What is a Ratio in Math? Understand Ratio & Proportion - [6-3-1]

Understanding Ratios Part 1

In this lesson, we will learn about ratios and how they are used in math. A ratio is a comparison of two numbers, and it involves using fractions to compare the two numbers.

Introduction to Ratios

• Ratio and proportion concepts go together like peanut butter and jelly.

• A ratio is a comparison of two numbers. It involves using fractions to compare the two numbers.

• A ratio can only exist if there are two numbers to compare.

Comparing Boys and Girls in a Room

• We have three boys and six girls in a room. We want to compare the number of boys to the number of girls.

• To perform this comparison, we use fractions. The fraction bar represents "compared to."

• For every three boys, we should encounter six girls because the ratio between boys and girls is locked.

• The ratio of three boys compared to six girls can be simplified by dividing both top and bottom by 3. This simplifies the fraction into one boy compared to two girls.

Understanding Ratios

In this section, the speaker explains what ratios are and how to simplify them. They use examples of boys and girls in a room and fences of different lengths to illustrate the concept.

Introduction to Ratios

• A ratio is a way of comparing two numbers.

• Ratios can be written as fractions or with a colon.

• Simplifying ratios involves reducing them to their simplest form.

Example: Boys and Girls in a Room

• If there are three boys and six girls in a room, the ratio of boys to girls is 3:6 or 1:2.

• This ratio can be simplified by dividing both sides by 3, resulting in a simplified ratio of 1:2.

• The simplified ratio means that for every one boy, there are two girls.

Example: Fences of Different Lengths

• If one fence is four meters long and another fence is six meters long, the ratio of their lengths is 4:6.

• This ratio can be simplified by dividing both sides by 2, resulting in a simplified ratio of 2:3.

• The simplified ratio means that for every two meters of the first fence, there are three meters of the second fence.

Understanding Ratios

In this section, the speaker explains what ratios are and how they can be used to compare two numbers.

Definition of a Ratio

• A ratio is a comparison of two numbers.

• The individual numbers do not matter, it's the comparison between the two that matters.

Simplifying Ratios

• To simplify a ratio, make it into a fraction and reduce it to its simplest form.

• For example, 4:6 can be simplified to 2:3.

Example Problem: Classroom Sizes

• Given two classrooms with 8 students in one and 20 students in the other, find the ratio of students in the first classroom to those in the second classroom.

• The ratio is 2:5 or 2/5. This means that for every eight students in the first classroom, there are twenty total students.

Example Problem: Cups of Coffee

• Given 15 cups of coffee with milk out of a total of 20 cups, find the ratio of cups with milk to total cups.

• The ratio is 3:4 or 3/4. This means that for every three cups with milk, there are four total cups.

Understanding Ratios

In this section, the speaker explains how to write and simplify ratios using different examples.

Comparing Populations with Headbands

• A ratio is used to compare two populations of people that have headbands in a race.

• The ratio between 80 participants compared to 90 participants is written as 80 out of 90 or 80 compared to 90.

• The simplified ratio is 8 compared to 9.

Comparing Kilograms of Mass

• To compare the ratio of flour to salt in a mixture, we express it as a fraction.

• We can simplify the fraction by dividing both top and bottom numbers by their common factor.

• The simplified ratio is for every four kilograms of flour, there should be seven kilograms of salt.

Comparing Dogs and Pets

• When comparing dogs out of pets, we write it as a fraction and simplify it by dividing both top and bottom numbers by their common factor.

• The simplified ratio is five dogs out of six pets total or five compared to six.

Comparing Distances

• To compare distances between two boats, we write it as a fraction and simplify it by dividing both top and bottom numbers by their common factor.

• The simplified ratio is eight feet down the first boat for every eleven feet down the other one or eight compared to eleven.

Comparing Coin Flips

• To compare the ratio of heads to total number of coin flips, we express it as a fraction and simplify it by dividing both top and bottom numbers by their common factor.

• The simplified ratio is seven heads for every ten coin flips total or seven compared to ten.

Understanding Ratios

In this section, the speaker explains how to use skills learned in fractions to simplify ratios and convey the relationship between two things.

Simplifying Ratios

• Skills learned in fractions can be used to simplify ratios.

• The goal is to get to the simplest ratio with smaller numbers that still conveys the relationship between two things.

• Practice is necessary for understanding ratios.