction if necessary.

Therefore, 2 and 2/3 + 1 and 1/4 = 47/12.

In conclusion, mixed fractions are a combination of whole numbers and fractions. They

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