How do we simplify complex fractions and complex rational expressions?

Slides:

Advertisements

Similar presentations

Complex fractions.

Advertisements

12-8 Mixed Expressions and Complex Fractions Objective Students will be able to simplify complex fractions.

6-3: Complex Rational Expressions complex rational expression (fraction) – contains a fraction in its numerator, denominator, or both.

Warm-Up. Quote: He _______ has ______ is ______ ______! ~______~

3.4 Dividing Rational Numbers. Multiplicative Inverse Two numbers whose product is 1 Reciprocals.

Dividing Rational Expressions Use the following steps to divide rational expressions. 1.Take the reciprocal of the rational expression following the division.

DIVIDING RATIONAL NUMBERS

Adding and subtracting fractions and mixed numbers

Adding Fractions 1.Add numerators — 8 Adding Fractions with Like Denominators =

Multiplying & Dividing Rational Expressions. Simplified form of a rational expression - Means the numerator and denominator have NO common factors. To.

Lesson 8-1: Multiplying and Dividing Rational Expressions

Example 3 Dividing Mixed Numbers ÷ – 3 19 = 17 6 – Multiply by the reciprocal of 17 6 – 6 – = 3 () 6 – 19 Use rule for multiplying fractions.

Chapter 6 Section 4 Addition and Subtraction of Rational Expressions.

9.5 Addition, Subtraction, and Complex Fractions Do Now: Obj: to add and subtract rational expressions Remember: you need a common denominator!

Adding, Subtracting, Multiplying, & Dividing Rational Expressions

9.5: Addition, Subtraction, and Complex Fractions Objectives: Students will be able to… Add and subtract rational expressions Simplify complex fractions.

11-8 Mixed Expressions and Complex Fractions Algebra 1 Glencoe McGraw-HillLinda Stamper.

Vocabulary  Rational Expression – a ratio of 2 polynomial expressions.  Operations with rational numbers and rational expressions are similar.  Just.

 Multiply rational expressions.  Use the same properties to multiply and divide rational expressions as you would with numerical fractions.

Dividing Fractions and Mixed Numbers Objective: Learn to divide fractions and mixed numbers.

Multiplying Fractions and Mixed Numbers 3 X 1. Step 1: Convert the mixed numbers to improper fractions. 3 = 7 X 3 = = 25 1 = 5 X 1 = = 8.

Warm up # (-24) =4.) 2.5(-26) = 2-7(-8)(-3) = 5.) -5(9)(-2) = 3.

MULTIPLY and DIVIDE RATIONAL NUMBERS. MULTPILYING MIXED NUMBERS 1)Change all Mixed numbers to improper fractions 2)Simplify A) Up and Down B) Diagonally.

Chapter 4 Notes 7 th Grade Math Adding and Subtracting Fractions10/30 2. Find a common denominator 3. Add or subtract the numerators Steps 4. Keep the.

9-4 Multiplying and Dividing Rational Expressions (Day 1) Objective: Students will be able to simplify complex fractions.

Aim: How do we multiply or divide complex numbers? Do Now: 1. Multiply: 2. Multiply: 3. Multiply: 6 + 7x + 2x i HW: p.216 # 26,30,32,36,38,40,50,52.

Complex Rational Expressions, Equations. Complex Rational Expression = fraction which will contain at least one rational expression in the numerator OR.

8.5 – Add and Subtract Rational Expressions. When you add or subtract fractions, you must have a common denominator. When you subtract, make sure to distribute.

Why do we invert and multiply?

Fractions Review. Fractions A number in the form Numerator Denominator Or N D.

Objective 8 Multiply and divide fractions © 2002 by R. Villar All Rights Reserved.

Unit 4 Day 4. Parts of a Fraction Multiplying Fractions Steps: 1: Simplify first (if possible) 2: Then multiply numerators, and multiply denominators.

Adding and Subtracting Rational Expressions

6.2 Multiplying and Dividing Rational Expressions.

Bellwork Write each rational number as a fraction in simplest form.

Table of Contents Dividing Rational Expressions Use the following steps to divide rational expressions. 1.Take the reciprocal of the rational expression.

Algebra II Honors POD homework: p eoo, odds Factor the following:

To simplify a rational expression, divide the numerator and the denominator by a common factor. You are done when you can no longer divide them by a common.

AIM: How do we simplify complex fractions? Do Now: Perform the operation: 1) x__ + 1__ x + 2 x – 2 2) 2z - z²_ z - 1 z² - 1 HW # 9 – pg 64 #11,12,13 (Review.

TODAY IN CALCULUS…  Warm Up: Synthetic Division  Learning Targets :  You will add and subtract rational expressions.  You will simplify rational expressions.

3.9 Mult/Divide Rational Expressions Example 1 Multiply rational expressions involving polynomials Find the product. Multiply numerators and denominators.

Multiply and Divide Fractions and Decimals. Mixed Numbers, Improper Fractions, and Reciprocals Mixed Number: A number made up of a fraction and a whole.

Objectives Add and subtract rational expressions.

11.5 Adding and Subtracting Rational Expressions

Aim: How do we multiply or divide complex numbers? Do Now:

AIM: How do we simplify, multiply and divide rational expressions?

Adding, Subtracting, Multiplying and Dividing Fractions

Multiplying and Dividing Rational Expressions

Do Now: Multiply the expression. Simplify the result.

Multiplying and Dividing Rational Numbers

8.1 Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions

Aim: How do we multiply or divide complex numbers? Do Now:

Math 2-6: Warm-up.

Multiplying and Dividing Rational Expressions

Without a calculator, simplify the expressions:

Mult/Divide Rational Expressions

Adding and Subtracting with Unlike Denominators

Change to Mixed Number---7/4

Division of Fractions.

Warm-up: Find each quotient.

Rational Expressions and Equations

9.4: Rational Expressions

7.4 Adding and Subtracting Rational Expressions

Dividing Fractions and Mixed Numbers

Rational Expressions and Equations

29. Add and Subtract Rational Expressions

Section 7.3 Simplifying Complex Rational Expressions.

Unit 3: Rational Expressions Dr. Shildneck September 2014

DIVIDE TWO RATIONAL NUMBERS

Presentation transcript:

How do we simplify complex fractions and complex rational expressions? Do Now Finish this sentence: Dividing by a fraction is the same as…

What is a complex fraction? A complex fraction is fraction with another fraction in the numerator or denominator. Ex.

So how can we simplify them? Remember, fractions are just division problems. We can rewrite the complex fraction as a division problem with two fractions. This division problem then changes to multiplication by the reciprocal.

What if we have mixed numbers in the complex fraction? If we have mixed numbers, we treat it as an addition problem with unlike denominators. We want to be working with two fractions, so make sure the numerator is one fraction, and the denominator is one fraction Now we can rewrite the complex fraction as a division of two fractions

Example

Try on your own…

What about complex rational expression? Treat the complex rational expression as a division problem Add any rational expressions to form rational expressions in the numerator and denominator Factor Simplify “Bad” values

Example

Example

Try on your own

One more for you

Review Treat the complex fraction as a division problem Change any mixed numbers into improper fractions Simplify “Bad” values

Summary/HW What are some challenges or potential pitfalls that one must remember when dealing with complex fractions? HW pg 128, 1-19 odd