TheMathBooklets: Order of Operations

Showing posts with label Order of Operations. Show all posts

Wednesday, 25 March 2020

S3: Radian measure of angle

DEGREE AND RADIAN

Both degree and radian is a measure of angle.

Radian is defined as the angle from the centre of a circle which intercepts an arc equal in length to the radius of the circle.

360^o = 2π rad

=> 1^o = 2π rad / 360^o

2π rad = 360^o

=> 1 rad = 360^o / 2π

Converting between Degree and Radian

360^o = 2π rad

π rad = 180^o

Example

What is the value of 240^o in rad?

360^o = 2π rad

240^o = 2π rad x 240^o

360^o

= 4π/3 rad

Example

What is the value of 3 radian in degree?

2π rad = 360^o

1 rad = 360^o / 2π

3 rad = 360^o x 3 / 2π

= 171.81^o

	Degree	Radian
	1^o =π rad 180	1 rad = 180^o π
One Circle	360	2πrad
Circumference	2πr	2πr
Arc(S)	θ x 2πr 360	rθ
Area of circle	πr²	πr²
Area(segment)	θ x πr² 360	1 r² 2

Monday, 20 January 2020

N1-G123 Numbers and Orders of Operations

Recap

1. Positive number are numbers greater than 0

Example: 1, 50, 1238

2. Negative numbers are less than 0

Example: -1 , -85, -454

3. Zero 0 is neither positive or negative

The four number operations are

Symbol. Some Words/phrases

+ add, sum, plus, total, more than, increased by

- subtract, difference, minus,less than, decreased

x multiply, product, times

/, ÷ divide, quotient

Also,

1. When there is no sign ’attach’ to a number => the number is positive

2 + 3 = 5;

2, 3 and 5 are all positive numbers

2. The sign + , - ‘belongs’ to the number on the right

-2 (negative 2)

3. The sign + , - is also add and minus

* NEGATIVE number is different from – MINUS OR SUBTRACT

5 + (-3) = 2 is positive 5 add negative 3

5 – 3 = 2 is positive 5 minus positive 3

5 + (-3) = 5 - 3

<< Know the difference of the '-' Negative number and Minus Subtract >>

5 - 3 = 5 + (-3) = -3 + 5 = 2

Addition

(1) (+) + (+) a + b = b + a

8 + 5 = 5 + 8 = 13

(2) (+) + (-) a + (-b) = a – b

8 + (-5) = 8 – 5 = 3

(3) (-) + (+) -a + b = b – a

-8 + 5 = 5 – 8 = -3

(4) (-) + (-) -a + (-b) = -a – b

-8 + (-5)= -8 – 5 = -13

Subtraction

(1) (+) – (+) a – (+b) = a – b

8 – (+5) = 8 – 5 = 3

(2) (+) – (-) a – (-b) = a + b

8 – (-5) = 8 + 5 = 13

(3) (-) – (+) -a – (+b) = -a - b

-8 – 5 = -13 [ -(8 + 5) = -13]

(4) (-) – (-) -a – (-b) = -a + b = b – a

-8 – (-5) = -8 + 5 = -3 [-5 + 8 = -3]

Multiplication

(1) (+) x (+) a x b = ab

6 x 5 = 30

(2) (+) x (-) +a x -b = -ab

6 x -5 = -30

(3) (-) x (+) -a x +b = -ab

-6 x 5 = -30

(4) (-) x (-) -a x -b = +ab

-6 x -5 = 30

Division

(1) (+) x (+) a ÷ +b = a/b

6 ÷ 2 = 3

(2) (+) x (-) +a ÷ -b = -a/6

-6 ÷ -2 = -6/2 = 3

(3) (-) x (+) -a ÷ b = -a/b

6 ÷ -2 = -6/2 = -3

(4) (-) x (-) -a ÷ -b = ab

-6 ÷ -2 = 6/2 = -3

Explanation for positive and negative numbers multiplications

a x -b = -ab

5 x -2 = -2 + (-2) + (-2) + (-2) + (-2)

= -10

=> + x - = -

Negative number and negative number multiplications

-5(0) = 0

-5 [ 3 + (-3) ] = 0

-5 x 3 + -5 x -3 = 0

-15 + (-5)x(-3) = 0

(-5) x (-3) must be equal to 15 for -15 + (-5) x (-3) = 0

=> -5 x -3 = 15

=> - x - = +

Order Of Operations

First Order : ( ) ^e Bracket order/power Exponential

Second Order : ÷ X Multiplication And Division

Third Order : + - Addition And Subtraction

Do the question by: (1) completing all FIRST order,

(2) follow by all SECOND order,

(3) and then the THIRD order.

Step 1: Underline by the ORDER

Step 2: Do calculation using order

Step 3: Repeat step 1-2 until question is solved.

** Order within bracket -> must follow order as well

Example

Find the value of:

9 + 3 x 4 – (3 + 5) ÷ 2

9 + 3 x 4 – (3 + 5) ÷ 2 (Step 1 : Underline by Order)

= 9 + 3 x 4 – (8) ÷ 2 (Step 2 : Do calculation)

= 9 + 3 x 4 – 8 ÷ 2 (Step 3 : <<do ÷ and x>, repeat step 1-2> )

= 9 +12 – 4 (Step 3 : <do + and - > )

= 21 – 4 = 17

Example:

Calculate 24 ÷ 4 x 5 ÷ 6

[For computation with only the same order, working from left to right]

24 ÷ 4 x 5 ÷ 6 [ all are 2^nd order - Do from left to right ]

= 6 24 x 5 (Step 2)

4 6 [ Write ÷ as a denominator]

= 5

Example:

Calculate 25 + 144 – 2 x 5 x 12 [15/1/5a/1]

25 + 144 – 2 x 5 x 12 (Step 1)

= 25 + 144 – 120 (Step 2)

= 25 + 144 – 120 (Step 3)

= 169 – 120 (Step 3)

= 49

Practice

1. 55 – (-4) – 26 =

2. 35 – (-24) + (-43) =

3. 24 ÷ 8 x 7 =

4. 5 x 3 ÷ 8 x 12 =

5. -5 x 3 x 2 =

6. 5 x -3 ÷ 8 x (-12) =

7. Find the following without using the calculator.

a. [-44 – (-23)] x (8 -3)]

b. 300 ÷ 4 + [(-3)² + (-24)]

c. - [365 + (-217)] x (3 – 7)} + 30

d. -64 + 81 + [(-1)100 – (-3)]

e. -3 – 9 x -3 + 20 x (36 + 2)

f. -2 x (-3) – 3 x 5 x (-2)

Sunday, 4 November 2018

N6-L6 : Whole Numbers Practice : Order of Operations

WHOLE NUMBERS – L6 (N6) Date/Time:______ Tutor:

(Part 1) Revise(10-15mins) Start Time:

1. Order of Operations

2. Four Operations: To review/revise previous lessons

(Part2) Practice(25-40mins)

Start Time:

Find the value of

1. 20 - (9 + 3 x 2) ÷ 3

2. (35 +5 x 3) ÷ 10 – 2

3. (20 x 2 + 2) ÷ 7 + 3

4. 30 + 2 x (6 + 3 x 3) – 25 ÷ 5

5. 1 + 8 x 3 – 4 x 5 + 6 ÷ 6

6. 10 ÷ 2 – 3 x 1 + 7 x 6

Total Mark: /6

(III) Word Problems and PSLE questions (15-25mins) Start Time:

PSLE 2018F/S

7. Find the value of 7 x 6 – 5 + 4 x 2. (2/p1/s)

(1) 9

(2) 29

(3) 45

(4) 51

8. Study the pattern below. The first four figures are shown. (15/p2/f)

The table below shows the number of sticks and dots used to form each figure.

(a) How many dots are used to form Figure 12?

(b) How many sticks are used to form Figure 14?

9*. Use all the digits 6, 5, 2, 8 to form the number closest to 6000

10. John had 437 stamps. He kept 245 stamps for himself and gave the rest to his friends. Each friend received 12 stamps. How many friends were there?

11. A farmer has 20 chickens and rabbits. There is a total of 58 legs. How many chickens are there? How many rabbits are there?

12. Kevin is 8 years old. His father is 34 years old. In how many years’ time will his father’s age three times of Kevin age?

Extra Practice

1. 9 + 2 x 3 – (3 + 8 ÷ 4) ÷ 2

2. 16 – 12 ÷ 3 + (7 + 2 x 2) – 4

3. Bobby has 6 times as many stamps as Calvin. They have 84 stamps altogether. How many stamps does Bobby have?

4. 432 passengers are flying to Bangkok. The number of passengers flying to Hong Kong is 67 more than the number flying to Bangkok. How many passengers are flying to Hong Kong?

5. At a concert, there were 983 men, 745 women, 286 girls and 217 boys.

(a) How many adults attended the concert?

(b) How many children were there?

(D) What is the sum for the number of women and girls?

Factors/Multiples

6. Wendy wanted to pack 50 oranges and 75 apples into as many bags as possible, with no remainder. She packed the same number of fruit in each bag. The number of apples in each bag was the same. How many apples were there in each bag?

7*. Benny used a calculator to divide a 4-digit number by a 1-digit number. For the 1-digit number, he made a mistake by pressing 4 instead of 5. He obtained the incorrect answer of 260. What should be the correct answer?

Answer Key

1. 15

2. 3

3. 9

4. 85

5. 7

6. 44

7. 3

8a. 169

8b. 420

9. 5862

10. 16

11. 9

12. 5