W RITING AND S OLVING P ROPORTIONS Sports A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person.

Slides:

Advertisements

Similar presentations

U NIT 3: R ATIOS AND P ROPORTIONAL R ELATIONSHIPS MCC7.RP.1 MCC7.RP.2a MCC7.RP.2b MCC7.RP.2c MCC7.RP.2d MCC7.RP.3 MCC7.G.1.

Advertisements

Transparency 2 Click the mouse button or press the Space Bar to display the answers.

I DENTIFYING AND W RITING P ROPORTIONS Objective: Learn to find equivalent ratios and identify proportions.

SOLVING PROPORTIONS USING CROSS PRODUCTS Section 8.5.

How can you represent a relationship between two quantities?

R ATIOS AND P ROPORTIONS Objective: Finding Equivalent Ratios to Create Proportions.

Chapter 7 The Basic Concepts of Algebra © 2008 Pearson Addison-Wesley. All rights reserved.

7 th Grade Math Ms. Richardson.  To write a percent as a fraction  You can write 16 percent as or 16%  Your turn now:  Write the percent as a fraction.

Can we go on! You have 5 minutes to complete check-up.

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.

Use the cross products property EXAMPLE 1 Write original proportion = x 6 Solve the proportion =. 8 x 6 15 Cross products property Simplify. 120.

Writing and Solving Proportions. Proportions Proportion is an equation stating that two ratios are equivalent. Proportional are two quantities that form.

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.

Can we go on! You have 5 minutes to complete check-up.

Finding a Percent of a Number Lesson 6-7. Using a Proportion Set up a proportion that uses the percent over 100. Cross multiply to write an equation.

estimate and find solutions to application problems involving proportional relationships such as similarity, scaling, unit costs, and related measurement.

Ratios and Proportions

The key to solving word problems is DON’T BE SCARED.

RATIOS & PROPORTIONS What are ratios? What are proportions? How to solve ratio and proportion problems.

1.4 S OLVING L INEAR E QUATIONS A __________ ____________ in one variable x is an equation that can be written in the form where a and b are real numbers,

Gravity. Gravity is a pulling force It pulls things down towards the earth.

Chapter 7: Similarity.

Proportional Reasoning Today you will learn to: test if ratios can form a proportion. use cross products. M7.A.2.2.3: Use proportions to determine if two.

Proportional Reasoning Section 2.3. Objectives:  To solve problems using proportional reasoning.  Use more than one method to solve proportional reasoning.

4-3 Equivalent Ratios and Proportions: 4-3 Classwork: WORKBOOK, page 175 Problems 7 through 12 You have 20 minutes to complete.

§ 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,

6.1.1 RATIOS, PROPORTIONS, AND THE GEOMETRIC MEAN Chapter 6: Similarity.

Writing and Solving Proportions BEFORE: You wrote and compared ratios. NOW: You’ll write and solve proportions. WHY? So you can find out how much an elephant.

Transparency 3 Click the mouse button or press the Space Bar to display the answers.

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

8-1 R ATIOS AND P ROPORTIONS M11.C D Objectives: 1) To write ratios and solve proportions.

1. What Are You Learning? I CAN solve proportions. 2.

Section 4-4 p. 170 Goal – to use proportions to solve problems.

B ELL R INGER T HROW B ACK T HURSDAY Write each expression using exponents x 4 x 4 x 4 x 4 2. Y x Y x Y 3. (p)(p)(p) 4. (3w)(3w)(3w)(3w)

3.3 Solving Equations by Using Multiplication and Division Multiplication Property of Equality –If each side of an equation is multiplied by the same number,

Solving Addition and Subtraction Equations. Inverse operation is an operation that “undoes” another operation. Addition and subtraction are inverse operation.

Finding a Percent of a Number

Cross Products and Proportions

S OLVING P ROPORTIONS Lesson 2-7. Warm Up: You are making beaded necklaces using a pattern in which 2 large red beads are followed by 3 small blue beads.

2.2 Solving Two- Step Equations. Solving Two Steps Equations 1. Use the Addition or Subtraction Property of Equality to get the term with a variable on.

5 minutes Warm-Up Solve. 2) 1).

S IMILARITY Day 1: Ratios and Proportions. 7.1 F ORMS OF R ATIOS Essential Question: What are the important things to remember when using ratios?

P ROPORTIONS AND R ATIOS EQ: How can finding equivalent ratios help us solve proportions?

Using Equivalent Ratios EXAMPLE 1 Sports A person burned about 210 calories while in-line skating for 30 minutes. About how many calories would the person.

Vocabulary ratio: a comparison of two numbers through division often expressed as a fraction. Proportion: An equation that states that two ratios are equal.

Holt Algebra Rates, Ratios, and Proportions Warm Up Solve each equation. Check your answer. 1. 6x = m = y =18.4 Multiply. 6.7.

In the Real World Sports A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding.

Algebra 1 Foundations, pg 136  Students will be able to solve and apply proportions.

Lesson 4-2 Solving Proportions

Finding a Percent of a Number

Solving Linear Equations and Inequalities

Finding a Percent of a Number

A proportion is an equation that states two ratios are equal

6.3 Solving Proportions Using Cross Products

Proportions and Percent Equations

2-7 Solving Proportions.

Finding a Percent of a Number

Proportions TeacherTwins©2014.

Lesson 5.2 Proportions Students will be able use cross multiply to determine if the two ratios are equivalent.

Finding a Percent of a Number

Finding a Percent of a Number

Solving Equations Using Multiplication and Division

5 minutes Warm-Up Solve. 2) 1).

Lesson 6 Ratio’s and Proportions

Solving 1 and 2 Step Equations

Ch. 2 Vocabulary 12.)Proportion 13.) Cross products (of proportion)

EXAMPLE 4 Solve proportions Solve the proportion. ALGEBRA a x 16

Using Cross Products Chapter 3.

Presentation transcript:

W RITING AND S OLVING P ROPORTIONS Sports A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding for 60 minutes? In Example 1, you will use a proportion to answer this question. A proportion is an equation that states that two ratios are equivalent. Algebra =, where b and d are nonzero numbers.

E XAMPLE 1 U SING E QUIVALENT R ATIOS Sports A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding for 60 minutes? In Example 1, you will use a proportion to answer this question. To find the number C of calories the person would burn while skateboarding for 60 minutes, solve the proportion =. Answer: Ask yourself, what number can you multiply by 30 to get 60? The answer is 2. So, multiply 150 x 2 to get 300. So the person would burn about 300 calories while skateboarding for 60 minutes.

E XAMPLE 2 S OLVING P ROPORTIONS U SING A LGEBRA Solve the proportion =.

E XAMPLE 2 W RITING AND S OLVING A P ROPORTION Setting Up a Proportion There are different ways to set up a proportion. Consider the following problem. Yesterday you bought 8 bagels for $4. Today you want only 5 bagels. How much will 5 bagels cost?

W RITING AND S OLVING A P ROPORTION

L ESSON 5: S OLVING P ROPORTIONS U SING C ROSS P RODUCTS In the Real World Science At space camp, you can sit in a chair that simulates the force of gravity on the moon. A person who weighs 105 pounds on Earth would weigh 17.5 pounds on the moon. How much would a 60 pound dog weigh on the moon? You’ll find the answer in Example 2. In the proportion, the products 2 6 and 3 4 are called cross products. Notice that the cross products are equal. This suggests the following property.

C ROSS P RODUCTS P ROPERTY Cross Products Property Words The cross products of a proportion are equal. Cross Products Property Words The cross products of a proportion are equal.

E XAMPLE 1 S OLVING A P ROPORTION U SING C ROSS P RODUCTS Use the cross products property to solve.

Science At space camp, you can sit in a chair that simulates the force of gravity on the moon. A person who weighs 105 pounds on Earth would weigh 17.5 pounds on the moon. How much would a 60 pound dog weigh on the moon? E XAMPLE 2 W RITING AND S OLVING A P ROPORTION

Penguins At an aquarium, the ratio of rockhopper penguins to African penguins is 3 to 7. If there are 50 penguins, how many are rockhoppers? First, determine the ratio of rockhoppers to total penguins. Then, set up proportion. E XAMPLE 3 W RITING AND S OLVING A P ROPORTION

Y OUR T URN In John’s class, the ratio of boys to girls is 5 to 8. If there are 39 students in his class, how many are girls?