Division is the only operation whose end result is not always Whole Number. Many times its result in Partial number, and it has been called **Fraction**.

Fraction Contains Two parts: a **Numerator** and a **Denominator**.

In another word, If tommy ate 1/4 of cake, it means that the cake was cut into 4 equal parts and tommy ate one of the equat parts.

A Proper Fraction is a fraction where the Numerator is smaller than the Denominator.

Improper fractions have numerators that are larger than or equal to their denominators. It can be expressed as a mixed number or as a Whole number

**Converting Mixed Numbers to Improper Fractions**

To change a mixed number into an improper fraction, multiply the whole number by the denominator and add it to the numerator of the fractional part.

**Converting Improper Fractions to Mixed Numbers
**

To change an improper fraction into a mixed number, divide the numerator by the denominator. The remainder is the numerator of the fractional part.

Equivalent fractons can be reduced to same lowest value.

Note:We can test if two fractions are equivalent by cross-multiplying their numerators and denominators. This is also called taking the cross-product.

- To compare fractions with same Denominators, the **Bigger the Numerator**, the **Bigger the fraction**.

- To compare fractions with same Numerators,the** Bigger the denominator**, the **smaller the fraction**.

- To compare fractions with **different denominators**, take the cross product(first multiply the numerator of the first fraction with denominator of the second fraction , and second multiply the denominator of the first fraction with the numerator of second fraction). Compare the cross products using the following rules:

a. If the cross-products are **equal**, the fractions are **equivalent**.

b. If the **first** cross product is **larger**, the first fraction is larger.

c. If the **second** cross product is **larger**, the second fraction is larger.

To add or Subtract fractions, they must have **same Denominators**.

- If they have same denominators, their **sum** is the sum of the numerators over the denominator and their **difference** is the difference of the numerators over the denominator. We **do not** add or subtract the **denominators**! Reduce if necessary.

- If they** don't** have same denominators, **change** all the denominators to the same number.

To add or subtract **mixed numbers**, simply convert the mixed numbers into improper fractions, then add or subtract them as fractions.

To multiply a fraction by a **whole number**, write the whole number as an improper fraction with a denominator of 1, then multiply as fractions.

When **two fractions** are multiplied, the result is a fraction with a numerator that is the product of the fractions' numerators and a denominator that is the product of the fractions' denominators.

To multiply **mixed numbers**, convert them to improper fractions and multiply.

- Reciprocal is useful for **Division** of fractions.

- The reciprocal of fraction is obtained by **switching its numerator and dinominator**.

- To find Reciprocal of **Mixed number**, first **convert** Mixed number to improper fraction and then switch its numerator and dinominator

- Notice that when you multiply a fraction and its reciprocal, the product is always 1.

To divide a number by a fraction, multiply the number by the reciprocal of the fraction.

To divide mixed numbers, convert mixed numbers to improper fractions, then multiply the first number by the reciprocal of the second.