** A proportion on the other hand is an equation that says that two ratios are equivalent**. For instance if one package of cookie mix results in 20 cookies than that would be the same as to say that two packages will result in 40 cookies. 20 1 = 40 2 A proportion is read as x is to y as z is to When you compare two ratios, you use proportions. You are asking if the first ratio is the same, less than, or more than the second ratio. Compare the ratios of brown-to-all girls and blonde-to-all girls: 10 16 = 6 16. 10: 16 = 6: 16. You can see these two ratios are not equal, so they are not proportional: 10 16 ≠ 6 16. 10: 16 ≠ 6: 1

** Proportion Ratio and proportions are said to be faces of the same coin**. When two ratios are equal in value, then they are said to be in proportion. In simple words, it compares two ratios A good way to work with a ratio is to turn it into a fraction. Be sure to keep the order the same: The first number goes on top of the fraction, and the second number goes on the bottom. You can use a ratio to solve problems by setting up a proportion equation — that is, an equation involving two ratios Proportion is an equation which defines that the two given ratios are equivalent to each other. For example, the time taken by train to cover 100km per hour is equal to the time taken by it to cover the distance of 500km for 5 hours. Such as 100km/hr = 500km/5hrs. Let us now learn Maths ratio and proportion concept one by one Ratios are the mathematical expressions used to compare two or more numbers having common factors. We also use ratios one daily basis. Although ratio is a simple mathematical concept still many people ask how to solve ratios. So we have written this article in the simplest language and steps wise with examples to solve ratios What types of word problems can we solve with proportions? Our mission is to provide a free, world-class education to anyone, anywhere. Khan Academy is a 501(c)(3) nonprofit organization

* Definition of Proportion*. A proportion can be used to solve problems involving ratios. If we are told that the ratio of wheels to cars is 4:1, and that we have 12 wheels in stock at the factory, how can we find the number of cars we can equip? A simple proportion will do perfectly Multiplying or dividing all terms in a ratio by the same number creates a ratio with the same proportions as the original, so, to scale your ratio, multiply or divide through the ratio by the scaling factor. For example, a baker needs to triple the size of a cake recipe

**Solve** Applications Using **Proportions**. The strategy for solving applications that we have used earlier in this chapter, also works for **proportions**, since **proportions** are equations. When we set up the **proportion**, we must make sure the units are correct—the units in the numerators match and the units in the denominators match 3. Determine if a proportion is true. 4. Solve proportions. 5. Solve application problems with proportions. 6. Solve problems involving similar figures with proportions. Ratios and Rates RATIOS are used, typically, to compare two like quantities. For example, if there are 13 males and 17 females, then the ratio of males to females is 13 to 17 Proportions Learn what a proportion is and how to set it up. Learn also about fourth proportional and how to find equivalent proportions. Solving proportions This lesson shows you how to set up a proportion and solve for x. Some special techniques to quickly simplify a proportion are also introduced An online proportion calculator allows you to solve proportion problems and find the missing variable value in a given proportion. The proportions calculator calculates the missing value by using the cross multiplication and proportion method. Well, stick to the context to understand how to solve proportions (step-by-step) & with a calculator.

- Ratio and Proportion Tips and Tricks and Shortcuts. The problems on Ratio and Proportion can be easily solved using some simple tips and tricks. Given below are some quick tricks and tips on Ratio. If x : y and z : a, then it can be solved as (x*z)/(y*a). If x/y=z/a=b/c, then each of these ratios is equal to (x+z+e) ⁄(y+a+f
- Ratios and proportions are essential for - effective performance. In this, article we shall learn how to calculate proportions and apply the knowledge to solve sample problems, but before that, let's begin by defining ratios. A ratio is a way of making comparisons between two or more quantities
- e the quantity of ingredients. Note : Translating a word problem into an equation is super important
- How To Solve Word Problems Using Proportions? This video shows how to solve word problems by writing a proportion and solving 1. A recipe uses 5 cups of flour for every 2 cups of sugar. If I want to make a recipe using 8 cups of flour, how much sugar do I use? 2. A syrup is made by dissolving 2 cups of sugar in 2/3 cups of boiling water
- ator then multiplying it by the numerator. For example 4*2/4 is the same thing as four times two fourths. So we want to find 2/4 of 4. The easiest way to do this is first to find out what one fourth of four, and that is the same thing as 4/4 or 1
- Solving proportions is the fundamental building block for most problems. We are providing in-detail material of ratios and proportions, models, estimation in problem-solving situations etc. Go through the complete article to know various Ratio and Proportion concepts, shortcuts and tricks

Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying, and solving the resulting equation. The exercise set will probably start out by asking for the solutions to straightforward simple proportions, but they might use the odds notation, something like this This math video tutorial provides a basic introduction into ratio and proportion word problems. Here is a list of examples and practice problems:My Website:.. * On the other hand, a proportion is two ratios which have been set equal to each other; a proportion is an equation that can be solved*. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other This ratio is key, as it will allow us to take any dimension of the original and set up a proportion to figure out the mural dimension. In terms of height, the ratio of the original painting to.

How To Solve Proportion Word Problems? When solving proportion word problems remember to have like units in the numerator and denominator of each ratio in the proportion. Examples: Biologist tagged 900 rabbits in Bryer Lake National Park. At a later date, they found 6 tagged rabbits in a sample of 2000 Get the latest interview tips,Job notifications,top MNC openings,placement papers and many more only at Freshersworld.com(www.freshersworld.com?src=Youtube)... Solving proportions by using cross product to find unknown terms is what this lesson is about. We will also show some principles, special techniques or shortcuts that can be used to quickly solve a proportion Ratio & Proportion of three variables This topic is from 8th standard but i am sure unless you know the concept its pretty hard to solve involving 3 variables. Let me give you an example

**Ratios** **and** **Proportions** A **ratio** is fundamentally a fraction, or two numbers expressed as a quotient, such as 3/4 or 179/2,385. But it is a special kind of fraction, one that is used to compare related quantities. For example, if there are 11 boys and 13 girls in a room, the **ratio** of boys to girls is 11 to 13, which may be written 11/13 or 11:13 Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional. To see this process in action, check out this tutorial

How do you solve 3 ratios? How to Calculate Ratios of 3 Numbers . Step 1: Find the total number of parts in the ratio by adding the numbers in the ratio together. Step 2: Find the value of each part in the ratio by dividing the given amount by the total number of parts. Step 3: Multiply the original ratio by the value of each part How to solve Ratio and Proportion - Tougher Problems Before looking into the topic let us look on Basics of Ratio & Proportion. ALL YOU NEED TO KNOW ABOUT RATIO'S-LEARN SERIES. ALL YOU NEED TO KNOW ABOUT PROPORTION'S-LEARN SERIES. PROBLEMS DISCUSSED BASED ON. 1)MIXING 2 ALLOYS TO FORM A 3rd ALLOY ** Unknown term: The missing or unknown number in a proportion**. We have seen in the lesson about proportions that we can use cross product to determine if the fractions or ratios are in proportions. Cross products can also be used to find an unknown term in a proportion To keep the proportion, we also need to divide on the right hand side - by 120. Both sides are divided by 120. From there on the equation is easy to solve. We have a number of grade 6 proportions worksheets in our free worksheet centre for you to practice

Equivalent ratios can be divided and/or multiplied by the same number on both sides, so as above, 12:4 is an equivalent ratio to 3:1. Ratios can inform you of the direct proportion of each number in comparison to the other. For example, when a pair of numbers increase or decrease in the same ratio, they are directly proportional In this video the tutor shows how to solve the missing ratios or proportions. He explains it with an example, where a number in one of the ratios is missing and he intends to find this value. He shows the example of cross multiplication, where you multiply the values on the either side of the equation diagonally and finally solves the equation which results in the value of the unknown value The ratio calculator performs three types of operations and shows the steps to solve: Simplify ratios or create an equivalent ratio when one side of the ratio is empty. Solve ratios for the one missing value when comparing ratios or proportions. Compare ratios and evaluate as true or false to answer whether ratios or fractions are equivalent CHAPTER 14 Dosage Calculation Using the Ratio and Proportion Method Objectives After reviewing this chapter, you should be able to: 1. State a ratio and proportion to solve a given dosage calculation problem 2. Solve simple calculation problems using the ratio and proportion method Several methods are used for calculating dosages. The most common methods are ratio Two or more figures are similar if the corresponding angles are equal, and the corresponding sides are in proportion. To solve the similarity problem, you usually need to create a proportion and solve for the unknown side. Similarity and Ratios - Example 1: A girl 180 180 cm tall, stands 340 340 cm from a lamp post at night

- The ratio is helpful to compare two things of the same unit whereas proportion is used to express the relation between two ratios. The ratio is represented using a colon: or slash / and proportion is represented using a double colon:: or equal to symbol =
- Let's solve both two different ways to get the number of feet in 13 meters. Notice that we can turn proportions sideways, move the = sideways too, and solve - this is sort of how we got from the first equation to the second above
- Ratio And Proportion Concept. Ratio - It is a way of comparing two numbers or quantities and showing the relationship between them. It is denoted by → ':' Ex: In a class, there are 60 boys and 40 girls.What is the ratio of boys and girls? Sol.: boys=60 and girls=40. Ratio= boys/girls =60/40=3/2=3:
- This is another type of problem that you may encounter when solving proportions. The format of the proportion is using a colon instead of a fraction. To work this out, we need to rewrite the proportion in fractional form, and then solve this as usual. Since a:b = c:d can be written as \Large{a \over b} = {c \over d}, then our original problem.
- ed by using the fundamental property of proportions. Problem Set up a proportion and solve for the unknown term. a. A number n compared to 45 is the same as 7 compared to 15. Find n
- ator of the second ratio and the multiplication of the deno

- g a ratio. For instance, 3 apples cost 45p would form the ratio apples : cost. When writing ratios into the form 1 : n students incorrectly assume that n has to be an integer or greater than 1
- Setting Up and Solving Proportions Homework Proportion word problems (7 questions). Bellwork Teacher selected Prior Knowledge Review bellwork and homework. Yesterday, we learned about ratios. A ratio is the comparison of two quantities by division. We also, learned about proportions. A proportion states that 2 ratios are equal
- Solving proportions is a crucial skill when studying similar polygons. The ratio of corresponding side lengths between similar polygons are equal and two equivalent ratios are a proportion. For solving proportions problems, we set up the proportions and solve for the missing side length - it will be a variable, or a variable expression
- A proportion is a set of 2 fractions that equal each other.This article focuses on how to use proportions to solve real life problems
- Understand ratio concepts and use ratio reasoning to solve problems. CCSS.Math.Content.6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak..
- R4 - How to Work Out Unequal Sharing and Grouping Problems for Ratio and Proportion One of the most confusing aspects of this strand is the unequal sharing part: for example, where you have 3 of one item for every 5 of anothe
- However, when two ratios are set equal to each other, they are called a proportion. For example, 1/2 is a ratio and 3/6 is also a ratio. If we write 1/2 = 3/6, we have written a proportion. We can..

Solve proportions by multiplying both sides of the equation by the product of the denominators, or cross multiply. When setting up a proportion, it is important to ensure consistent units in the numerators and denominators Ratios can be equivalent or not equivalent. Ratios that are not equivalent could be larger or smaller than one another. Ratios that are equivalent are said to be in proportion, or proportional. You work with proportions when making images larger and smaller, finding unknown lengths of objects, cooking, and making scale models. How to Solve. Answer the question based on the final ratios in the table. A step-by-step methodical approach to such questions will lead you to right answer more quickly. This was a sample of the in-depth instruction that Economist GMAT Tutor offers about solving ratio and proportion questions in the GMAT Quant section

Proportions or ratios are fundamental concepts of mathematics. A proportions is an equation that states that two ratios are equal. Hence proportion can be written in two ways as a:b=c:d or a/b=c/d. In these equations a and d are called as extremes and b,c are called as means. So when working with proportions we can state that product of the means is equal to the product of the extremes i.e. a. Ratio and Proportion are commonly asked questions in aptitude test and competitive exams. These problems require special arithmetic calculation ability to solve it quickly. Questions from these category could be so tricky, so you must equipped yourself with all the shortcut methods and fast calculation is one of the plus for ratio and. This is how to solve ratios effectively. Things that you should remember while solving ratios. Remember, one is studying the ratio of the best method. For instance, the ratio of colors can be represented as 3 reds to 9 blue can be represented as 3:9, not 9:3. The initial article in the statement arrives initially Solving for Ratios A ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, if the ratio of men to women is 1 to 5 then we know that for each man, there are 5 women

- Proportion A proportion is an equation stating that two rational expressions are equal. Simple proportions can be solved by applying the cross products rule. If, then ab = bc
- g the ratio are called terms. The numerator, 3, in this case, is known as the antecedent and the deno
- This set of 3 proportions mazes has students solve for x with two ratios separated by an equals sign. I encourage students to see if they can solve it without a calculator first. If that doesn't work, then they cross multiply. The more practice they get the more automatic it becomes

** The ratio is 2 to 5 or 2:5 or 2/5**. All these describe the ratio in different forms of fractions. The ratio can consequently be expressed as fractions or as a decimal. 2:5 in decimals is 0.4. A rate is a little bit different than the ratio, it is a special ratio. It is a comparison of measurements that have different units, like cents and grams How to solve ratio and proportion with 3 variables Finding the missing value in a proportion is much like finding the missing value for two equal fractions. There are three main methods for determining whether two fractions (or ratios) are equivalent

A proportion is an equation formed with two ratios that are equal. One method for solving a proportion problem is to find the appropriate equivalent ratio. We could have solved the original problem by setting up a proportion and then finding what the equivalent fraction would have to be ** My point is that to solve problems like above, you don't need to remember how to write a proportion or how to solve it — you can ALWAYS solve them just by using common sense and a calculator**. And this is something students should realize, too. Make them understand the basic idea so well that they can figure proportion problems out without using an equation, if need be Three ways to solve proportions Finding the missing value in a proportion is much like finding the missing value for two equal fractions. There are three main methods for determining whether two fractions (or ratios) are equivalent

Ratio & proportion in Year 6 (age 10-11) In Year 6, your child will find missing values using ratios. They will also solve ratio problems involving percentages, pie charts, multiplication, and division. The key word for this section is ratio Well, a ratio is the comparison of two or more numbers by division. Wait! That means a ratio is nothing more than a fraction. And an equation that states two ratios (fractions) are equal to each other is called a proportion Simply stated, a ratio is the relationship of two numbers and proportions are two ratios that are equal to each other. The picture above is a ratio; this ratio could indicate that there are 4 boys for every 3 girls, that there are 4 pears for every 3 oranges or that there are $ 4 in the piggy bank for every 3 dollars in the drawer When it comes to solve the ratios for complex numbers, simply use the online ratio calculator that helps you to find the missing value in the ratio and done simplification on the ratio as you want. References: From the authorized source of Wikipedia : Definition of ratio and formulas. Fromm the site of Wikijob.co : How to solve ratios

The various resources listed below are aligned to the same standard, (6RP03) taken from the CCSM (Common Core Standards For Mathematics) as the Ratio and proportion Worksheet shown above. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number. How to Solve Ratio and Proportion for CLAT 2020. As we know in the revised syllabus for CLAT 2020 (UG), the questions in the Quantitative Techniques are Data Interpretation based but even then, to solve those DI questions faster and accurately, it is important for you to be well acquainted with the basic mathematical concepts like Percentage, Ratio and Proportion, Profit and loss, Simple. How to Solve Fraction, Ratio, and Rational Number Questions. Now that we have discussed how fractions and ratios work indivisually, let's look at how you'll see them on the test. When you are presented with a fraction or ratio problem, take note of these steps to find your solution: #1: Identify whether the problem involves fractions or ratios Solving Proportions Notes (Math 7 Curriculum - Unit 7)These notes are a great way to introduce and practice solving proportions with word problems. Perfect for math binders.Topics Included:Solving Proportions Solving Proportions Using Cross ProductsSolving Proportions with VariablesSolving Proporti

solve equation 1 and 2 . Quantity of X and Y will be 750 grams and 250 grams so their ratio is 3:1 walnuts to the total ratio will be 1/4. Reply. A part can be any size in a ratio, what matters is the proportion that the ratio describes. Lets say 1 part = k, therefore d : f = 4k : 6k Unlimited math practice with meaningful, up-to-date tracking on your child's progress. Learn 4000+ math skills online. Get personalized guidance. Win fun awards Problem Solving using Proportions Writing proportions can be used to solve various word problems. If given a ratio or rate of two quantities, a proportion can be used to determine an unknown quantity. In order to do so, use the following steps. Step 1:Translate the word problem into a proportion, using x as the unknown quantity

There are several types of ratio and proportion problems. Usually the question gives n things with their ratios and the sum of n things. Example John and Mike have $50 with ratio 2/3 To solve this, you simply do the followings: John has 2k money and Mike has 3k money. Since the total money is $50: 2k+3k=50 k=10 So John has $20 and Mike has $30 Ratios are a part of life, not only in the desserts, but also in ecology, or our own well-being. What was my rate of rest to work this past week? In giving our kids the gift of proportions in a multisensory math approach, we provide them with the freedom to be playful in the kitchen Each relationship in the table can be described by two ratios. For example, because 1 quart = 2 pints, we can write two ratios 1 quart / 2 pints and 2 pints / 1 quart. Practice Problems. Problem 1 : An average human brain weighs 3 pounds. What is this weight in ounces ?Use a proportion to convert 3 pounds to ounces The grocery store is a good source of ratios in real life. While looking at the prices of various groceries, you can easily illustrate ratios using two different boxes of cereal. For example, if a 10-ounce box of cereal costs $3 and a 20-ounce box of cereal costs $5, the 20 ounce box is the better value because each ounce of cereal is cheaper

· A proportion is just two ratios that are equal to each other. · One way to determine if two ratios are a proportion is to determine if their quotients are the same. Since ratios can be written sometimes with fraction bars we can think of the problem as a division problem Rational Expressions - Proportions Objective: Solve proportions using the cross product and use propor-tions to solve application problems When two fractions are equal, they are called a proportion. This deﬁnition can be generalized to two equal rational expressions. Proportions have an important property called the cross-product. Ratios How do we solve ratio problems? Ratio . Definition: A comparison between quantities using division. Examples : 3:2 , 3:2:88, 3 to 2, 3 to 2 to 88. A 2 to 5 ratio can be represented as 2:5 . A ration between X and Y can be written. X/Y; X:Y; X to Y ; MEDIUM SAT PROBLEM #8 out of a 25 problem sectio An equation that equates two ratios is a proportion. For instance, if the ratio a/b is equal to the ratio c/d, then the following proportion can be written : The numbers a and d are the extremes of the proportion

Cross Multiplying is probably a new method for many people, and the following video shows several examples of solving ratio proportions by Cross Multiplying. This video writes the pairs of ratios as fractions. Eg. x : 6 = 2: 3 is written as x/6 = 2/3 . Remember any ratio can always be rewritten as a fraction : a : b = a / In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. To find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means. Here, 20 and 5 are the extremes, and 25 and 4 are the means

C. Determine if two ratios are proportional D. Solve for the missing number in a proportion E. Solve word problems Ratios • Definition: A ratio is a comparison between two numbers. A ratio statement can be written three ways: 2 3 , 3 to 2, 3:2 You want to bet on a horse race at the track and the odds are The proportion \(\dfrac{1}{2}=\dfrac{4}{8}\) is read 1 is to 2 as 4 is to 8. Proportions are used in many applications to 'scale up' quantities. We'll start with a very simple example so you can see how proportions work. Even if you can figure out the answer to the example right away, make sure you also learn to solve it using. Math worksheets: Solving proportions. Below are six versions of our grade 6 math worksheet on solving proportions. In these questions, the proportions are shown in the form of equivalent fractions. These worksheets are pdf files

Proportion Calculator. Use this calculator to easily solve proportion equations. Enter any three numbers in the denominators and enumerators for the two proportions and the fourth will be calculated for you to make Proportion 1 and Proportion 2 equal (having the same constant of proportionality) A proportion is like a comparison. Show them the Proportion movie. Reinforce how to solve a proportion by modeling an example on the board. Then, solve a few as a class. Next, it's time to practice calculating some proportions. Put some proportions on the board for the students to cross multiply For instance, the ratio of men to women is 4 is to 5 or ratio of sugar to milk is 2:5. Colons, fractions and 'is to' are primarily used to express ratios. Proportion. Convert ratios into equations and you get proportions. In the above example, M/W = 4/5 is a proportion formed from the sentence ratio of men to women is 4 is to. A rate is a ratio that compares two different kinds of numbers, such as miles per hour or dollars per pound. A unit rate compares a quantity to its unit of measure. A unit price is a rate comparing the price of an item to its unit of measure.. The rate miles per hour gives distance traveled per unit of time. Problems using this type of rate can be solved using a proportion, or a formula Ratios and proportions Here is a list of all of the skills that cover ratios and proportions! These skills are organized by grade, and you can move your mouse over any skill name to preview the skill. To start practicing, just click on any link

Using proportions to solve Chemistry problems This lesson is the continuation of the lesson Proportions of this module. The lesson presents some typical word problems related to Chemistry that can be solved using proportions. You will see how useful the proportions are in solving chemistry problems Provided by the Academic Center for Excellence 6 How to Solve Drug Dosage Problems Reviewed August 2012 Calculating Drug Dosages When performing drug calculations, one of the following four methods should be used: Ratio (Rainbow) Method, Proportion Method, Formula Method, or Dimensional Analysis. Each of these methods works as well as the others To solve this question, you must first identify, then simplify the two ratios: Ella's ratio = 18:54, simplify this by dividing both numbers by 18, which gives a ratio of 1:3; Jayden's ratio = 22:88, simplify this by dividing both numbers by 22, which gives a ratio of 1: Ratios, proportion, fractions are all related items that come up in both real life and mathematical situations. Ratio is a particularly valuable concept in the context of scale drawings. Here the ratio of the drawing to the actual object gives the idea of the relative size of the drawing to the object

Some people prefer to solve percent equations by using the proportion method. The proportion method for solving percent problems involves a percent proportion. A percent proportion is an equation where a percent is equal to an equivalent ratio A ratio is a comparison of two quantities. You can write a ratio as a fraction, using the word to, or using a colon. A rate is a ratio that compares two different units, such as distance and time, or a ratio that compares two different things measured with the same unit, such as cups of water and cups of frozen orange juice concentrate. To solve alloy related questions, a good knowledge of Ratio & Proportion concept is must. At first sight, ratio and proportion looks easy but it gets bit complicated if applied in alloys related topics

Let's solve a proportion with an example. Example: If ratio of pizzas to burgers is 3/5 in a party, how many of burgers will be there if there are total of 15 burgers. Solution: Step 1: Construct a proportion using the given values and x. 3/5 = x/15. Step 2: Apply cross multiplication to the above equation. 5x = 3 × 15. x = 45/5. x = 9. So. A true proportion is an equation that states that two ratios are equal. If you know one ratio in a proportion, you can use that information to find values in the other equivalent ratio. Using proportions can help you solve problems such as increasing a recipe to feed a larger crowd of people, creating a design with certain consistent features, or enlarging or reducing an image to scale

We build upon our examples so far to consider ratios with three parts and ratio problems that involve sharing an amount using a ratio. Further ratio problems For the final two examples this week, we use bar modelling to solve a problem of sharing and a problem that requires making ratios compatible Improve your math knowledge with free questions in Solve proportions and thousands of other math skills Extremes Means To solve problems which require the use of a proportion we can use one of two properties. The reciprocal property of proportions. If two ratios are equal, then their reciprocals are equal. The cross product property of proportions. The product of the extremes equals the product of the means Example: Write the original proportion Use this brilliant teaching pack of lesson resources to help Year 6 children to master how to solve problems involving ratio and proportion. This Diving into Mastery resource complements the White Rose Maths small step Ratio and Proportion Problems. Children will develop their fluency by using objects, diagrams and bar models to help them solve ratio and proportion problems in a. Ratios are said to be in proportion when their corresponding fractions are equal. What we really did above was notice that the fraction 78/162 was equal to the fraction 13/27 - because we could divide both numbers in the first ratio by six (6) to get the second ratio - so the ratios are equal as well, i.e., 78/162 = 13/27