Fractions 2

Dear all,

It has been awhile since the last update. We are now back to term 2 and before I proceed, here are a few updates and feedback of term 1.

Positives:

• Many of you did well for paper 1 and scored 30 over upon 40. Keep that up. Continue doing well for your paper 1. 
• I was glad to see a huge number of you turning up for the extra morning lesson :) 

Can be improved:

• Paper 2 is definitely a section many of you need to improve on. More practice is needed. Focus also on your 'Get me thinking' assessment book. 
• Concentration and 100% consistent effort. This aspect can be much better during this term. 

Geometry is also an area I find that you guys have not been able to excel in. Topics like area of square and perimeter of square and angles are past year topics you need to go back and revise again. 

Fraction 2:

• Read the problem sums carefully to find out what fraction is required. 
• Fraction out of a fraction --> fraction x fraction 
• Fraction out of a whole number --> fraction x whole number
• Whole number out of a whole number --> whole number 1 divide by whole number 2 

When we multiply fractions:

• Method 1: 
• Multiply numerator 1 and numerator 2 together 
• followed by denominator 1 x denominator 2 
• 2/3 x 3/4 = (2x3)/(3x4) = 6/12

• Method 2:
• Cross multiplying 
• Look at the numbers diagonal to each other (this will form a X)
• Find the two numbers' highest common multiple (if any) to simplify the numbers further
• Example: 3/4 x 4/6 (numerator 1 is 3. denominator 2 is 6. Both these numbers' highest common multiple is 3 so you can divide both numbers by 3) (Numerator 2 is 4 and denominator 1 is 4. Both these numbers' highest common multiple is 4 so I can divide both numbers by 4). 
• You will end up with the answer of 1/2
• Cross multiply is a good way to simplify your answer. 

• Method 3:
• Up-down simplification 
• Look at both sets of fractions first.
• You can simplify the fractions first. 
• 4/12 x 2/6 
• 4/12 can be simplified into 1/3
• 2/6 can be simplified into 1/3
• so 4/12 x 2/6 = 1/3 x 1/3 = 1/9

Topics to be tested for SA1:

1. All P1 - P4 work 
2. Whole numbers 1 and 2
3. Fractions 1 and 2
4. Ratio (Up to Word Problems 1)

Study hard. :)

Sincerely,

Mr Nelson Ong

Recap of topics learnt so far

Dear all,

As we move into the CA week, let us recap of what we have learnt thus far:

Whole Numbers

• We learnt about numbers up to a million.
• A million has six zeros. 1 000 000 (one million)
• Remember to read the number carefully and write the place value above each digit to be more careful and accurate when rounding off.
• in the number 8245, 5 is the ones, 4 is the tens, 2 is the hundreds and 8 is the thousands.
• When we round off, we always look at the number to the right of the digit. 
• When we round off 8245 to the nearest thousand, we circle 8 and underline 2 (the nearest digit to the right of the thousands place)
• 2 --> round it down.
• 8245 is approximately 8000. 
• 0-4 round it down!
• 5-9 round it up!
• Be sure when to use the equal and approximate sign.
• When we find the exact answer, we use the equal sign.
• When we are asked to round off or estimate, use the APPROXIMATE sign. 

Fractions

• The top number is the numerator and the bottom number is the denominator. 
• In the fraction 1/2, 1 is the numerator and 2 is denominator.
• When we add fractions, be sure to always look at the denominator first. 
• We need to change the denominator into the same number using the common multiple rule. 
• Then, we can proceed to add the fractions up.
• When we add fractions, we only add the numerator!!! The denominator is fixed!
• 1/2 + 1/3 = 3/6 + 2/6 = 5/6
• Improper fractions are fractions not simplified into their wholes and parts. Example: 7/3
• When we change 7/3 into mixed numbers, it becomes 2 whole and 1/3.
• If you are asked to simplify the fraction to its simple form, please make sure you find the highest common factor and divide both numerator and denominator. 
• 4/6 = 2/3 (highest common factor of 4 and 6 is 2) Divide the numerator and denominator by 2 each. 
• When we say that 2/9 -> 10, it is to mean that 2 units out of the total of 9 units is 10. so 2 units is 10, 1 unit is 5 and total units of 9 is 5 x 9 = 45.
• When we convert a fraction to a decimal, always convert the denominator to either 10, 100 or 1000.
• 1/2 = 5/10 = 0.5
• 1/8 = 125/1000 = 0.125
• 3/4 = 75/100 = 0.75
• In the decimal 0.125, 1 is in the tenths place, 2 is in the hundredths place and 5 is in the thousandths place.
• If you are asked to round off 0.125 to its nearest 1 decimal place (it refers to the tenths place), so we circle the number 1 and underline the number 2 (the digit nearest to the right). 2 --> round down. So, 0.125 when rounded off to the nearest 1 decimal place is approximately 0.1.
• Tenths (1 decimal place)
• Hundredths (2 decimal place)
• Thousandths (3 decimal place)

Other things to take note of:

• You must revise through your timeline.
• 1 h = 60min
• Know how to write your time in 24 hour format.
• 2400 = 12 am
• 1200 = 12pm
• 1300 = 1pm
• 0500 = 5am
• Know your units of measurement and conversion
• Area of square --> length x length 
• Area, we use square centimetres!!!
• All the lengths of a square is the same!
• If we are given an area of a square, to find the length, we take the square root of the area given. A same number x the same number = the area of a square.
• 2 x 2 = 4
• 3 x 3 = 6
• 5 x 5 = 25
• 6 x 6 = 36
• Perimeter of square --> length x 4
• Area of rectangle --> length x breadth
• Perimeter of rectangle --> 2 lengths + 2 breadths
• 1kg = 1000g
• 0.7kg = 0.7 x 1000 = 7/10 x 1000 = 700g
• 1m = 100cm
• 0.1m = 0.1 x 100 = 1/10 x 100 = 10cm

Go through your get me thinking book! Go through your file and finish up your corrections.

Homework:

• PTS Worksheet 5.

Remember to read carefully and highlight the key words. Look at the units being asked for in the final answer. The key here is to practise each day and go through questions in your textbook and worksheets again. Don't stress yourself out and if you are unsure of the steps of a question, move on first and then come back to revisit the question again at the end. Do not be too reliant on the calculator. You still need your mental calculation and to work out your long division steps too. I have realised many of you tend to be too dependent on your calculator and have forgotten how to do long division. This is especially important for paper 1 booklet A and B. You can do it. Just cut down on your careless mistakes. 

The target here is to ace your paper 1 and then worry more about your paper 2. 

Sincerely,

Mr Nelson Ong

Fractions and Conversion of Units

Dear all,

As promised, here is a list of some conversion of units which is an alarming problem when I was marking through your work this week. Some of you have forgotten about the conversion of units and this is important.

1kg = 1000g

1m = 100cm
1km = 1000m

1h = 60 min
1 min = 60 sec

Area of square -> side x side 
All sides of a square are similar.
Perimeter of a square -> 4 x one side

1 litre = 1000ml

Area of rectangle -> length x breadth
Perimeter of rectangle -> length + length + breadth + breadth

Recap on Fractions:

• We did addition and subtraction of mixed numbers
• When we add two mixed numbers, we first look at the denominators. If they are the same, we can proceed to add the fractions up. If they are not the same, we have to convert the denominators into a common same number first.
• in 1 whole 1/3 + 2 wholes 1/3, we add the wholes up first and then the fractions to get 3 wholes 2/3
• in 2 wholes 1/6 + 1 whole 1/3, we need to change the denominators into a same number first before addition takes place. 1 whole 1/3 = 1 whole 2/6. 
• So, 2 wholes 1/6 + 1 whole 2/6 = 3 wholes 3/6 (This can be simplified into 3 wholes 1/2)

• For subtraction of mixed numbers, if the numerator of the first number is bigger than the second number, then subtraction of mixed numbers becomes much easier.
• E,g 5/6 - 1/3 = 5/6 - 2/6 (Change 1/3 = 2/6)
• You will get an answer of 3/6
• However, if the numerator of the first fraction is smaller than the second fraction, then we have to change both mixed numbers into improper fractions.
• E.g 1 whole 1/6 - 2/3 = 1 whole 1/6 - 4/6 (2/3 = 4/6)
• 1 whole 1/6 = 6/6 + 1/6 = 7/6
• So, we take 7/6 - 4/6 = 3/6 (final answer)

Homework:

• Revision Practice Paper 2 (By Monday)
• Corrections for PTS Worksheet 1 and 2 if you have not passed up
• Fractions (1) for those who have not passed up

Sincerely,

Mr Nelson Ong

Division of Fractions

Dear all,

For today, we concentrated on division of fractions. When we divide a number, we can also express the answer as a fraction. We also learn about improper fractions and mixed numbers.

8 ÷ 3 = 8/3

8/3 is an improper fraction 
Improper fractions are fractions in which the numerator (top number) is greater than the denominator (lower number)
Improper fractions are fractions not expressed in whole and a fraction.
This is an important term you need to know as exam questions might ask you to express a mixed number as an improper fraction

8/3 is also 3/3 + 3/3 + 2/3. When you add up the numerators, they give you 8.
3/3 = 1 whole
In this case, 8/3 = 2 wholes + 2/3 (This is a mixed number)
Mixed numbers are fractions expressed in wholes and fractions.

Sincerely,
Mr Nelson Ong

Fractions 1

Dear all,

We would have completed Word Problems 2 and have started on Fractions Today.

Concepts to remember:

• Denominator refers to the number below in a fraction. (number of equal parts being divided of a whole)
• Numerator refers to the number above in a fraction. (number of parts used)
• Like fractions refer to a set of fractions with the same denominator like 1/2 + 1/2
• When we add fractions, we have to first look at the denominator. If the fractions have the same denominator, then we can proceed to adding them up. If not, we have to change the denominators to a same number first. When we add fractions, we only add the NUMERATOR. We do not add the denominator. Always remember that. 
• 1/3 + 1/3 = 2/3 (We only add 1 to 1 because they are the numerators) The denominator remains the same because the number of equal parts of a whole always remain the same. 
• For example, I cut a pizza into 3 equal parts. Tom ate one slice and I ate one slice. How many slices were eaten. 1 + 1 = 2. The total number of equal parts will always be 3 because the pizza is cut into 3 slices. So, this '3' represents the denominator. Tom ate 1 part so this becomes the numerator. The fraction of the pizza that Tom and I ate will be 1/3 + 1/3 = 2/3
• Unlike fractions refer to fractions in which the denominators are not the same. Therefore, before we can add them up, we need to change the denominator into a same number first through your common multiple concept. 
• In 1/3 + 2/6 (Since the denominators are not the same), we first have to convert the fractions to like fractions first. 1/3 = 2/6. Adding them up now, 1/3 + 2/6 = 2/6 + 2/6 = 4/6
• 4/6 can be simplified into 2/3. 
• You can read this website for more information 
• Click here!

Homework for the weekend:

Maths Workbook Fractions(1) Pages 65 - 68

Sincerely,

Mr Nelson Ong

Orders of Operations

Dear all,

There is a need to recap on orders of operations again with you. After marking through your work, I have come to realise that a handful of you are still clueless about what step to work out first. To summarise,

• Subtractions and Additions are of equal importance.
• Multiplication and Division are of equal importance.
• Multiplication and Division ARE MORE IMPORTANT than Subtraction and Additions.

Always work from left to right unless you have special conditions in the number statement. 

Example 1

2 + 4 - 5 

We identify the symbols first!

+ and - 

Both are of equal importance.

We work from left to right

2 + 4 - 5

= 6 - 5

= 1

Example 2

2 x 2 ÷ 4

We identify the symbols first!

x and ÷

Both are of equal importance.

We work from left to right

2 x 2 ÷ 4

= 4 ÷ 4

= 1

Example 3

5 - 3 x 4 ÷ 6

We identify the symbols first!

- and x and ÷

x and ÷ are MORE IMPORTANT than - 

We work on x and ÷ first, from left to right.

5 - 3 x 4 ÷ 6

= 5 - 12 ÷ 6

= 5 - 2 

= 3

Example 4

(4-2) x 6 + 4

Identify the symbols first!

( - ) and x and +

( ) are the most important, followed by x and then +.

Work from left to right.

(4-2) x 6 + 4

= 2 x 6 + 4

= 12 + 4

= 16

Homework:

Word Problems 2 Pages 45, 46, 47 and 49.

Sincerely,

Mr Nelson Ong

Orders of Operations

Dear all,

We have arrived at your first anticipated difficult topic and that is Orders of Operations. You will need to constantly practise on this topic to help you remember well. Lets' recap the rules.

Concepts:
1. When there is only subtraction and addition in a number equation, we work from LEFT to RIGHT. Always underline the first step (part of the number equation) you should work out first. 

8 - 2 + 6
We work out from left to right
We underline 8 - 2 first.
8 - 2 + 6 =
6 + 6 = 12

2. When there is only multiplication and division in a number equation, we work from LEFT to RIGHT. Once again, underline the first step (part of the number equation) you should work out first.

8 x 2 ÷ 4
We work out from left to right
We underline 8 x 2 first.
8 x 2 ÷ 4 =
16 ÷ 4 = 4

3. When there are addition/subtraction and multiplication/division in a number equation, we work from LEFT to RIGHT BUT we need to work out the MULTIPLICATION/DIVISION portion FIRST! Underline the part you need to work out first. 

8 - 16 ÷ 4 x 2
We underline 16 ÷ 4 first.
8 - 16 ÷ 4 x 2 =
8 - 4 x 2 =
Next, since multiplication comes first, we underline the multiplication portion which is 4 x 2.
8 - 4 x 2
8 - 8 = 0

4. When there are addition/subtraction/multiplication/division but there are BRACKETS in the number equation, we work out from LEFT to RIGHT but we WORK ON THE BRACKETS FIRST! Always underline the portions (brackets portion) you need to work out first. 

2 x (8 - 4 + 2)
We underline (8 - 4 + 2) as this is the first step we need to do.
2 x (8 - 4 + 2) =
2 x 6 = 12

Homework: 

• Worksheet on Orders of Operations

Have a blessed Chinese New Year everyone (pupils and parents)! Work hard and play hard. In 4 weeks' time, it will be your CA. Topics to be tested included what you have covered in P1 - 4 so remember to revise through too. We will cover up to fractions (1). We are on the way to completing Whole Numbers (2), leaving with us with only Fractions (1). Practice makes perfect. Enjoy yourselves this festive season.

Sincerely,
Mr Nelson Ong