# Fractions

Learn the definition
of factor.

Write fractions in lowest terms.

Multiply and divide fractions.

Add and subtract fractions.

Solve applied problems that involve

fractions.

Interpret data in a circle graph.

**Definitions**

**Natural numbers:**1, 2, 3, 4,…,

**Whole numbers: **0, 1, 2, 3, 4,…,

**Fractions:**

**Proper fraction: **has a value of less then 1; the
numerator

is smaller than or equal to the denominator.

**Improper fraction:** has a value of greater then 1; the

numerator is larger than the denominator.

**Mixed number: **is a combination of a whole number and a

fraction.

Ex. The improper fraction
can be written
, a mixed number.

**Objective
**

**Learn the definition of factor.**

In the statement 2 ×9 = 18, the numbers 2 and 9 are called

**factors**. Other factors of 18 include 1, 3, 6, and 18. The number

18 in this statement is called a **product.**

The number 18 is** factored** by writing it as a product of two or

more numbers.

Ex. 6 ·3, 18 ×1, (2)(9), or 2(3)(3)

A natural number greater than 1 is **prime** if its products

include only 1 and itself.

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

A natural number greater than 1 that is not prime is
called a

**composite number.**

Ex. 4, 6, 8, 9, 10, 12,…

**EXAMPLE 1 **

**Factoring Numbers**

Write 90 as the product of prime factors.

Solution:

Starting with the smallest prime factor is not necessary.
No matter

which prime factor is started with the same prime factorization will

always be found.

**Objective
**

**Writing fractions in lowest terms.**

A fraction is in **lowest terms**, when the numerator
and

denominator have no common factors other than 1.

**Basic Principle of Fractions:**

If the numerator and denominator are multiplied or

divided by the same nonzero number, the fraction remains

unchanged.

**Writing a Fraction in Lowest Terms:**

**Step 1:**

Write the numerator and the denominator as the

product of prime factors.

**Step 2:**

Divide the numerator and denominator by the

**greatest common factor**, the product of all

factors common to both.

**EXAMPLE 2 **

**Writing Fractions in Lowest **

Terms

Write in lowest terms

**Solution:**

When writing fractions in lowest terms, be sure to

include the factor 1 in the numerator or an error may

result.

**Objective
**

**Multiply and divide fractions.**

**Multiplying Fractions:**

If and
are fractions, then ,

That is, to multiply two fractions, multiply their
numerators

and then multiply their denominators.

**Dividing Fractions :**

If
and
are fractions, then
.

That is, to divide two fractions, is to multiply its **
reciprocal;
**

the fraction flipped upside down.

**EXAMPLE 3 **

**Multiplying Fractions**

Find each product, and write it in lowest simple terms.