# Fraction

## • What is Fraction?

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.

## • Proper Fraction

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

## •Improper Fraction & Mixed Number

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 Fraction

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.

## • Comparing Fraction

- 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.

## • Addition and Subtraction of Fraction

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.

## • Multiplication of 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

- 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.

## •Division of Fractions

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.