PROPORTIONS Write ratios Use properties of proportions

Slides:

Advertisements

Similar presentations

7.1 Ratios and Proportions

Advertisements

CN #3 Ratio and Proportion

EXAMPLE 4 Solve proportions SOLUTION a x 16 = Multiply. Divide each side by 10. a x 16 = = 10 x5 16 = 10 x80 = x8 Write original proportion.

Objectives Write and simplify ratios.

EXAMPLE 2 Using the Cross Products Property = 40.8 m Write original proportion. Cross products property Multiply. 6.8m 6.8 = Divide.

Using Cross Products Lesson 6-4. Cross Products When you have a proportion (two equal ratios), then you have equivalent cross products. Find the cross.

SOLVING LINEAR EQUATIONS. Example 1 Solve take 3 from both sides divide both sides by 2.

Find the slope of the line through each pair of points.

6.2.1 Use Proportions to solve Geometry Problems.

Ratio and Proportion.

7.1 Ratio and Proportion Textbook page 357.

7-1 Ratio and Proportion Warm Up Lesson Presentation Lesson Quiz

1/29/13. Find the slope of the line through each pair of points. 1. (1, 5) and (3, 9) 2. (–6, 4) and (6, –2) Solve each equation x + 5 x + 6 x =

Chapter 11 Sections 11.1, Rational Expressions.

Warm Up Find the slope of the line through each pair of points. 1. (1, 5) and (3, 9) 2. (–6, 4) and (6, –2) Solve each equation. 3. 4x + 5x + 6x = 45 4.

Example #1 Add the whole numbers, then add the fractions. Rewrite with a common denominator.

Chapter 12 Final Exam Review. Section 12.4 “Simplify Rational Expressions” A RATIONAL EXPRESSION is an expression that can be written as a ratio (fraction)

{ Section 8.1 Ratio and Proportion OBJECTIVE: To write ratios and solve proportions To write ratios and solve proportions BIG IDEA:Proportionality ESSENTIAL.

Warm-Up Solve each equation for x. 1) 3x = 5 2) 2x – 1 = 10 3) 5x + 3x = 14.

Problem Solving in Geometry with Proportions

7-1 Using Proportions Recognize and use ratios and proportions.Recognize and use ratios and proportions. Apply the properties of proportions.Apply the.

Ratio and Proportion 7-1.

§ 2.3 The Multiplication Property of Equality. Martin-Gay, Beginning Algebra, 5ed 22 Multiplication Property of Equality If a, b, and c are real numbers,

Unit 7 Similarity. Part 1 Ratio / Proportion A ratio is a comparison of two quantities by division. – You can write a ratio of two numbers a and b, where.

Solving Proportions. 2 ways to solve proportions 1. Equivalent fractions (Old) Cross Products (New)

Unit Goals – 1. Solve proportions and simplify ratios. 2. Apply ratios and proportions to solve word problems. 3. Recognize, determine, and apply scale.

  A ratio is a way to compare two quantities that are measured in the same units by using division  45 : 100 Ratio.

EXAMPLE 2 Solving an Equation Involving Decimals 1.4x – x = 0.21 Original equation. (1.4x – x)100 = (0.21)100 Multiply each side by 100.

Bell work  The total number of students out for a fall sport is 204 in our school of 1900 total students. What is the ratio of athletes to total students?

Lesson 6-1 Proportions. Objectives Write ratios Use properties of proportions.

Groundhog Day A 16 inch tall groundhog emerges on Groundhog Day near a tree and sees its shadow. The length of the groundhog’s shadow is 5 inches, and.

6.1 Ratios, Proportions and Geometric Mean. Objectives WWWWrite ratios UUUUse properties of proportions FFFFind the geometric mean between.

Ratios and Proportions

CHAPTER 7.1 RATIO AND PROPORTION. RATIO A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b; a:b; or a/b,

Find the slope of the line through each pair of points.

7.1 OBJ: Use ratios and proportions.

You are helping to hang balloons in the gym for a school dance You are helping to hang balloons in the gym for a school dance. There are a.

Ratios and Proportions

Lesson 5-1: Using Proportions

8.1 Ratio and Proportion.

Ratio and Proportion Unit IIA Day and 8.2.

Ratio & Proportions Practice

Lesson 5-1 Using Proportions.

LEARNING GOALS – LESSON 7:1 EXAMPLE 1A: WRITING RATIOS

8.1 Ratio and Proportion.

8.1 Exploring Ratio and Proportion

Section 5.3A Solving Proportions Section 5.3A Solving Proportions

7-1 Ratios and Proportions

Ratio and _________.

Rates (unit Rate) Ratio Solving

Ratio Ratio – a comparison of numbers A ratio can be written 3 ways:

Lesson 3.1 How do you solve one-step equations using subtraction, addition, division, and multiplication? Solve one-step equations by using inverse operations.

6.1 Ratios, Proportions, and the Geometric Mean

Using Proportions.

Fractions IV Equivalent Fractions

Lesson 5-1 Using Proportions.

Objectives Write and simplify ratios.

Adding and Subtracting Rational Expressions

By, Mrs. Muller Proportions.

7.1 Notes Ratios and Proportions

Lesson 5-1: Using Proportions

Ratios, Proportions, and the Geometric Mean

Which fraction is the same as ?

Section 8.1 Ratio and Proportion

A rational expression is a quotient of two polynomials

7.1 Ratio and Proportion.

Lesson 6 Ratio’s and Proportions

Ratio A ratio is a comparison of two numbers such as a : b. Ratio:

Using Cross Products Chapter 3.

Presentation transcript:

PROPORTIONS Write ratios Use properties of proportions “Circle Limit IV (Heaven and Hell)” M. C. Escher, 1960

Example 1 – Write a Ratio In 17 seasons as a major-league baseball player, Chipper Jones of the Atlanta Braves made 2490 hits in 8142 times at bat. What is his overall major-league batting average? number of hits number of times at bat Batting average = or about 0.306

Example 2 – Extended Ratios in Triangles In a triangle, the ratios of the measures of the three sides is 4:6:9, and its perimeter is 190 inches. Find the lengths of the sides of the triangle.

Example 2 – Extended Ratios in Triangles cont. Recall that equivalent fractions can be found by multiplying the numerator and denominator by the same number. Thus: We can rewrite 4:6:9 as 4x:6x:9x and use those measures for the sides of the triangle. 9x 4x 6x

Example 2 – Extended Ratios in Triangles cont. Write an equation to represent the perimeter of the triangle as the sum of the measures of its sides. 9x 4x 6x

Example 2 – Extended Ratios in Triangles cont. Use the value of x to find the measures of the sides of the triangle. 4x = 4(10) or 40 inches 6x = 6(10) or 60 inches 9x = 9(10) or 90 inches

USE PROPERTIES OF PROPORTIONS An equation stating that two ratios are equal is called a proportion. Every proportion has two cross products.

Example 3 – Solve Proportions by Using Cross Products Solve the proportion Original problem Cross products Simplify Divide each side by 35

Example 4 – Solve Proportions by Using Cross Products Original problem Cross products Simplify Add 10 to each side Divide each side by 6

Example 5 – Solve Problems Using Proportions The Gulfstream V business jet has a length of 96 feet and a wingspan of 94 feet. A toy model is made in proportion to the real airplane. If the wingspan of the toy is 36 cm, find the length of the toy.

Example 5 – Solve Problems Using Proportions cont.