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Submitted by Arya.A BEd Mathematics VICTORY COLLEGE OF TEACHER EDUCATION OLATHANNI

RATIO

THE NATIONAL ANTHEM Jana-gana-mana-adhinayaka, jaya he Bharata-bhagya-vidhata. Punjab-Sindh-Gujarat-Maratha Dravida-Utkala-Banga Vindhya-Himachala-Yamuna-Ganga Uchchala-Jaladhi-taranga. Tava shubha name jage, Tava shubha asisa mage, Gahe tava jaya gatha, Jana-gana-mangala-dayaka jaya he Bharata-bhagya-vidhata. Jaya he, jaya he, jaya he, Jaya jaya jaya, jaya he! PLEDGE India is my country. All Indians are my brothers and sisters. I love my country, and I am proud of its rich and varied heritage. I shall always strive to be worthy of it. I shall give my parents, teachers and all elders respect, and treat everyone with courtesy. To my country and my people, I pledge my devotion. In their well-being and prosperity alone lies my happiness.

Dear friends, This book will help you to know more about the wonderful concepts of mathematics. It will help you to study some important mathematical areas like ratio,definition of ratio,ratio with values,part to part and whole ratio, ratio and proportion

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Table of content 1. What is ratio? 2. converstion of ratio 3. Ratio compares with values 4. part-to part and whole ratios 5. Ratio and proportion

Chapter-1

WHAT IS Ratio?

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Ratio Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'. For example, in a group of 30 people, 17 of them prefer to walk in the morning and 13 of them prefer to cycle. To represent this information as a ratio, we write it as 17: 13. Here, the symbol ': ' is read as "is to". So, the ratio of people who prefer walking to the people who prefer cycling is read as '17 is to 13'.

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What is Ratio? The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related. For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole. For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.

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Ratio Formula We use the ratio formula while comparing the relationship between two numbers or quantities. The general form of representing a ratio of between two quantities say 'a' and 'b' is a: b, which is read as 'a is to b'. Expressing a Ratio as 'a is to b' The fraction form that represents this ratio is a/b. To further simplify a ratio, we follow the same procedure that we use for simplifying a fraction. a:b = a/b. Let us understand this with an example. Example: In a class of 50 students, 23 are girls and the remaining are boys. Find the ratio of the number of boys to the number of girls.

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Total number of students = 50; Number of girls = 23. Total number of boys = Total number of students - Total number of girls = 50 - 23 = 27 Therefore, the desired ratio is, (Number of boys: Number of girls), which is 27:23.

Calculation of Ratios In order to calculate the ratio of two quantities, we can use the following steps. Let us understand this with an example. For example, if 15 cups of flour and 20 cups of sugar are needed to make fluffy pancakes, let us calculate the ratio of flour and sugar used in the recipe.

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Step 1: Find the quantities of both the scenarios for which we are determining the ratio. In this case, it is 15 and 20. Step 2: Write it in the fraction form a/b. So, we write it as 15/20. Step 3: Simplify the fraction further, if possible. The simplified fraction will give the final ratio. Here, 15/20 can be simplified to 3/4. Step 4: Therefore, the ratio of flour to sugar can be expressed as 3: 4 How to Simplify Ratios?

A ratio expresses how much of one quantity is required as compared to another quantity. The two terms in the ratio can be simplified and expressed in their lowest form. Ratios when expressed in their lowest terms are easy to understand and can be simplified in the same way as

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we simplify fractions. To simplify a ratio, we use the following steps. Let us understand this with an example. For example, let us simplify the ratio 18:10.

Step 1: Write the given ratio a:b in the form of a fraction a/b. On writing the ratio in the fraction form, we get 18/10. Step 2: Find the greatest common factor of 'a' and 'b'. In this case, the GCF of 10 and 18 is 2. Step 3: Divide the numerator and denominator of the fraction with the GCF to obtain the simplified fraction. Here, by dividing the numerator and denominator by 2, we get, (18÷2)/(10÷2) = 9/5. Step 4: Represent this fraction in the ratio form to get the result. Therefore, the simplified ratio is 9:5.

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Tips and Tricks on Ratio: In case both the numbers 'a' and 'b' are equal in the ratio a: b, then a: b = 1. If a > b in the ratio a : b, then a : b > 1. If a < b in the ratio a : b, then a : b < 1. It is to be ensured that the units of the two quantities are similar before comparing them.

Exercise 1.Definition of ratio 2.What is ratio? 3.What was the formula of ratio? 4.Calculation of ratios 5.How to simplyfy ratio? 6.What are the steps invovled in simplifying ratio? 7. steps in calcutaing ratio

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Chapter-2 Conversion Ratio: Definition, How It's Calculated, and Examples

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What Is the Conversion Ratio? The conversion ratio is the number of common shares received at the time of conversion for each convertible security. The higher the ratio, the higher the number of common shares exchanged per convertible security.

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Understanding the Conversion Ratio There are two main types of capital fundraising tools: debt and equity. Debt must be paid back, but it is often cheaper to raise capital by issuing debt than by acquiring equity due to tax considerations. Equity does not need to be paid back, which is helpful in difficult times or when earnings growth is negative.

The Formula for the Conversion Ratio Is Conversion Ratio =

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Conversion Ratio= Conversion Price of Equity/ Par Value of Convertible Bond

Examples of the Conversion Ratio The following examples show the conversation ratio in the case of convertible bonds and convertible preferreds. Convertible Bonds Convertible debt is a debt hybrid product with an embedded option that allows the holder to convert the debt into equity in the future. The registration statement tells investors the number of shares to be granted.

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Convertible Preferreds Convertible stock is a hybrid equity product. Preferred stockholders receive a dividend like a bond, which ranks higher than equity in case of liquidation, but they have no voting rights. Converting to stock gives the preferred shareholder voting rights and allows them to benefit from share price appreciation.

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Equivalent Ratios Equivalent ratios are similar to equivalent fractions. If the antecedent (the first term) and the consequent (the second term) of a given ratio are multiplied or divided by the same number other than zero, it gives an equivalent ratio. For example, when the antecedent and the consequent of the ratio 1:3 are multiplied by 3, we get, (1 × 3) : (3 × 3) or 3: 9.

Here, 1:3 and 3:9 are equivalent ratios. Similarly, when both the terms of the ratio 20:10 are divided by 10, it gives 2:1. Here, 20:10 and 2:1 are equivalent ratios. An infinite number of equivalent ratios of any given ratio can be found by multiplying the antecedent and the consequent by a positive integer.

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Ratio Table

A ratio table is a list containing the equivalent ratios of any given ratio in a structured manner. The following ratio table gives the relation between the ratio 1:4 and four of its equivalent ratios. The equivalent ratios are related to each other by the multiplication of a number. Equivalent ratios are obtained by multiplying or dividing the two terms of a ratio by the same number. In the example shown in the figure, let us take the ratio 1:4 and find four equivalent ratios, by multiplying both the terms of the ratio by 2, 3, 6, and 9. As a result, we get 2:8, 3:12, 6:24, and 9:36.

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Exercise 1.What is conversion of ratio? 2.Write some examples of converstion of ratio? 3. What is meant by equivalent ratio? 4.Explain and draw ratio table.

Chapter-3

A ratio compares values.

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A ratio says how much of one thing there is compared to another thing. ratio 3:1 There are 3 blue squares to 1 yellow square Ratios can be shown in different ways: Use the ":" to separate the values: 3 : 1 Or we can use the word "to": 3 to 1 Or write it like a fraction: 3/1

A ratio can be scaled up:

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Here the ratio is also 3 blue squares to 1 yellow square, even though there are more squares.

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Using Ratios

The trick with ratios is to always multiply or divide the numbers by the same value.

Example:

4 : 5 is the same as 4×2 : 5×2 = 8 : 10

ratio 4:5 times 2 is 8:10

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Recipes Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.

So the ratio of flour to milk is 3 : 2 To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4: 3×4 : 2×4 = 12 : 8 In other words, 12 cups of flour and 8 cups of milk. The ratio is still the same, so the pancakes should be just as yummy.

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Exercise 1.How to compare ratio with values? 2.What was the trick with ratios? 3.A recipe of dosa batter isuses 4 cup of rice flour and 3 cup of dal?

Chapter-4

"Part-to-Part" and "Partto-Whole" Ratios

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"Part-to-Part" and "Part-to-Whole" Ratios The examples so far have been "part-topart" (comparing one part to another part).

But a ratio can also show a part compared to the whole lot.

Example: There are 5 pups, 2 are boys, and 3 are girls

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five pups Part-to-Part: The ratio of boys to girls is 2:3 or 2/3 The ratio of girls to boys is 3:2 or 3/2 Part-to-Whole: The ratio of boys to all pups is 2:5 or 2/5 The ratio of girls to all pups is 3:5 or 3/5 Scaling We can use ratios to scale drawings up or down (by multiplying or dividing). The height to width ratio of the Indian Flag is 2:3 So for every 2 (inches, meters, whatever) of height there should be 3 of width.

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indian flag If we made the flag 20 inches high, it should be 30 inches wide. If we made the flag 40 cm high, it should be 60 cm wide (which is still in the ratio 2:3 Example: To draw a horse at 1/10th normal size, multiply all sizes by 1/10th

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This horse in real life is 1500 mm high and 2000 mm long, so the ratio of its height to length is 1500 : 2000 What is that ratio when we draw it at 1/10th normal size? 1500 : 2000 = 1500×1/10 : 2000×1/10 = 150 : 200

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Exercise 1.Difference between part -to-part and part -to- whole ratio 2.Can you list some examples of ratios? 3. Three apples and mangoes are in an bascket.What is the ratio between them?

Chapter-5

Ratio and Proportion

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What are ratios and proportions? A ratio is a comparison of two quantities. The ratio of a to b can be expressed as a:b or a/b.

[Examples] A proportion is an equality of two ratios. We write proportions to help us establish equivalent ratios and solve for unknown quantities.

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What skills are tested?

The ratio of lemon juice to sugar is a part-to-part ratio. It compares the amount of two ingredients. The ratio of lemon juice to lemonade is a part-to-whole ratio. It compares the amount of one ingredient to the sum part:whole=part:sum of all partsstart text, of all ingredients. p, a, r, t, end text, colon, start text, w, h, o, l, e, end text, equals, start text, p, a, r, t, end text, colon, start text, s, u, m, space, o, f, space, a, l, l, space, p, a, r, t, s, end text To write a ratio: 1. Determine whether the ratio is part to part or part to whole. 2. Calculate the parts and the whole if needed.

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3.Plug values into the ratio. 4.Simplify the ratio if needed. Integer-tointeger ratios are preferred. How do we use proportions? If we know a ratio and want to apply it to a different quantity (for example, doubling a cookie recipe), we can use proportional relationships, or equations of equivalent

ratios, to calculate any unknown quantities. a:b=c:d a/b=c/d

To use a proportional relationship to find an unknown quantity:

1.Write an equation using equivalent ratios.

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2.Plug in known values and use a variable to represent the unknown quantity. 3.If the numeric part of one ratio is a multiple of the corresponding part of the other ratio, we can calculate the unknown quantity by multiplying the other part of the given ratio by the same number. 4.If the relationship between the two ratios is not obvious, solve for the unknown quantity by isolating the variable representing it.

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Exercise 1.A pancake recepie uses 1/4 cup of all purpose flour and 1/4 cup of rice flour.What is the ratio of all purpose flour to rice flour in the receipe? A. 1:4 B. 1:2 C. 1:1 D. 2:1 E. 4:1 2.Pippin owns 2 cats,3 dogs and a lizard as pets.What is the ratio of the number of cats to the total number of pets Pippin owns? A. B. C. D. E.

1/6 1/3 2/5 1/2 2/3

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3. Nicholas drinks 8 ounces of milk for every 5 cookies he eats.If he eats 20 cookies,how many ounces of milk does he drinks?

Notes