Chapter 1 Decimals, Percents and Fractions

7/30/2019 Chapter 1 Decimals, Percents and Fractions

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CHAPTER

1DECIMALS,

FRACTIONS

ANDPERCENT

( Textbook Chapters 1, 2 and 3 )

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1. Decimals

1.1 Rounding whole numbers.

Rule of rounding

1. Identify position to be rounded. Draw a line under that place.2. If digit to the right of the number to be rounded is 5 or more,

increase by 1; if 4 or less, do not change.3. Change all digits to the right of the number to be rounded to

zero.

Example

i. Round 76 to the nearest ten. Answer: 80

ii. Round 726 to the nearest ten. Answer: 730iii. Round 241 to the nearest hundred. Answer: 200iv.Round 1, 498, 586 to the nearest million. Answer: 1, 000,

000

Exercises

Round as indicated.

1. 847 to the nearest ten.2. 18, 952 to the nearest hundred.3. 263, 568 to the nearest thousand.4. RM 5.0384 to the nearest cent.5. RM 3,528.48 to the nearest dollar.

Answers

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1.2 Addition, subtraction, multiplication and division of wholenumbers.

Exercises

1. One week, Aminah earned the following commissions: Monday, RM124;Tuesday, RM88; Wednesday, RM62; Thursday, RM137; Friday, RM195.Find her total commissions for the week.

2. In May, the landlord of an apartment building received RM720 from eachof eight tenants. After paying RM2,180 in expenses, how much money didthe landlord have left?

3. A rental business buys three airless sprayers at RM1,540 each, fiverototillers at RM695 each, and eight 25-foot ladders at RM38 each. Findthe total cost of the equipment purchased.

4. At a recent garage sale, the total sales were RM584. If the money were

divided equally among Thava, Rosnah, Maria, and Husin, how much dideach receive?

Answer

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1.3 Addition, subtraction, multiplication and division of decimals.

Exercises

1. Add 9.83, 6.4, 17.592, and 3.087.2. Siti Rohani earned RM759.27 in commission, RM235.75 as premium, andreceived RM87.04 for mileage. Find the total amount that she received.

3. Subtract 39.428 and 27.98.4. Multiply 8.34 with 4.2.5. Find the gross pay of a Kedai Kopi Mat employee working 28.5 hours at a

rate of RM7.15 per hour.6. Calculate: 27.52 32.

Answer

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2 Fractions

2.1 Types of fractions.i. Proper fraction: Numerator smaller than denominator.

Eg;2 3 15 1

, , ,3 4 16 8

ii. Improper fraction: Numerator equal or greater thandenominator.

Eg;17 19 11 5 7

, , , ,8 12 12 3 7

iii. Mixed fraction: Whole number and proper fraction.

Eg;2 5 5

2 ,3 , 93 8 6

2.2 Converting fractions.

2.2.1 Mixed to improper.

Eg;2 23

7 3 7 23 3

= +

2.2.2 Improper to mixed.

Eg;17 2

35 5

2.3 Adding, subtracting, multiplying, and dividing fractions.

i.2 1

5 5+

ii.2 3

3 8

iii.3 2

3 84 3

iv.7 1

8 4

2.4 Converting decimals to fractions.

i. 0.47 =47

100ii. 0.30 =

3

10

iii. 0.98iv. 0.654

v. 0.55vi. 0.75

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3.1.2 Write fraction as percent.

To write a fraction as a percent, multiply the fraction by 100%.

Eg; 2 0.4 40%5

= =

Exercises

i. ii. 3/8

iii. 4/5

Answer

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3.2 Write a percent as a decimal.

To write a percent as a decimal, move the decimal point two places to theleft and drop the percent sign.

Eg; 50% = 0.5

Exercise

i. 35%ii. 50%

iii. 325%iv. 37 %

Answer

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3.3 Write a percent as a fraction.

To write a percent as a fraction, first change the percent to a decimal, thenwrite the decimal as a fraction in lowest terms.

Eg;15 3

15% 0.15100 20

= = =

Exercises

i. 56%ii. 31%

iii. 9%iv. 4%

Answer

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3.4 Write a fractional percent as a decimal .

To write a fractional percent as a decimal by first changing the fraction to adecimal, leaving the percent sign. For example, first write % as 0.5%.

Then write 0.5% as a decimal by moving the decimal point two places tothe left and dropping the percent sign.

Eg;1

% 0.5% 0.0052

= =

Exercises

i.1

%5

ii.3%

4

iii.5

%8

Answer

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3.5 Part, Base and Rate.

These are the three components of a percent problem

Base: the whole or total.Rate: a number followed by percent (%).Part: result of multiplying the base and the rate.

Formula

P = B x RPart Base Rate

Example 1

A shop gives a 10% discount on all shoes. Find the discount on a RM175shoes?

0.1x RM175 = RM17.50 discount

Example 2

If the sales tax rate is 4%, find amount of sales when the sales tax isRM18.

18450 sales

0.04B RM= =

Example 3

Production rose from 3820 units to 5157 units. Find the percent ofincrease.

5157 3820 = 1337 change1337

0.35 35%3820

R = = =

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Exercises

a. Find the sales tax on an automobile priced at $12,345.00 if the rate of salestax is 6% of the sales price.

b. A workers gross pay for the week was $500. If 23% was withheld for EPF

deduction, how much did the worker take home?c. At a local university, 10,580 male students (46% of the student body) areenrolled. What is the total number of students?

d. A car dealer sold 125 cars last month to people entering his showroom. Howmany customers visited the dealership if the 125 who purchased carsrepresent 2 % of those who visited the showroom?

e. Outdoor Sports purchased 40 boats for the season. If they sold 25 of theboats, what percent of the boats remain in the inventory?

Answer

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3.6 Increase and Decrease Problem.

- increase problems indicated by phrases such as after an increase of,more than or greater than

- decrease problems indicated by: after a decrease of, less than or after

a reduction of- base is ALWAYS the original amount, 100%.

Example 4

This years sales are RM121,000 which is 10% more than last yearssales. Find last years sales.

Original + increase = New value100% + 10% = 110%

121,000 121,000 110,000110% 1.1

RM RMB RM= = =

Example 5

After a deduction of 10% from the price, a customer paid RM135. Find theoriginal price.

Original Decrease = New value100% - 10% = 90%

135150

0.9

B RM= =

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Exercises

a. Album sales were up 4% from last years sales to 785.2 million. Find lastyears sales.

b. If sales are $1,250,000 after a 15% decrease, what were the sales beforethe decrease?c. After Fleetfeet deducted 10% from the price of a pair of sneakers, Nancy

paid $135. What was the original price of the shoes?d. If an owner sold her apartment for $86,330, an increment of 11% of the

original price, how much had the owner paid originally?e. Ellin says that her sales have increased exactly 20% per year for the last two

years. Her sales this year are $170,035.20. Find her sales two years ago.(Hint: the two 20% cannot be added together, because of 2 separate years,therefore 2 separate bases)

Answer

Recommended further exercises:CUMMULATIVE REVIEW QUESTIONNAIRES ON PAGE 135 OF THETEXTBOOK.

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Chapter 1 Decimals, Percents and Fractions

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