Summary QMI1500 Summarised Study Notes

QMI1500

NOTES

,Study Unit 1: Numbers and Working with Numbers


1.1 Priorities and Laws of Operations:

B O D M A S or B E D M A S
+; −;×;÷

Adding and Subtracting

All numbers can be represented on a number line.




Numbers greater than zero are .

Numbers less than zero are .

The number zero is neutral.



On a number line, numbers get greater as you move right.

Therefore 5 is bigger than 3 (5>3).

Numbers get smaller as you move left.

Therefore -5 is smaller than -3 (-5<-3).



Exercise 1

1. 53 5.  4 p  3q

2. 4x  6x 6. 3  (2)

3. 57 7.  1d  (3d )

4.  6ab  2ab 8. 3  (6)  (2)

Any integer and its additive inverse add up to zero.

1

,Exercise 2

1. 22

2. 454

3.  5  21  10  21  5



Multiplying and Dividing

Note: Multiplication can be indicated in 3 different ways

- A multiplication sign
- A point
- Brackets



Note the following:

The product of any number with zero is zero.

The product of any number with 1 is the number.

The product of any number and its inverse is 1.



When multiplying always remember:

(+) × (+) = (+) (+) × (−) = (−)

(−) × (−) = (+) (−) × (+) = (−)



The rules for division are the same as the rules for multiplication.

It is preferable to turn a  into a fraction.
(+) (+)
= (+) = (−)
(+) (−)

(−) (−)
= (+) = (−)
(−) (+)




2

, When squaring or cubing integers, follow the same rules you use for multiplication.

Squaring a number involves multiplying the same number twice.

Cubing a number involves multiplying the same number three times.



Exercise 3

1. (3)(2)

2. 57

3. (3) 2  (4)

4. −(2)(4)
−4
5. 2

6. 2(−4)2 + 2(−3) − 12

7. (−2)3 − 3(3) + 2
−2(5)−8
8. −4(5−3)




Now we will combine the rules above with BODMAS



Exercise 4

1. 5 ×4 ÷2−3 ×2+6 ÷3

2. (5 × 4 ÷ 2 − 3 × 2 + 6) ÷ 3

3. 3 − 52 + 2 × 4 + (−3)2 − √16 + 9 ÷ 5




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