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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Simplifying Fractions

To simplify a fraction means to write the fraction in simplest form. A
fraction is "simplified" when the numerator and denominator have
no common factors other than1.

Consider the following fractions. Can they be simplified? To see if they can, we use divisibility rules and prime factorization to
factor the numerator and denominator. Then we cancel common factors.

Divisibility Rule for 2

 Rule for 2 Divisibility rules are based on patterns of multiplication. When we list the multiples of 2,we get even numbers, numbers that end in 2,4,6,8 or 0: Multiples of 2: 2, 4, 6, 8, 10, ... This means all even numbers can be divided by 2. Example 1: Simplify The numerator and denominator are even numbers. To simplify the fraction, divide each number by 2 and cancel the common factor of 2: Divisibility Rule for 3

 Rule for 3 If a number's digits add to a multiple of 3,the number can be divided by 3. For example, 84 is divisible by 3 because its digits add to a multiple of 3: 97 is not divisible by 3 because its digits don't add to a multiple of 3: Example 2: Simplify The numerator and denominator can be divided by 3: To simplify the fraction, divide each number by 3 and cancel: Divisibility Rules for 5 and 10

 Rule for 5 If a number ends in 0 or 5,divide the number by 5. Multiples of 5: 5, 10, 15, 20, … Rule for 10 If the number ends in 0, divide by 10. Multiples of 10: 10, 20, 30, … Example 3: Simplify Divide each number by 5 and cancel the common factor: Example 4: Simplify Canceling the 0's,divides each number by 10: Applying Divisibility Rules

Example5:Can the fraction be simplified?

Since the numerator,51,can be divided by 3 and the denominator,85,
can be divided by 5,we can apply each rule separately. Notice the
the numbers share a common factor of 17: divide 51 by 3 divide 85 by 5

Practice Exercise 1

Simplify each fraction.    Check answers

Solution − Practice Exercise 1

Simplify each fraction.  ←When the number in the numerator cancels, we must write a"1." ← Cancel the 0's first.

Prime Factorization

A prime number is divisible by itself and1.Prime numbers include,

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, …

A number that is not prime is called composite because the number
can be written as a product of its prime factors. For example, the
number6 is composite because we can factor 6 and write it as a
product of its prime factors,2 and 3:

6 = 2· 3