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A quick update !! I created this post to thank everyone for their support of MyMathsJournal and some quick updates.
You would have wondered - Why do I bother typing all these appreciation to everyone, right? Without the people listed above, MyMathsJournal would not have come to today. All my determination and strength had come from you guys, and that is why I put in a lot of effort to type the Maths Concepts out. I may be inactive at times, but the people I've listed above still show strong support. Thank you people! People have also be wondering, why do I even bother to thank the people who just simply tag at the tagboard ? The tagboard is something very important to MMJ. MMJ can know how many times do people often visit the blog and this also decides if MMJ should keep running. If the tagboard is inactive, I wouldn't even bother to type all the maths concept out and simply quit. Spam messages will be immediately deleted from the tagboard, if found. Now for some quick updates.
That's all (: Maths;; Simultaneuous Another lengthy concept D: I didn't post yesterday so I thought I'd post a difficult-to-understand-concept today. (: New blogskin, by MMJ. So here it goes, with a simple example :D
In the similtaneuous world, we always have to make equations (also known as number statements) to make solving easier. We need to at least have 2 of these equations to solve the question. However, make as many equations as you can I choose out the 2 most simplest ones. Look at the below equations I formed from the question: 1. 5/5 [P] + 3/3 [B] -> 80 2. 3/5 [P] + 1/3 [B] -> 36 3. 2/5 [P] + 2/3 [B] -> 44 Lemme explain how all the above equations are formed. For [1], it is mentioned that 80 pears and bananas at first. So, all of the pears and bananas make up to 80. For [2], it is mentioned that when 2/5 of the pears and 2/3 of the bananas were eaten, there were 36 of these fruits left. So, it is obvious that 3/5 of the pears and 1/3 of the bananas make up to 36. 3/5 of the pears and 1/3 of the bananas refers to the amount of fruits that were left. For [3], when we take the total[80] minus away the number of fruits left[36], we can find the number of fruits that were taken away[44]. Thus, 44 is equivalant to 2/5 of the pears and 2/3 of the bananas. Next, we choose which 2 equations to choose. I choose [1] and [2]. Any of the above 2 equations is acceptable. Keep this in mind - What is the question asking for? How many pears were there in the basket at first? They are looking for pears, not bananas. Thus, we have to make the OTHER object, which is the banana, THE SAME. Continue reading to see what I mean. 5/5 [P] + 3/3 [B] -> 80 3/5 [P] + 1/3 [B] -> 36 9/5 [P] + 3/3 [B] -> 36 x 3 = 108. Look at the 2nd equation. There are 1/3[B]. So, we make the bananas in the first and second equation the same. Thus, I multiply the 2nd equation numbers [3/5], [1/3] and [36] by 3, to get my third equation. (The one in bold) The purpose of making the other object the same is to totally cancel it. What I mean is... <9/5 [P] + 3/3 [B] -> 108 5/5 [P] + 3/3 [B] -> 80 4/5 [P] -> 108 - 80 = 28 How do I know these? Simple - Since we used the second equation to make the same as the first one, we take the first one to compare. Notice that they have a similar item - 3/3 [B]. Then, when we minus, we will cancel out all the stuff that are same. Look.. 9/5 [P] + 3/3 [B] -> 108 5/5 [P] + 3/3 [B] -> 80 We minus them together... 9/5 [P] + 5/5 [P] + 9/5 [P] - 5/5 [P] -> 108 -80 4/5 [P] -> 28 Since we know that 4/5 [P] is 28, we find 5/5 [P]. 4/5 [P] -> 28 1/5 [P] -> 28 / 4 = 7 5/5 [P] -> 7 x 5 = 35
Maths;; Difference remains the same Test Yesh, it's test time again. Yay? I have no participants in all of my tests leh! -Feels negleted- Come on people, just try lar, it won't hurt a little bit. Also test your understanding in that concept mar. D: Only 5 questions. Calcuators are allowed. Question 1: Max is 11 years old now. His father is 43 years old now. In how many years' time will his father be 3 times as old as Max? Question 2: Tank A had 890 litres of water. Tank B had 170 litres of water. When an equal amount of water was added in both tanks, Tank A had3 times as much water as Tank B. How much water was added to each of the tanks? Question 3: Old MacDonald had a total of 156 chickens and pigs in the ratio of 7:6. After he had sold an equal number of chickens and pigs, the number of chickens and pigs left was in the ratio of 7:3. How many animals did he sell altogether? Question 4: Sam had a total of 240 red beads and blue beads in the ratio of 5:3. After he gave away and equal amount of each type of bead, the number of red bead and blue beads left was in the ratio of 5:2. How many beads did he give away? Question 5: May had 850 stamps and Lynn had 70 stamps. Mr Lim gave each of them an equal number of stamps. As a result, the ratio of May's stamps to Lynn's stamps is 5:1. How many stamps must May give to Lynn so that they will have the same number of stamps? Done? Submit your answers here! Maths;; Remainder Concept Remainder concept is widely used in setting questions, and it may be quite confusing is there are too many remainders. A good method to solve these kind of questions is by using the model, but many have seen so much of these questions that they don't even need to use the model anymore. The keywords in the Remainder Concept questions are ... of the remainder. This means that the whole is not the total of the whole thing, but the whole represents the remainder. Take note that 'of' represents times. (Multiply). Let's take a look at an example below:
Now, let's draw a model to see what everything means. :D
So, it is obvious that 15 is equal to 5 units. We have to find 1 unit. 15 / 5 = 3 Each unit is 3. The question asks: How many red markers were there? Red markers is 3 units, so we find 3 units. 3 x 3 = 9 Simple right? :D Maths;; External Transfer Test ========================= Yesh it's the test again. I figured out that maybe each concept I type, there will be a test. Do it if you have the time (: All questions are set by yours truly, please do not copy >< All marks and participants will be reflected at the Wall of Fame. Once again, grab a pencil and paper, GO GO GO! Calculators are allowed. ========================= Question 1: The number of chicken eggs to the number of duck eggs Farmer Brown had at first was 3:1. After buying 36 more chicken eggs and selling a dozen duckeggs, ratio changed to 5:1. How many duck eggs did Farmer Brown had left? ========================= Question 2: Carol had 1/4 as much red pens as blue pens. When she gave away 9 of her red pens and 11 of her blue pens, the ratio of red pens is to blue pens is 1:5. How many blue pens did Carol had at first? ========================= Question 3: James's stamps were 20% of Jason's stamps. When James recieved a dozen more stamps while Jason have away 10 of his stamps, the ratio of James's stamps is to Jason's stamps became 4:5. How many stamps did Jason had at first? ========================= Question 4: Rachel had blue balloons and red balloons in the ratio of 2:7. She gave 15 red balloons away and bought another 15 balloons. Then she shound out that she had an equal number of red balloons and blue balloons. How many blue balloons did she have at first? ========================= Question 5: A box contained some green and red markers in the ratio of 7:2. Saadiah removed 28 green markers and put naother 16 red markers into the box. How many green markers were there in the box at first? ========================= -End of test- Submit your answers here!
Maths;; Difference remains the same This concept applies to a lot of stuff. It is just if you can see it or not.
Now let's look at the below example for AGE:
When we have an age question, note that when some one is older by one year, the other person also grows old by 1 year. In this case, for example, 2 years later, Aminah's mother will be 40 years old whereas Aminah will be 10 years old. When the same number increase/decreases, the difference remains the same. Thus, now we have to find the difference between Aminah's mother and Aminah herself. 38 - 8 = 30 Then we draw a model to explain the relationship between Aminah and her mother's age.
Now, it is obvious that 2 units is 30. (3units - 1 unit = 2 units) Thus, find 1 unit. 30 / 2 = 15 You can either choose Aminah or Aminah's mother to compare. I chose Aminah because it is easier. We have to find the grey shaded part (indicated in the model). So, we take 15-8, 8 comes from the age at first. 15 - 8 = 7 But wait, want to check if your answer is correct? Well then, let's take Aminah's mother model to compare. Since 1 unit is 15, we find 3 units. 15 x 3 = 45 Then we minus the age she had at first again, which is 38. 45 - 38 = 7 So, it is absolutely correct that the final answer is 7. Maths;; Before and After Concept Test ============================================= Read the post of Before and After Concept? If you had not, then go to contents and click on before and after concept. If you have, then great! Test your understanding! No worries, only 5 questions. ^^ Each value of 1 mark, no method marks. {Lazy} Ready for the challenge, get a piece of paper and pencil and OFF YOU GO!. Calculators are allowed ============================================= Question 1: Nicole and Jolin had an equal amount of money each. After Nicole spent $65 and Jolin spent $14, the ratio of Nicole's money to Jolin's money was 2:5. How much money did each girl have at first? ============================================= Question 2: Ben and Frank had an amount of marbles in the ratio of 1:2. After Frank gave away $10 and Ben received $15, the ratio changed to 2:5. How much did Frank had at first? ============================================= Question 3: Sarah's stamps was 4/5 of Sam's stamps. If Sarah gives away 6 of her stamps while Sam gives away 10 of his stamps, they will have a equal amount of stamps. How much stamp did Sarah have? ============================================= Question 4: Sophia and Yuki had an equal amount of hairclips at first. Whn Sophia spoiled 3 of her hairclips while Yuki bought another 12, the ratio of Sophia's hairclips to Yuki's hairclips became 3:4. How much hairclips did each of them had at first? ============================================= Question 5: Adam, Bobby and Chris had an equal amount of action figures at first. When Adam broke 7 of his action figures and Bobby broke 5 of his, their ratio of action figures became 4:5:7. How many action figures did Chris have now? ============================================= Got your answers, how to submit then? Simply click here and good luck!
Maths;; External Transfer Also known as Everything Change. This concept is pretty useful, it can be used in almost all Maths questions, as long as there is at first, the change, and the final. It also can be used in Before-After concept and differences remain the same concept. (: Now, let's look at the below example:
First of all, we have to draw out a simple table to show the relationship between Brand A and B.
The name we use in the initial is parts whereas the name in final used is units, so that we won't confuse ourselves. Next step, we make the Final units in Brand A and B the same. So, in A, 4 x3 and in B, 3 x 4. Also, do this to the rest of the stuff. (Initial and change)   Now you should able to see the light since the final units are the same. If not, you can draw out a model to help yourself to see clearer of what is happening.
You should able to see that 1 part = 48-40. 48-40=8 (1 part) Now the question is asking for: How many Brand B laptops did the store had at first? Thus, we look at what we have at first in our FIRST table, which is 5 parts. We CANNOT look at the 2nd table. Remember ar.. So, we look for 5 parts. 8 x 5 = 40 Maths;; Before And After Concept This concept is relatively easy - as long as you pick up the technique of drawing models. I have noticed that quite a number of pupils from our class don't really like to draw models, especially the weaker ones, but ratio method is also acceptable. But, in this post, I'm only going to demostrate the model method. Model Method The main focus is to draw our case 2 model first, followed by case 1. Let's take an example below. Salleh's money was three Case 1 is in blue while case 2 is in red. Let's draw the model for Case 1 first.  The grey shaded part represents 1 unit. As Salleh has 3 and a half units while her brother has 1 unit, I decided to cut up each unit into 2 so that all of the units in the above model are equal. Now, Salleh has 7 units while her brother has 2 units.Now, from our first model, we bring it down and draw the model for Case 1.  Let's call each unit in case one as parts. Now, you can see that 1 unit (case2) is equals to 2 parts plus $90 dollars. Stuck ? That's the problem! We drew Case 1 first. Hehe. Now let's start back to the top, this time, Case 2 first.  Once again, the shaded part represents one unit. Take note that instead of adding the moeny, we remove, because we are working backwards. Now, we move on to Case 1 ^^. But first of all, how are we going to deal with 3 1/2 units? Well, we multiply 3 1/2 by 2, which is also 7. And, not forgetting to multiply 1 by 2, which equals to 2. Be fair mar! Finally, Salleh has 7 units while her brother has 2.
In case 1, the shaded parts represents that the unit has been removed ;) The 7 units and 2 units are now changed to parts. Now, I want to divide the 7 parts by 2, because Salleh has at first 2 units and I want to find how many parts are there in 1 unit. So, in order to divide without any remainder, we multiply 7 by 2 and 2(brother) by 2 too. So, Salleh has 14 units while her brother has 4. This part is utterly confusing. Dijested ther information already? Now let's continue. Now, since 2 units (Salleh) is equals to 14 parts plus $30, we divide 14 and 30 by 2 in order to find what is in 1 unit. 14 / 2 = 7 (Parts) $30 / 2 = $15 Thus, we know that one unit consists of 7 parts and $15. But, remember that we multpied by 2 for all the parts and money for Salleh, we do not have to divide by 2 for him as he already have 1 unit at first. Finally, for Salleh's case, 1 unit is equals to 7parts + $15 while for her brothers case, 1 unit is equals to 2parts + $90. Saw something? Yes! But if you didn't, here is a model to show what exactly happens. This is a little like simultaneous.  So we know that 7 parts - 2 parts = $90 - $15. The answer is 5 parts = $75. Now we find 1 part, which is $75 divided by 5, and the answer is $15. The question is: How much did Salleh had at first? This is referring to Case 1. And the total parts for Salleh in Case 1 is 14. 14 x $15 = $350 |
