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6.2.1 Integers, PT3 Practice

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Question 1:
Evaluate 5 + (–7)   

Solution:

Therefore,
5 + (–7) = 5 – 7
= –2


Question 2:
Evaluate –6 – (–5)   

Solution:

Therefore,
–6 – (–5) = –6 + 5   
= –1


Question 3:
Simplify –3 + 7 + (–2)
  
Solution:


Therefore,
–3 + 7 + (–2) = 4 + (–2)
= 4 – 2
= 2


Question 4:
Simplify 5 + (–4) + (–3)  

Solution:


Therefore,
5 + (–4) + (–3)
= 5 – 4 – 3
= –2

6.2 Integers

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6.2 Addition and Subtraction of Integers

6.2.1 Addition of Integers
1. Addition of integers can be done on a number line.
(a) To add a positive integer:
Move to the right (positive direction) on the number line.

(b) To add a negative integer:
Move to the left (negative direction) on the number line.



2. Integers with the same signs are called integers with like signs.
Example:
2 and 7, –25 and –5.

3. Integers with the different signs are called integers with unlike signs.
Example:
+2 and –7, –25 and 5.

Example 1:
Solve the following.
(a) 3 + (+4)
(b) 2 + (–5)

Solution:
(a)

Therefore,
3 + (+4) = 3 + 4
= 7

(b)
Therefore,
2 + (–5)
= –3


6.2.3 Multiplication and Division of Integers
1. Multiplication and division of like signs gives (+)

( + ) × ( + ) = + ( + ) ÷ ( + ) = + ( − ) × ( − ) = + ( − ) ÷ ( − ) = +


2. Multiplication and division of unlike signs gives (–)

( + ) × ( − ) = − ( + ) ÷ ( − ) = − ( − ) × ( + ) = − ( − ) ÷ ( + ) = −

Example:
  (a) –25 ÷ 5 = –5
  (b)   8 × (–5) = –40
 

5.2.2 Percentages, PT3 Practice

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Question 6:
Liza had 360 apples. She sold ⅝ of the apples. Then she gave 27 of the remaining apples to her neighbour.
Calculate the percentage of apples that Liza has left.

Solution:
Number of apples sold = 5 8 ×360 =225 Number of apples left =360−225−27 =108 Percentage of apples left = 108 360 ×100% =30%


Question 7:
Mei Ling took part in a science quiz competition. She answered 12 questions correctly. She answered 25% of the questions incorrectly.
Find the total number of questions in the quiz.

Solution:
75%→12 correct answers 25%→? incorrect answers Number of incorrect answers = 25 75 3 ×12 =4 Total number of questions =12+4 =16


Question 8:
Diagram below shows the prices of two items.


 Kenny buys a pair of track pants and 2 pieces of sweaters.
Calculate the total amount Kenny has to pay.

Solution:
Price of a pair of track pants after 25% discount =RM150.00−( 25 100 ×RM150.00 ) =RM150.00−RM37.50 =RM112.50 Total amount Kenny has to pay =( RM100.00×2 )+RM112.50 =RM312.50


Question 9:
Table below shows the prices and the discounts for the same brand of school bag sold at four shops, P, Q, R and S. 


Which shop offers the cheapest price?

Solution:
Shop P, Price per item after discount =RM100−( 20 100 ×RM100 ) =RM80 Shop Q, Price per item after discount =RM110−( 30 100 ×RM110 ) =RM77  Shop R, Price per item with no discount =RM170÷2 =RM85 Shop S, Price per item with no discount=RM90 Shop Q offers the cheapest price.


Question 10:
Table below shows dividend received by Janice from her investment.


Janice reinvests RM204 from the total dividends she received into ASB investment.
What is the remaining percentage that she did not use in her reinvestment?

Solution:
Dividends from ASB =3%×RM 2000 = 3 100 ×RM 2000 =RM 60 Dividends from ASN =4%×RM 7000 = 4 100 ×RM 7000 =RM 280 Total dividends =RM 60+RM 280 =RM 340 Percentage of dividends not reinvested = 340−204 340 ×100 = 136 340 ×100 =40%


5.2.1 Percentages, PT3 Practice

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Question 1:
Rahman bought a house at RM180 000. The market price of the house increases by 15 % per year. After a year, Rahman sold his house at the price of RM 205 000.
Is the selling price higher compared to the market price? Show your working.

Solution:
Market price =115%×RM180 000 = 115 100 ×RM180 000 =RM207 000 RM207 000>RM205 000 The market price of the house is higher than the selling price of the house.


Question 2:
A company makes a profit of RM 50 000 in year 2016. The projection of profit increase is fixed at 20 % from the previous year.
Predict the company profit in year 2018.

Solution:
Profit in year 2017 =RM50 000× 120 100 =RM60 000 Profit in year 2018 =RM60 000× 120 100 =RM72 000


Question 3:
Sharon wants to buy a new car with the price of RM 78 500. Her father gives her some money, which is 30 % of the car price. The deposit for the car is 1 5 of the price.
Would her father’s contribution be enough for her deposit? Give your reason with calculation.

Solution:
30% of the car price given by Sharon's father = 30 100 × RM 78500 =RM 23550 Deposit of the car price needed = 1 5 × RM 78500 =RM 15700 RM 23550> RM 15700, therefore her father 's contribution is enough for the deposit.


Question 4:
The profit of Company P and Company Q in March are RM38 000 and RM48 000 respectively. In April, the profit of Company P has increased by 20%.
Given the profit for both companies are equal in April, find the percentages decrease in profit of Company Q.

Solution:
Profit of Company P in April = 120 100 ×38000 =RM45600 Drop in profit of Company Q =RM48000−RM45600 =RM2400 Percentage decrease in profit = 2400 48000 ×100% =5%


Question 5:
A biscuit making company needs 200 tonnes of flour every month. Factory K supplies 80 tonnes, while the rest is supplied by Factory M. In a particular month, Factory K faces a problem which forces it to reduce its output by 15%.
Find the total percentage of the flour output of Factory M in order to accommodate the requirement of the biscuit making company.

Solution:
New flour supply from Factory K = 85 100 ×80 =68 tonnes New flour supply from Factory M =200−68 =132 tonnes Total percentage of flour output of Factory M = 132 120 ×100% =110%