Back To Course

CAHSEE Math Exam: Help and Review22 chapters | 255 lessons | 13 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, learn the different ways that mathematicians write ratios. Also learn how ratios are used when cooking. You will also discover how to effectively use ratios to help you get things done.

A **ratio** compares two values. It shows you that when you have this much of something, you will need to have that much of something else.

You see ratios used in cooking and when working with model toys. The recipe for hummingbird food, for instance, calls for 4 parts of water for every part of sugar. What this ratio tells you is that however much sugar you put in, you need to put in 4 times as much water. If you use 1 cup of sugar, you need 4 cups of water. If you use 1 tablespoon of sugar, you need 4 tablespoons of water.

When you want to write a ratio mathematically, there are three specific formats you can choose from. You can choose to write it in colon form with a colon separating the two numbers. Or you can choose to use the word 'to' in between the numbers. Also, you can write it as a fraction. All are valid and all mean the same thing. When you write it as a fraction though, you will want to keep it in fraction form even if you can simplify it further. As in the hummingbird food recipe, the ratio in fraction form would stay 4/1 even though it can be simplified to just 4.

Use ratios to describe any two things that have a fixed value when compared to each other. The dimensions of photos, for example, have a fixed value when you compare the length to the width or vice versa. A photo that has a width of 5 and a length of 7 will have a width to length ratio of 5:7. A larger photo, such as one with a width of 8 and a length of 10, has a ratio of 8:10.

Another real world application of ratios is in the building of model toys. Many model toy cars come scaled at 1/12th of life size. What this means is that every measure of the toy car equals 12 measures in real life. What measures 1 cm in the toy car will measure 12 cm in the real world.

In many ratio problems, you will need to scale your ratios to find your answer. Going back to the model toy car, if you had the measurements of the real car in front of you, you can use the ratio to calculate the measurements of the toy car by multiplying the real world measurements by the ratio. If the real tire measured 61cm in diameter, then the toy tire will measure 5.08 cm. This is because 61 x (1/12) = 5.08. Whatever real world dimensions you had will just need to be multiplied by the ratio to get the toy dimensions.

You can also scale ratios to find new measurements that maintain the same ratio. Let's say you had a photo whose dimensions are 5 inches wide by 7 inches long. The ratio of this photo is 5 to 7. We don't write dimensions in a ratio form because dimensions are not ratios but exact measurements and are written with either a multiplication symbol or the word 'by.' You like how the picture's width is that much shorter than its length with a ratio of 5:7. You can use this ratio to figure out other possible dimensions that will maintain the same width to length ratio.

To do this, you first figure out how much bigger or smaller you want one of your dimensions to be. Let's say I want the width to be 10 inches wide instead of 5. Well, 10 inches is 2 times bigger than 5. I'd have to multiply the 5 by 2 to get to 10. So, to figure out my length, I'd have to multiply it by the same amount, by 2. My new dimensions then are 10 inches by 14 inches to maintain the same ratio of 5 to 7.

Ratios are commonly used when cooking and when describing dimensions. There are three ways to write ratios. One is with a colon, the second is with the word 'to' and the third is as a fraction. Scaling a ratio requires the multiplication of the same number to both values.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
14 in chapter 10 of the course:

Back To Course

CAHSEE Math Exam: Help and Review22 chapters | 255 lessons | 13 flashcard sets

- Ratios & Rates: Definitions & Examples 6:37
- How to Solve Problems with Money 8:29
- Proportion: Definition, Application & Examples 6:05
- Calculations with Ratios and Proportions 5:35
- Percents: Definition, Application & Examples 6:20
- How to Solve Word Problems That Use Percents 6:30
- How to Solve Interest Problems: Steps & Examples 6:05
- Compounding Interest Formulas: Calculations & Examples 7:45
- Taxes & Discounts: Calculations & Examples 8:07
- How to Solve Problems with Time 6:18
- Distance Formulas: Calculations & Examples 6:31
- Fibonacci Sequence: Examples, Golden Ratio & Nature 5:17
- Productivity Ratio: Formula, Calculation & Analysis 3:41
- What is Ratio in Math? - Definition & Overview 4:46
- Go to CAHSEE Ratios, Percent & Proportions: Help & Review

- AFOQT Information Guide
- ACT Information Guide
- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- FTCE Middle Grades Math: Connecting Math Concepts
- Social Justice Goals in Social Work
- Developmental Abnormalities
- Overview of Human Growth & Development
- ACT Informational Resources
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- Staircases: Types, Design & Construction
- Accounting for Nonprofit Organizations
- Hinge Joints in the Body: Definition, Movement & Examples
- Factors Affecting the Distribution of Wealth & Income
- Progressive Verb Tense Activities
- Protocols for Routing Mobile Ad-Hoc Networks: Proactive, Reactive, Hybrid
- EIGRP: Definition, Protocol & Functionality
- Quiz & Worksheet - What is Salsa Dancing?
- Quiz & Worksheet - Four Uses of Mass Communication
- Quiz & Worksheet - Microscopy Types & Uses
- Quiz & Worksheet - Orwell's 1984 as a Dystopia
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- High School Science Worksheets and Printables
- Active Learning | Definition & Strategies for Teachers

- Business 102: Principles of Marketing
- DSST Human Cultural Geography: Study Guide & Test Prep
- Business 104: Information Systems and Computer Applications
- Glencoe Earth Science: Online Textbook Help
- Foundations of Education: Help and Review
- Holt World History - Human Legacy Chapter 32: Latin America
- PLACE Mathematics: Solving Trigonometric Equations
- Quiz & Worksheet - Pros & Cons of Cross-Curricular Teaching
- Quiz & Worksheet - Teaching Cursive Writing
- Quiz & Worksheet - Zero-Tolerance Policies in the Workplace
- Quiz & Worksheet - Return of Investment Formula
- Quiz & Worksheet - Early Childhood Classroom Technology

- Building Client Relationships in Business
- What Is Assortative Mating?
- Homeschooling in Vermont
- Response to Intervention (RTI) in Florida
- How Organizations Can Leverage Employee Education Benefits to Attract and Retain Top Talent
- WIDA Can Do Descriptors for Grades 9-12
- Texas Teacher Certification Renewal
- Illinois Science Standards for 3rd Grade
- Response to Intervention (RTI) in Illinois
- The Tell-Tale Heart Lesson Plan
- Sequence of Events Lesson Plan
- 4th Grade Ohio Science Standards

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject