**Introduction to illustrator fractions :**

**Definition of Fractions:**

Fractions are widely used in mathematics, science and the world around us. They have been used by human king since the time of the ancient Egyptians and are still used by people to solve problems in their everyday lives.

Decimal fractions came into common use in the 16^{th} century. illustrator fractions:

`(9)/(18)`

Notice that each of the digits from 1 to 9 has been used in this fraction. When this fraction is simplified, we see that:

`(9)/(18)`=`(1)/(2)`

It is very important that we know the different types of fractions.

1) Proper fraction

2) Improper fraction

3) Mixed fraction

**Proper fraction**

Fraction where the denominator is not lesser than the numerator,

**illustrator** **fractions**: `(1)/(2)`

Here numerator (1) is less than the denominator (2)

**Improper fractions:**

Fraction, where the denominator is not bigger than the numerator.

**illustrator** **fractions:** `(10)/(6)`

Here numerator (10) is greater than the denominator (6)

**Mixed fractions:**

Fractions where there is a whole number together with a fraction.

**illustrator** **fractions :**2 `(1)/(2)`(means 2+`(1)/(3)`)

We change a mixed fraction to an improper fraction as follows:

`2(1)/(3)`=`((2*3)+1)/(3)`=-`(15+4)/(5)`=`(-19)/(5)`

We change an improper fraction to a mixed fraction as follows:

`(3)/(2)` means there are three halves (3 x`(1)/(2)`).

This means the same as 1+ `(1)/(2)` = 1`(1)/(2)`

**Algebraic fractions:**

Fractions, which have algebraic terms or expressions in their numerators, or and denominators,

**illustrator** **fractions****:** `(2ab)/(3)`;`(3)/(x)`.

It takes `(1)/(4)` hour to prepare a salad for dinner, another `(1)/(3)` hour to make a main dish and `(1)/(2)`hour to make dessert. Can the entire meal be made in no more than 1 hour? Explain how you can decide.

**Sol:**

**Step 1:**

Think about what the problem asks you to find:

“No more than 1 hour” means 1 hour or less.

Is the sum of `(1)/(3)`+`(1)/(4)`+`(1)/(2)` less than or greater than 1?

**Step 2:**

Use estimation to solve the problem:

`(1)/(3)`+`(1)/(4)`>`(1)/(2)` you know that `(1)/(2)`+`(1)/(2)`=1

It follows that `(1)/(3)`+`(1)/(4)`+`(1)/(2)`.

(Remember, > means “is greater than”.)

**Answer:** so, the entire meal cannot be prepared in 1 hour.