Ratios and Proportions REVIEW CONCEPTS. What is a ratio? A ratio is a comparison of two numbers. Ratios can be written in three different ways: a to b.

Slides:

Advertisements

Similar presentations

Ratio, Proportion, and Percent

Advertisements

Ratio and Proportion.

Eighth Grade Math Ratio and Proportion.

Ratio Lesson 4-1 and Proportion.

Ratio and Proportions. Ratio of a to b The quotient a/b if a and b are 2 quantities that are measured in the same units can also be written as a:b. *

1.1 Problem Solving with Fractions

Ratios and Proportions

Answers to page 74 #22-31.

2.5 Solving Proportions Write and use ratios, rates, and unit rates. Write and solve proportions.

How do I solve a proportion?

Any questions on the Section 6.5 homework?. Section 6.6 Rational Expressions and Problem Solving.

Solve the equation -3v = -21 Multiply or Divide? 1.

Ratio and Proportion.

Lesson 4-1 Ratio and Proportion

8-3 6 th grade math Solving Proportions Using Cross Products.

7.1 Ratio and Proportion Textbook page 357.

3.4 Ratios & Proportions Ratios & Proportions Goals / “I can…”  Find ratios and rates  Solve proportions.

Ratios: a comparison of two numbers using division

1 ratios 9C5 - 9C6 tell how one number is related to another. may be written as A:B, or A/B, or A to B. compare quantities of the same units of measurement.

Introduction to Pharmaceutical Calculation

Unit Three Ratios and Proportional Relationships Why do we learn vocabulary in math??

Solving Percent Problems Section 6.5. Objectives Solve percent problems using the formula Solve percent problems using a proportion.

Section 7.1 Introduction to Rational Expressions Copyright © 2013, 2009, and 2005 Pearson Education, Inc.

PRESENTATION 9 Ratios and Proportions

Proportions Objectives: 1) solve equations with variables in numerators 2) Solve equations with variables in denominators.

Ratio, Rate, Proportion, and Percent. Ratio  Comparison of two numbers by division  Can be written three different ways 4 to 9 4 :

Copyright © Ed2Net Learning, Inc.1 Percent of Change Grade 7 Pre-Algebra.

Proportions Mrs. Hilton’s Class. Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry.

4.1 Ratio and Proportion Ratio – comparison of two numbers by division. –Can be written: a to b a : b where b ≠ 0. If a and b represent quantities measured.

Objectives Write and use ratios, rates, and unit rates.

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

RATIOS AND PROPORTIONS

PODPOD advanced Kobe runs from baseline to baseline (94ft) in 4 seconds to score the game winning basket. How many miles per hour does he run? basic 25.

Finding a Percent of a Number

Math Pacing Ratios and Proportions Solve each equation

Lesson 11-5 Warm-Up.

Multistep Equations Learning Objectives

MTH 231 Section 7.3 Proportional Reasoning. Overview In grades K – 4, a main focus is the development of the additive principles of arithmetic. In the.

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.

Algebra 1 Chapter 2 Section : Solving Proportions A ratio is a comparison of two quantities. The ratio of a to b can be written a:b or a/b, where.

3.9 Proportions Goal to solve problems involving 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.

Mathsercise-C Fractions Ready? Here we go!. Fractions Work out: x 4545 Give your answer in its simplest form Answer Question 2 When multiplying.

§ 3.2 Ratio and Proportion. A ratio compares quantities by division. The ratio of a to b can be expressed as a:b or Ratio Blitzer, Introductory Algebra,

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.

Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.

Solving a Proportion by “Cross” Multiplying

Ratios and Proportions

7.1 Ratio and Proportions Pg 356

Equivalent Ratios By, Mrs. Muller.

Algebra Bell-work 9/1/17 1.) 3x – 3 – x = 2x – 3 2.) 3x – 7 = 3x + 5

8.1 Ratio and Proportion.

Chapter 14 Rational Expressions.

8.1 Ratio and Proportion.

Ratio and _________.

Ratios 4 Possible Ways to Write a Ratio #1

Section 6.2 Linear Equations in One Variable

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

Using Proportions.

Percent of Change By, Mrs. Muller.

Ratio, Proportion, and Other Applied Problems

You solved problems by writing and solving equations.

7-1 Ratios and Proportions

Algebra 1 Section 2.6.

Ratios and Proportions

Write a proportion that compares hours of work to pay.

Lesson 6 Ratio’s and Proportions

Using Cross Products Chapter 3.

Presentation transcript:

Ratios and Proportions REVIEW CONCEPTS

What is a ratio? A ratio is a comparison of two numbers. Ratios can be written in three different ways: a to b a : b ab NOTE: Ratios must be expressed in lowest terms. 3 to 4 3 : 4 34

How to simplify ratios. Simplify ratios the same way you simplify fractions: Find a common factor. 16:4 = 4:1 18:24 = 3:4 125:25 = 5:1

Example 1: Part to Whole In a 100g sample of copper alloy, there is 55g of copper and 45g of tungsten. What is the ratio of copper alloy to tungsten? The ratio of copper alloy to tungsten is 20:9. Tungsten : Copper Alloy 45 : : 20

Example 2: Part to Part In a 100g sample of copper alloy, there is 55g of copper and 45g of tungsten. What is the ratio of copper to tungsten? The ratio of copper to tungsten is 11:9. Copper : Tungsten 55:45 11:9

Proportions A proportion is an equation that equates two ratios.

Cross-Product Property 2x6=12 3x4 = 12 ad = bc Therefore:

Example 3: Step 1: Cross Multiply Step 2: Multiply Step 3: Divide

Example 4: Direct Proportion In a 100g sample of copper alloy, there is 55g of copper and 45g of tungsten. How much copper is in a 120g sample of copper alloy? Step 1: Set up the proportion Original Copper Original Alloy New Copper New Alloy

Example 4: Continued… Step 2: Cross Multiply Step 3: Solve for the unknown Therefore, there are 66g of copper in a 120 sample of copper alloy.

Example 5: Direct Proportion The ratio of tungsten to copper in a sample of copper alloy is 9:20. If you have a sample of copper alloy that has is 220g of copper, how many grams of tungsten is in the sample? Step 1: Set up the proportion Ratio of Tungsten Ratio of Copper Amount of Tungsten Amount of Copper

Example 5: Continued… Step 2: Cross Multiply Step 3: Solve for the unknown Therefore, there are 99g of tungsten in the sample of copper alloy.

Example 6: Direct Proportion

Indirect Proportion An indirect proportion is a comparison between two ratios that are INVERSELY proportional This means that an increase in one quantity leads to a decrease in the other quantity When we solve for inverse proportions, we need to invert one of our ratios

Example 1: Indirect Proportion If it takes 3 carpenters 30 days to build one house, how many days would it take 5 carpenters to build the same house? Let’s think about this to see if it is a direct or indirect proportion. If we INCREASE the number of carpenters, will the amount of time it takes to build the house decrease?

Example 1: Indirect Proportion (Cont) If it takes 3 carpenters 30 days to build one house, how many days would it take 5 carpenters to build the same house? Setting up the proportion if it was direct: But because it is indirect: We switch the two values on the bottom

Example 1: Indirect Proportion (Cont) If it takes 3 carpenters 30 days to build one house, how many days would it take 5 carpenters to build the same house? Solving for X yields 18 days

Example 2: Indirect Proportion If it takes 8 carpenters 26 days to complete a project, how many days would it take 11 carpenters to complete the same project? ORIGINAL: INVERTING: X = 18.9 Days

Other Examples A journeyman takes 2 hours to install a door. An apprentice takes 3.5 hours to do the same job. How long would it take them do install a door if they were working together? Let’s try to understand what this question is asking The first thing we need to do is to figure out how much of the door each of them can complete PER hour The journeyman takes 2 hours for 1 door. So in 1 hour he completes 0.5 of the door (1/2) The apprentice takes 3.5 hours for 1 door. So in 1 hour he completes of the door (1/3.5)

Example Cont Combining the two, JourneymanApprentice = This means they complete of the door in 1 hour (60 minutes). Setting up the proportion: X = minutes

Example Cont X = minutes We don’t want to leave our answer in minutes so we will use a proportion to convert to hours. X = hours * 60 minutes = minutes Therefore, it would take the apprentice and the journeyman 1 hour and 16 minutes to install a door if they are working together

Trying another one A journeyperson takes 3 hours to install two doors. An apprentice takes 6.75 hours to install 2 doors. If they are working together to install two doors, how long will it take them? Try it yourself!

Trying another one A journeyperson takes 3 hours to install two doors. An apprentice takes 6.75 hours to install 2 doors. If they are working together to install two doors, how long will it take them? Journeyperson: 2/3 = doors per hour Apprentice = 2/6.75 = doors per hour = doors per hour 0.963X = 120 X = minutes X = hours 0.077*60 = 4.62 minutes Therefore, it would take them 2 hours and 5 minutes to install two doors