Ratio

Institut pendidikan guru malaysia KAMPUS PULAU PINANG

RATIO... NAMA PELAJAR

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1. ABDUL BAITH AFKAR BIN RUSLAN 2.MOHAMMAD NAQIUDDIN BIN MUSTAFA KAMAL 3.WAN AHMAD ASYRAF BIN WAN AHMAD HASBI 4.SAIFUL RIDHUAN BIN MOHD 5.MOHD ZUHASNAN BIN ABDULLAH 6.MUHD ABDILLAH BIN MAT ALI

NO. KAD PENGENALAN

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1. 910414-03-5135 2. 911113-08-5643 3.910513-01-6079 4.911020-11-5225 5.900406-11-5451 6.911130-03-5701

KUMPULAN/UNIT

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PENGAJIAN AGAMA (1 PA)

NAMA M.P.

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NAMA PENSYARAH TARIKH SERAHAN

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MATHEMATIC

PUAN HASLIZA BINTI IBRAHIM

12th OF AUGUST 2009 (WEDNESDAY)

INTRODUCTION

IN THE NAME OF ALLAH THE MOST GRACIOUS AND THE MOST MERCIFUL We were very grateful and we also very thankful to god because finally we had done the mathematic’s assignment successfully. We were really enjoyed while finishing this assignment together. At first we thought this work that given by our mathematic’s lecturer was very tough and difficult to do, but when we worked together it was not same with what we thought. So, it was the great enjoyable from god. The title of our assignment was about ratio. We knew that, the ratio was one of the topic in mathematic’s subject that we will learn. So, as the preparations to learn that topic, we did this assignment. From this assignment, we can know what is ratio and other informations about ratio, then it will make us more understand while learning about ratio that will teach by our lecturer. Here, some early introductions we will show to the reader about ratio : A "ratio" is just a comparison between two different things. For instance, someone can look at a group of people, count noses, and refer to the "ratio of men to women" in the group. Suppose there are thirty-five people, fifteen of whom are men. Then the ratio of men to women is 15 to 20. Expressing the ratio of men to women as "15 to 20" is expressing the ratio in words. There are two other notations for this "15 to 20" ratio: odds notation: 15 : 20 fractional notation:

15

/20

Given a pair of numbers, you should be able to write down the ratios. For example: •

There are 16 ducks and 9 geese in a certain park. Express the ratio of ducks to geese in all three formats.

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Consider the above park. Express the ratio of geese to ducks in all three formats.

That’s was just the early informations about ratio. The other informations, you can see in the next pages of this assignment. -2As the closer, before we forgot something, we also were very thankful to our friends from other groups that gave some help to us. We really happy

to have friends like them. Besides that, we hoped that, this assignment about ratio will give the good impacts to ourselves and others. We also hoped that, the knowledges about ratio can be applicated in our life. THANK YOU.........................

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RATIO

1. What is Ratio?

A ratio is a comparison of two numbers or quantities of the same kind and the same unit. Generally, the two numbers in the ratio are separated with a symbol - colon (:). Suppose we want to write the ratio of 9 and 12, we can write this as 9 : 12 or 9/12, or 9 to 12. We say the ratio is nine to twelve. Let's return to the 15 men and 20 women in our original group. I had expressed the ratio as a fraction, namely, 15/20. This fraction reduces to 3/4. This means that you can also express the ratio of men to women as 3/4, 3 : 4, or "3 to 4". This points out something important about ratios: the numbers used in the ratio might not be the absolute measured values. The ratio "15 to 20" refers to the absolute numbers of men and women, respectively, in the group of thirty-five people. The simplified or reduced ratio "3 to 4" tells you only that, for every three men, there are four women. The simplified ratio also tells you that, in any representative set of seven people (3 + 4 = 7) from this group, three will be men. In other words, the men comprise 3/7 of the people in the group. These relationships and reasoning are what you use to solve many word problems:

•

In a certain class, the ratio of passing grades to failing grades is 7 to 5. How many of the 36 students failed the course? Copyright © Elizabeth Stapel 1999-2009 All Rights Reserved The ratio, "7 to 5" (or 7 : 5 or 7/5 ), tells me that, of every 7 + 5 = 12 students, five failed. That is, 5/12 of the class flunked. Then ( 5/12 )(36) = 15 students failed.

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In the park mentioned above, the ratio of ducks to geese is 16 to 9. How many of the 300 birds are geese? The ratio tells me that, of every 16 + 9 = 25 birds, 9 are geese. That is, geese. Then there are ( 9/25 )(300) = 108 geese.

9

/25 of the birds are

Generally, ratio problems will just be a matter of stating ratios or simplifying them. For instance:

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Express the ratio in simplest form:

$10 to $45

This exercise wants me to write the ratio as a reduced fraction:

.10/45 = 2/9. This reduced fraction is the ratio's expression in simplest fractional form. Note that the units (the "dollar" signs) "canceled" on the fraction, since the units, "$", were the same on both values. When both values in a ratio have the same unit, there should generally be no unit on the reduced form.

•

Express the ratio in simplest form: 240 miles to 8 gallons

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When I simplify, I get (240 miles) / (8 gallons) = (30 miles) / (1 gallon), or, in more common language, 30 miles per gallon. In contrast to the answer to the previous exercise, this exercise's answer did need to have units on it, since the units on the two parts of the ratio, the "miles" and the "gallons", do not "cancel" with each other. Conversion factors are simplified ratios, so they might be covered around the same time that you're studying ratios and proportions. For instance, suppose you are asked how many feet long an American football field is. You know that its length is 100 yards. You would then use the relationship of 3 feet to 1 yard, and multiply by 3 to get 300 feet.

Steps in ratio.....

-52. Step 1 in ratio

Ratio Important Points a) If each term of a ratio is multiplied or divided by the same non-zero number, the ratio remains the same e.g. 2/3 is same as (2 x 4)/(3 X 4) b) If the ratio of terms is in fraction form, convert it into whole numbers. For converting to whole numbers, find the LCM of the denominators and multiply each term by it e.g. Ratio 1/2 : 1/3. The LCM of the denominators 2 and 3 is 6. Then, ratio 1/2 : 1/3 = (1/2 x 6) : (1/3 x 6) = 3 : 2. c) In the ratio a : b, ‘a’ and ‘b’ are called terms of the ratio. The term ‘a’ is called first term or antecedent and term ‘b’ is called second term or consequent. d) Ratio ‘a’ is to ‘b’ is the fraction a/b, written as a : b. Similarly ‘2’ is to ‘3’ is the fraction 2/3 written as 2 : 3. e) Ratio a : b is said to be in its simplest form if the HCF of ‘a’ and ‘b’ is 1 e. g 8 : 12 = 8/12 = 2/3 or 2 : 3. The ratio 2 : 3 is in the simplest form. f) Ratio between two quantities of the same kind and in the same units is obtained on

dividing the first quantity by the second quantity. g) Ratio has no units. (Do not write ration is 2 : 3 cm or m) h) Ratio is generally reduced to its lowest level/form i) Ratio of 1 : 7 is not the same as ratio of 7 : 1. j) Ratio of 5 to 9 is written as 5/9 or ‘5 : 9’ and is read as ‘5 is to 9’. k) Symbol ‘:’ (colon) is used to express a ratio e.g. 2 : 3. l) To compare ratios, write them as fractions. One ratio is equal to other ratio if its fraction is equal to the fraction of other ratio. m) To find the ratio of two different units, first express them in the same units. For example, to find the ratio of 20cm and 1m, first convert meters into centimeters 1m x 100 = 100cm. Then, find the ratio. The ratio of 20cm and 100cm = 20cm/100cm = 1/5 = 1 : 5. -63. Step 2 in ratio Example 1: Reduce 36 : 72 to the simplest form. Solution: Given: Ratio 36 : 72. To find: Simplest form of ratio. HCF of 36 and 72 is 36. 36 : 72 = 36/72 (divide each term by HCF i.e. 36) = (36/36)/(72/36) (simplify) =½ =1:2 Answer: Ratio 36 : 72 in simplest form is 1 : 2. 4. Step 3 in ratio Example 2: Find the simplest form of ratio of 1.5kg to 500g. Solution: Given: 1.5kg to 600g. To find: Simplest form of ratio. Ratio of 1.5kg to 600g = 1.5kg/600g (convert kg to grams).** = (1.5 x 1000)g/600g. = 1500/600 (divide both terms by HCF i.e. 300). = 5/2. = 5 : 2. Answer: Required ratio is 5 : 2.

** The ratio is found between two numbers or quantities of the same kind and the same unit.

-75. Step 4 in ratio Example 3: Which ratio is greater 2: 3 or 5 : 7. Solution: Given ratios 2 : 3 and 5 : 7. To find: Which ratio is greater. First ratio 2 : 3 = 2/3. Second ratio 5 : 7 = 5/7. LCM of denominators 3 and 7 is 21. Multiply both ratios by 21. Therefore, First ratio = 2/3 x 21 (simplify). = 2 x 7. = 14. Second ratio = 5/7 x 21 (simplify). = 5 x 3. = 15. Since 15 > 14, Ratio 5 : 7 > 2 : 3 Answer: Ratio 5 : 7 is greater than ratio 2 : 3. 6. Step 5 in ratio Example 4: Are the ratios 3 to 4 and 6 : 8 equal? Solution: Given: Ratios 3 : 4 and 6 : 8 To find: Are they equal. Method I: First ratio 3 : 4 = ¾. Second ratio 6 : 8 = 6/8 (divide both terms by HCF i.e. 2). = 3/4 Each ratio is 3/4. Therefore, the ratios are equal.

Answer: The ratios are equal. Method II: The ratios are equal if 3/4 = 6/8. These are equal if their cross products are equal. Therefore, 3 × 8 = 4 × 6. 24 = 24. Since both of these products are equal to 24, the ratios are equal. Answer: The ratios are equal.

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7. Step 6 in ratio Example 5: Simplify the ratio: 2/3 : 4/7 : 3. Solution: Given: 2/3 : 4/7 : 3. To find simplest form Ratio 2/3 : 4/7 : 3 = 2/3 : 4/7 : 3/1**. LCM of denominators 3, 7, and 1 is 21. Multiply each term of the given ratio by 21. Therefore, Ratio 2/3 : 4/7 : 3/1 = (2/3 x 21) : (4/7 x 21) : (3/1 x 21). = (2 x 7) : (4 x 3) : (3 x 21) = 14 : 12 : 63 Answer: Simplified ratio is 14 : 12 : 63. **While solving fractions you should write whole numbers in fraction form dividing it by 1 e. g. 3 (whole number) = 3/1 (fraction). Note: If the terms are in fractions, find the LCM of the denominators and multiply given terms with it. 8. Step 7 in ratio

Ratio Example 6: Joliet has a bag with 8 mangoes, 14 apples, 12 oranges and 1 pine-apple. What is the ratio of mangoes to oranges? Solution: Step 1: Write what is given and what is to be found. Given: Mangoes 8, apples 14, oranges 12 and pineapple 1. To find: Ratio between mangoes and oranges.

Step 2: Write the expression. (Hint: Write the numerator equal to the first quantity and the denominator equal to the second quantity. In this case first quantity is mangoes). Ratio of mangoes to oranges = Number of mangoes/Number of oranges. Step 3: Substitute the values of mangoes and oranges. Ratio of mangoes to oranges = 8/12.

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Step 4: Simplify the expression. (Hint: Divide both numerator and denominator by HCF to obtain simplest form). Ratio of mangoes to oranges = 8/12 (divide both terms by HCF i.e. 4).** = 2/3. = 2 : 3. Step 5: Write the answer. Ratio of mangoes to oranges is 2 : 3. (** HCF of 8 and 12 is 4) Note: The answer can be written as: Ratio is 2 : 3 or 2/3 or 2 to 3.

-109. Step 8 in ratio Example 7: The ratio of the rose flowers and sunflowers is 5 : 10. If the number of rose flowers is 40, find the number of sunflowers.

Solution: Given: Ratio of the rose flowers and sunflowers 5 : 10, no of rose flowers 40. To find: Number of sun flowers. Let number of sunflowers is ‘a’. Method I: Ratio 5 : 10 = 5/10. Ratio of the rose flowers and sunflowers = Number of rose flowers/number of sunflowers. Substitute the values of ratio, rose flowers and sunflowers. 5/10 = 40/a (cross multiply). 5 x a = 40 x 10. 5 x a = 400 (divide both sides by HCF i.e. 5). a = 80. Answer: Number of sun flowers is 80. Method II: Ratio of the rose flowers and sunflowers = Number of rose flowers/number of sunflowers Substitute the values of ratio, rose flowers. 5/10 = 40/? 1/2 = 40/? 1/2 = 40/80 Answer: Number of sunflowers 80. 10. Step 9 in ratio Example 8: Divide $5000 between Mary and Helen in the ratio 2 : 3. Solution: Given: Divide $5000 between Mary and Helen in the ratio 2 : 3. To find: Amount got by Mary and Helen respectively. Total parts = 2 + 3 = 5. Mary gets two parts and Helen gets 3 parts. Therefore, Mary gets 2 out of 5 parts or 2/5 and Helen gets 3 out of 5 parts or 3/5. Mary gets 2/5 of $5000 = 2/5 x 5000. = $2000. Helen gets 3/5 of $5000 = 3/5 x 5000. = $3000. Answer: Mary gets $2,000 and Helen $3000.

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11. Step 10 in ratio Example 9: There are 15 parrots and 8 ducks in a park. (a) What is the ratio of parrots to ducks in all three formats/forms? (b) What is the ratio of ducks to parrots in all three formats/forms? Solution: Given: Parrots 15, and ducks 8.

To find (a) Ratio of parrots to ducks in all three formats/forms. (b) ratio of ducks to parrots in all three formats/forms. (a) Ratio of parrots to ducks = Number of parrots/Number of ducks = 15/8 Other two forms of ratio are 15 : 8 and 15 to 8. Answer: Three forms of ratio are 15/8, 15 : 8, and 15 to 8. (b) Ratio of ducks to parrots = Number of ducks/Number of parrots = 8/15 Other two forms of ratio are 8 : 15 and 8 to 15. Answer: Three forms of ratio are 8/15, 8 : 15, and 8 to 15. Note: In the above example, the number of parrots and ducks is same, but the order in which they were listed in (a) and (b) is different. In ratios, order is very important. 12. Step 11 in ratio Example 10: Find the ratio of the second quantity to the first quantity – 30 seconds to 1mi 15 seconds Solution: Given: 30 seconds and 1mi 15 seconds To find: Ratio of the second quantity to the first quantity. Ratio of the second quantity to the first quantity. = Second quantity/first quantity. = 1mi 15 second/30 seconds (convert to same units) = (1 x 60 + 15) seconds/30 seconds = 75/30 (divide both terms by HCF i.e. 15) = 5/2 =5:2 Answer: Required ratio is 5 : 2 -1213. Step 12 in ratio Example 11: The ratio of the angles of a triangle is 2 : 3 : 4. Find the measure of each angle. Solution: Given: Ratio of angles 2 : 3 : 4. To find: Measure of each angle. The measure of all the angles of a triangle is 180 degrees. Let the measure of angles be A, B and C Therefore, Measure of angles A + B + C = 180 degrees. Sum of the ratio of terms = 2 + 3 + 4 = 9

Therefore, Measure of Angle A = 2/9 of 180 degrees. = 2/9 x 180. = 2 x 20 = 40 degrees. Measure of Angle B = 3/9 of 180 degrees. = 3/9 x 180. = 3 x 20. = 60 degrees. Measure of Angle C = 4/9 of 180 degrees. = 4/9 x 180. = 4 x 20. = 80 degrees. Answer: The measure of angles A, B and C is 40, 60 and 80 degrees. Note: You can adopt this method to find the ages of son, daughter and father etc. 14. Step 13 in ratio Example 12: Tom has 108 marbles. He gives these marbles to his friends A, B and C in the ratio 1/2 : 1/3 : 1/4. Find the number of marbles received by A, B, and C. Solution: Given: Marbles 104 to be given to A, B and C in the ratio 1/2 : 1/3 : 1/4. To find: Number of marbles received by each. (Hint: Multiply the given ratios by LCM of their denominators). LCM of the denominators 2, 3 and 4 = 12. Therefore, 1/2 : 1/3 : 1/4 = (1/2 x 12) : (1/3 x 12) : (1/4 x 12) =6:4:3 Sum of the ratio terms = 6 + 4 + 3 = 13 Therefore, A gets 6/13 of 104 marbles

= 6/13 x 104 =6x8 = 48 marbles. B gets 4/13 of 104 marbles. = 4/13 x 104 =4x8 = 32 marbles. C gets 3/13 of 104 marbles. = 3/13 x 104 =3x8 = 24 marbles. Answer: A gets 48 marbles, B gets 32 marbles and C gets 24 marbles. (Check: 48 + 32 + 24 = 104)

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-1415. Step 15 Example 13: Two numbers are in the ratio 2 : 5 and their difference is 48. Find the numbers. Solution: Given ratio 2 : 5 of two numbers, their difference 48. To find: Numbers. Let the smaller number be 2a, the greater number will be 5a. Then, 5a – 2a = 48 (simplify). 3a = 48 (divide each side by 3). a = 16. Therefore, Smaller number = 2a (substitute value of a) = 2 x 16 (multiply) = 32 Greater number = 5a (substitute value of a) = 5 x16 (multiply) = 80 Answer: the numbers are 32 and 80. Check: 80 – 32 = 48. 16. Step 16 Example 14: Divide $217 into two parts such that the first one is 2/5 of the second. Solution: Given amount $217, one part is 2/5 of second part. To find; Amount of part one and two. Let the two parts be a and b Then, a = 2b/5 (divide each side by b) a/b = 2/5

Therefore, Ratio of part a and b is 2/5 or 2 : 5 Sum of the ratio terms = 2 + 5 = 7 Then, Part a is 2/7 of $217 = 2/7 x 217 (divide each side by 7) = 2 x 31 (multiply) = $62 Part b is 5/7 of $217 = 5/7 x 217 (divide each side by 7) = 5 x 31 (divide each side by 7) = $155 Answer: One part is $62 and second part is $155. Check: One part = 2/5 of the second part (given). = 2/5 x 155 = 2 x 31 = $62.

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Closer Based on the informations about ratio given, we knew that it was the important topic in mathematic. Truthly, it was the difficult topic for someone who did not learn it. So this assignment will help the readers to learn this topic theoretically. Someone can be experted in this topic if they learned very well. This was because, any topics in mathematic were difficult to learn if someone did not understand well especially sub-topics in additional mathematics. Mathematics was fun and easy subject to learn. Without this subject, our life became more uncomfortable. This was because, our daily life were related with mathematic especially in business management. We can see for the example at supermarket, shopping complex and many more, all of this places use mathematic’s application in any affairs. As the addition, ratio was the most interesting topic in mathematic compared to other topics. Ratio also can be applicated in daily life. A “ratio” is just a comparison between two different things. For instance, someone can look at a group of people, count noses, and refer to the “ratio of men to women” in the group. Suppose there are thirty-five people, fifteen of whom are men. Then the ratio of men to women is 15 to 20. As the conclusion, ratio was the important topic in mathematic. We must learn to understand well this topic, if not it will become the most difficult topic to us in mathematic. Lastly, we were very gratefulagain, because we had done this assignment successfully and joyfully. We hoped that, all the informations about ratio given, can add the knowledge all the readers in mathematic. We also hoped, all the readers will understand kindly about this topic, so that they can applicate in their life.

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CONTENTS (PAGES) INTRODUCTION

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RATIO >DEFINITION (4-5) >STEP 1 IN RATIO (6 ) >STEP 2 AND 3 IN RATIO (7 ) >STEP 4 AND 5 IN RATIO (8 ) >STEP 6 AND 7 IN RATIO (9-10) >STEP 8 AND 9 IN RATIO (11) >STEP 10 AND 11 IN RATIO (12) >STEP 12 AND 13 IN RATIO (13-14) >STEP 14 AND 15 IN RATIO (15) CLOSER

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The professional version of Equation Editor. Free trial. www.Dessci.com/MathType. Accessed on 5th of August 2009 2. Wonderful site for math

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A Maths programme from the UK to transform math teaching www.numicon.com. Accessed on 5th of August 2009 4. "Secret To Forex Riches?

I lost money hand over fist until I discovered this 1 Forex trick." ForexNittyGritty.com/HowIDidIt. Accessed on 5th of August 2009 ETY