Is it no secret that most students do not do well in fractions. Indeed, as one of the topics in PSLE mathematics, fractions is one of the most basic topics to be mastered. There are many fundamental concepts to be grasped in order to master fractions in PSLE. Often times students neglect this topic, only to realise that they are unable to do the question in an exam paper. Is fractions really that tough? Is it impossible for students to understand fractions? The answer is a no. Fractions, when broken down to its fundamentals, is indeed very easy to master. Hence this article aims to dissect the different types of fraction questions and tackle them. Step by step guidance with full explanations will be given. This will ensure high mastery of the topic, equipping students to attempt any fraction questions that come along their way.
PSLE Fractions Problems And How To Solve Them
When it comes to PSLE, the questions that comes out are more or less testing the same few concepts that students have been taught in P5 and P6. However, it might seem abstract to the students, and hence they have lesser motivation to complete the questions on time.
In mastering PSLE fractions in just 5 minutes, we will show to you, in simple format, on how you can possibly master PSLE fractions in the shortest time ever.
Basic Fractions Operations
The basic operations in fractions are division, multiplication, addition and subtraction. There are rules to follow in these operations. If you are wondering how to teach your child fractions, the first step is to master the following rules:
- Division: A ÷ b/c = A x c/b (flipping the fraction to change division to multiplication sign)
- Multiplication: a/b x c/d = ac/bd
- Addition/Subtraction: ensure that the denominator is the same before performing the addition/subtraction operation. Form common denominator for both fractions.
a/b + c/d
Common denominator: find the lowest common multiple of ‘b’ and ‘d’.
i.e. the smallest number that can be divided by both b and d. If ‘b’ must be multiplied by 2 to arrive at common denominator, then ‘a’ must be multiplied by 2 too.
Different types of fraction questions
The main skills required in mastering PSLE fractions questions are as follows
Involving division of a whole number by a proper fraction
This concept is one of the most fundamental concepts in fractions. Most students get this wrong, simply because of conceptual errors. Indeed, if this concept is not understood by the child, the whole idea of fractions will be lost to the child. But is this easy to understand? Yes! Here is an example of a question.
Example: Jamie wants to help her mother with thread cutting. What is the greatest number of pieces of thread, each measuring 3/7 m, that can be cut from a ball of thread which is 14 m long?
To find the greatest number of thread needed, we need to divide 14 by 3/7. Referring to the aforementioned division of fractions, flip the fraction to become 7/3. Note that we keep the 1st number intact.
14 ÷ 3/7 = 14 x 7/3 = 98/3 = 32 ⅔
This means that 32 ⅔ pieces can be cut from a ball of thread. Therefore, maximum number of whole pieces of thread that can be cut from the ball of thread is 32. Students often get this wrong, as they missed out on the keyword “greatest number” in the question.
Involving division of a proper fraction by a proper fraction
This skill is one of the most fundamental skill needed to solve PSLE Fraction questions. Indeed, most of the PSLE fraction questions requires this skill in order to proceed to the next section of the question. This means that if the student is unable to solve the first part, they will be unable to proceed and solve the 2nd part of the question correctly. One example of a question requiring the above concept is as follows.
Example: Simon helped fill water bottles for athletes during the school sports meeting. The capacity of a bottle was 6/13 litres. What is the smallest number of such bottles he needed to hold 3/4 litres of water?
To find the number of bottles needed, we need to divide 3/4 by 6/13. Referring to the aforementioned division of fractions, flip the fraction to become 13/6.
3/4 ÷ 6/13 = 3/4 x 13/6 = 13/8 = 1 ⅝
1 bottle is not enough to fill all the water, therefore the smallest number of bottles is 2 (i.e. round up 1 ⅝ to 2.)
Here is another example of a variation of the above question.
Example: Jason wants to put up street lights along one side of a road for the benefit of the community. The road is 4/7 km long. He puts up the lights at 2/35 km apart. There is a street light at each end of the road. How many street lights does Jason need?
Similar to the previous skill, the first step is to divide 4/7 by 2/35.
4/7 ÷ 2/35 = 4/7 x 35/2 = 10
This means that there are 10 spaces between the first and last street light. Since the question is asking for the number of street lights, and there are street lights at the start and end, total number of street lights = 10 + 1 = 11.
Involving subtraction and division of a proper fraction by a proper fraction
Some questions are not as straight forward as division only. There are questions that involves two modes of operation. Here is an example of a PSLE styled fraction question.
Example: Dave had 3/4 litres of paint. He used 1/2 litres to paint a chair for his grandparents. Then he poured the remaining paint into containers of capacity 5/32 litres each. What is the smallest number of containers that he needed?
3/4 – 1/2 = 1/4
1/4 ÷ 5/32 = 1/4 x 32/5 = 1 ⅗
Rounding up 1 ⅗ to the bigger whole number, he needs at least 2 containers to store the remaining paint.
Involving division of a proper fraction by a proper fraction and fraction subtraction
Example: Rebecca helped her mother make 5/6 litres of lemonade to treat their guests. She poured the lemonade into cups. Each cup had a capacity of 1/4 litres. She filled some cups completely except for 1 cup. How much lemonade was in the cup that was not completely filled? (Express fraction in simplest form)
5/6 ÷ 1/4 = 5/6 x 4 = 3 ⅓
This means she filled up 3 ⅓ cups with lemonade: 3 cups are full, while the 4th cup is partially filled.
3 x 1/4 = 3/4 (total amount in 3 cups)
5/6 – 3/4 = 10/12 – 9/12 = 1/12
There was 1/12 litres of lemonade in the cup that was not completely filled.
Breakdown The Question And Identify Strategy To Solve
Based on the above examples, it can be clearly seen that the four operations of fractions are fundamental to solving any fraction question. The next most important skill is understanding of the question. Question analysis is crucial in helping your child ace any fractions question.
Make sure to identify the exact item or quantity to which the fraction refers to. Then perform the necessary operations to obtain the answer. Let’s go through the steps in question analysis, using the a sample question for skill e.
Julie bought some chocolate milk in the supermarket. After drinking 3/4 of it, she poured the remaining milk into bottles of 1/8 ℓ each. 3 bottles were filled up exactly. How much chocolate milk did she buy at first? (Express your answer as a mixed number in simplest form)
Identify the following:
Amount that Julie drank: 3/4 of the total
Amount remaining: poured into 3 bottles, each having capacity of 1/8 litres.
Since Julie drank 3/4 of the total amount, it means that the remaining 1/4 was poured into the bottles, and have a volume of 3/8 litres. Calculate the remaining amount.
In order to find the total amount of chocolate milk she bought, multiply the remaining amount by 4.
This is an example of how a question can be broken down, extracting the important information and eventually get the answer.
Conclusion: fractions can be mastered with practice
Having addressed all the skills and techniques required in tackling fraction questions, you may think that you are fully equipped to help your child master these questions. However, it is of great importance that your child does many practice questions on fractions, in order to fully grasps the concepts mentioned above.