  # Fractions

OBJECTIVES:
1. To understand fractions
2. To reduce fractions
3. To compare fractions
4. To find fractions between two given
fractions

Solve:

1. x + 2 = 5
2. x + 4 = 3
3. 6x = 3

A fraction is an ordered pair of numbers a and b (not
necessarily integers), b≠ 0, written The number a is called the numerator of the fraction , and
the number b is called the denominator of the fraction.

If a and b are integers, we call the fraction a rational
numbers (Q). Q = { a and b are integers, b≠0}

Example: Classify each of the expressions above as rational numbers,
fractions or both?

Any integer x is view as VENN DIAGRAM:
OF THE REAL
NUMBERS

N: Natural Numbers
W: Whole Numbers
I: Integers
Q: Rational Numbers
R: Real Numbers TRUE OR FALSE: Assign page 297 Preliminary Problem

MODELS FOR FRACTIONS

1. Colored Regions Model What fraction is shaded? ____ What fraction is shaded?______  What fraction of the balls are shaded? Shade 2/5 of the balls.

3. Number Line Model

Shade 5/6 of the unit segment TRY THESE
Draw a number line and include the following points.  4. Fraction Strip Model page A-29 Act Book

When students are asked to show and understanding of the concept
of a fraction, the area model is preferred over the set model
because the total area is more flexible.

Fraction strips can be folded into parts so that the resulting strip
is equal in length to the given fraction. Folds may be made
ONLY on the lines of the strips. Some of the English words for rational numbers are the same as
the words for position:
the third person in line and one third for 1/3.
This causes confusion for students. The Chinese read 1/3 as “out of
three parts, (take) one.

Proper fraction- A fraction where A proper fraction is a fraction greater than 0 but less than 1.

Examples of proper fractions Improper fraction-A fraction a/b , where An improper fraction is a fraction that is greater than 1.
Examples of improper fractions Equivalent Fractions

Paper Folding Fold in half Fold in half  represent the same rational number and are
equivalent fractions or equal fractions. Notice that the value of the fraction does not change when
the numerator and denominator are multiplied by the same
number.

TRY THESE: Name four rational numbers equivalent to 1/4 .
Remember: Fractions that express the same quantity are
called equivalent fractions.

Fundamental Law of Fractions

Let a/b be any fraction and n be a nonzero whole number,
then Actually, n can be any nonzero number.

This law show us that We can use this law to “build up” fractions and also to
simplify “reduce” them.

SIMPLIFY: Definition of Simplest Form - (lowest terms)
A rational number a/b is in simplest form if a and b have no
common factors greater than 1, that is a and b are relatively
prime. (that is, the GCD (a, b) = 1).

TRY THESE: Write each of the following in simplest
form. Equality of Fractions
Methods to determine if two fractions are equal

A. Reduce to simplest form. B. Rewrite both fractions with the same least
common denominator. C. Write both fractions with any common
denominator Let’s use method 3 to explain our next Property.
When are equivalent? therefore thus if and only if ad = bc.

Property
Two fractions are equal if, and only if, ad = bc.

Use the above property to determine if the following
fractions are equal: Ordering Fractions
Methods to order fractions

A. Like Denominators : It is simple to compare fractions
that have like denominators; just compare the numerators.
The one with the greater numerator is the greater fraction

Theorem 5.1 If a, b, and c are integers and and only if, a > c.

Insert <, >, or =. B. Unlike Denominators:
1. Area Model or Fraction Strips
Compare 2. Getting the LCD and comparing 3. Using Cross Products

THEOREM 5.2 If a, b, c, and d, are integers and b > 0,
d> 0, then if, and only if, ad > bc.

Therefore, because 3(12) > 5(7). because 3(13) > 4(9) because 15(9) > 16(8)

TRY THESE TRY THESE Arrange each of the following in ascending
order. Do not convert the fractions to decimals. Denseness of Rational Numbers

Property -Given rational numbers there is a
rational number between these two numbers

1. Find a fraction between 1/3 and 1/2 .
Rewrite with a common denominator.

2. Find a fraction between 7/8 and 5/6
. How many rational numbers lie between 7/8 and 5/6 ?

Try This: Find three fractions between 1/4 and 1/3.

Class work Fraction Circle Worksheet
Homework Math XL section 5.1 and problems from the
book page 310-313 # 1,4, 6, 7, 8, 10, 12, 20, 35

 Prev Next

Start solving your Algebra Problems in next 5 minutes!   Algebra Helper Download (and optional CD) Only \$39.99 Click to Buy Now: OR   2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of June 22nd you will pay only \$39.99 instead of our regular price of \$74.99 -- this is \$35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1\$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor: Step 2 : Let Algebra Helper solve it: Step 3 : Ask for an explanation for the steps you don't understand: Algebra Helper can solve problems in all the following areas:

• simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
• factoring and expanding expressions
• finding LCM and GCF
• (simplifying, rationalizing complex denominators...)
• solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
• solving a system of two and three linear equations (including Cramer's rule)
• graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
• graphing general functions
• operations with functions (composition, inverse, range, domain...)
• simplifying logarithms
• basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
• arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!   Algebra Helper Download (and optional CD) Only \$39.99 Click to Buy Now: OR   2Checkout.com is an authorized reseller
of goods provided by Sofmath "It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..." C. Sievert, KY Sofmath 19179 Blanco #105-234San Antonio, TX 78258 Phone: (512) 788-5675Fax: (512) 519-1805 Home   : :   Features   : :   Demo   : :   FAQ   : :   Order Copyright © 2004-2021, Algebra-Answer.Com.  All rights reserved.