Thinking Cap 5 by Pelangi Publishing

Whole Numbers (1)

otes 100 000

Numbers to 10 Million

In numerals

In words

1000 10 000 100 000 1 000 000 10 000 000

One thousand Ten thousand One hundred thousand One million Ten million

Millions

Hundred Ten Thousands Thousands Thousands Hundreds

3 000 000 + 600 000 + 80 000 +

In numerals In words

We leave a space between the thousands digit and the hundreds digit to guide us to read the numbers easily.

4 4000

700

Ones

3 684 725 Three million, six hundred and eighty-four thousand, seven hundred and twenty-five

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Tens

ÂŠ Pelangi Publishing Singapore Pte. Ltd.

1/17/14 9:15 AM

Mathematics Primary 5 Unit 1 Whole Numbers (1)

Rounding off to the Nearest Thousand and Estimation The halfway point between two thousands is 500. If a number is before the halfway point, we round it to the thousand before. If it is on the halfway point or greater, we round it to the next thousand. TH

Round to

4000 The nearest thousands are 4000 and 5000.

It shows that 4315 is before the halfway point.

T. TH

The nearest thousands are 8000 and 9000.

Round to 78 000

It shows that 125 500 is exactly on the halfway point.

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78 750

79 000

78 750 is between 78 000 and 79 000. It is nearer to 79 000 than to 78 000. 78 750 is 79 000 when rounded off to the nearest thousand. 78 750  79 000

Round to

125 000 The nearest thousands are 5000 and 6000.

5000

4315 is between 4000 and 5000. It is nearer to 4000 than to 5000. 4315 is 4000 when rounded off to the nearest thousand. 4315  4000

It shows that 78 750 is after the halfway point.

H. TH T. TH TH

4315

125 500

126 000

125 500 is exactly halfway between 125 000 and 126 000. 125 500 is 126 000 when rounded off to the nearest thousand. 125 500  126 000 2

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

xample 1 The figure below shows the estimated population of some cities in 2012.

Singapore Population : 5 312 400

Paris Population : 2 167 994

Bangkok Population : 8 282 985

New York Population: ?

London Population : 8 308 369

(a)

The population of Singapore was 3 024 297 less than the population of New York. What was the population of New York?

(b)

A report showed that only 5 175 677 of the population in London were born in United Kingdom. How many people were born in foreign countries?

(c)

The total number of registered vehicles in Bangkok was about 7 500 000 in year 2012. How many of the population did not own a vehicle? (Assume each person only owned a vehicle.)

(d)

What was the population of Paris when rounded off to the nearest thousand?

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

olution (a)

Population of Singapore = 5 312 400

Population of New York = 5 312 400 + 3 024 297

= 8 336 697

The population of New York was 8 336 697.

(b)

Population of London = 8 308 369

Population born in United Kingdom = 5 175 677

8 308 369 – 5 175 677 = 3 132 692

3 132 692 people were born in foreign countries.

(c)

Population in Bangkok = 8 280 985

Number of registered vehicles = 7 500 000

8 280 985 – 7 500 000 = 780 985

780 985 of the population in Bangkok did not own a vehicle.

(d)

Population of Paris = 2 167 994

2 167 000

2 167 994 is between 2 167 000 and 2 168 000.

It is nearer to 2 168 000 than to 2 167 000.

2 167 994  2 168 000

The population of Paris is 2 168 000 when rounded off to the nearest thousand.

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2 167 994

2 168 000

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

xample 2 The table below shows the total expenditure of a family in a year. Description

Expenditure

Food

$9180

Utilities

$6334

Housing loan

$10 392

Clothing and services

$4790

Healthcare

$4400

Insurance

$13 725

Savings

$6840

Entertainment

$4467

Taxes

$6226

(a)

Estimate the yearly income of the family by first rounding off each number to the nearest thousand.

(b)

How much more money is spent on housing loan than on food each month? (Assume the same amount of money is spent every month.)

(c)

If there are 5 members in the family, find the amount of money spent on insurance by each member in a year.

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

olution (a)

Description

Expenditure rounded to the nearest thousand dollars

Expenditure

Food

$9180

$9000

Utilities

$6334

$6000

Housing loan

$10 392

$10 300

Clothing and services

$4790

$5000

Healthcare

$4400

$4000

Insurance

$13 725

$14 000

Savings

$6840

$7000

Entertainment

$4467

$4000

Taxes

$6226

$6000

Yearly income = $9000 + $6000 + $10 300 + $5000 + $4000 + $14 000 + $7000 + $4000 + $6000 = $65 300

The yearly income of the family is $65 300.

(b)

Yearly expenditure on housing loan = $10 392

Monthly expenditure on housing loan = $10 392 ÷ 12 = $866

Yearly expenditure on food = $9180

Monthly expenditure on food = $9180 ÷ 12 = $765

$866 – $765 = $101

$101 more is spent on housing loan than on food each month.

(c)

Amount of money spent on insurance = $13 725

Amount of money spent by each member = $13 725 ÷ 5 = $2745

Each member spent $2745 on insurance in a year.

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

ractice Solve the following word problems. 1.

Using all the digits above, form the greatest and the smallest numbers. Then, find the difference between the two numbers.

2. One of the longest non-stop flights in the world is the trip from Los Angeles to Singapore, taking about 18 hours to complete. If the aircraft travels 784 kilometres per hour, find the distance between the two cities.

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

3. Mr Clarkson is renovating his new house. Estimate the total amount of money that he needs for the renovation by first rounding off each cost to the nearest thousand dollars. Description

Cost

Doors and windows

$9560

Wallpapers and flooring

$6699

Furniture for 3 rooms

$2321 per room

4. Keith is advised to send his car in for a service when the mileage reaches 40 000 km. His car has travelled 28 524 km. If he drives 151 km every day, how many days after will he need to send his car in for a service?

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

5. A watch factory produced an equal number of digital watches and analogue watches in a year. 8600 digital watches and 10 500 analogue watches underwent the acceptance testing process. The number of untested digital watches was thrice the number of untested analogue watches. Find the total number of watches produced by the factory in a year.

6. Shannon has $780 more than Roy in her savings account. Peter has $8150 more than the total amount that Shannon and Roy have. If Peter has $15 140 more than Shannon, how much money does Peter have in his savings account? Round off your answer to the nearest thousand.

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

7. There were 8542 cars in Car Park A last month. Car Park B had 754 more cars than Car Park A last month. Car Park A charged $5 per entry while Car Park B charged $4 per entry. Which car park collected more parking fee last month? How much more?

8. A family is planning to travel from Singapore to Thailand by car. They find out that it requires a total of 137 litres of petrol for the journey. A litre of petrol can travel for 12 kilometres. (a) Find the total distance of their journey. (b) If the petrol price is $2.09 per litre, how much will they need to spend for the whole journey? Round off your answer to the nearest whole number.

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

9. Oktoberfest is the largest beer festival, held annually in Germany. In year 2012, the amount of beer consumed by Oktoberfest patrons was enough to fill 3 olympic-size swimming pools. If an average olympic-size swimming pool can hold about 2 500 000 litres of water, what was the total amount of beer consumed by the Oktoberfest patrons in 2012?

10. A stall sold two types of cookies during a festive season. Chocolate cookies cost $15 per pack while almond cookies cost $18 per pack. The owner earned $13 425 at the end of a week. If 425 packs of almond cookies were sold, how many packs of chocolate cookies were sold in a week?

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

11. Mr Hopkins is translating some books written by a foreign author. He is able to translate 18 pages of the book in a day. If the total number of pages in each book is 438, how many days will be taken to translate 15 similar books?

12. The total mass of 17 empty bottles was 3 kg 995 g. Anne poured 2 kg 108 g of milk equally into each bottle. What was the mass of each bottle of milk?

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Mathematics Primary 5 Unit 1 Whole Numbers (1)

13. A farmer collected 5600 avocados. He packed some of them into 25 crates, each containing 150 avocados. He then packed the remaining avocados into crates of 100. How many avocados were left unpacked?

14. A submarine is situated 2655 m below sea level. In a training exercise, it descends 155 m every hour. (a) Find the new position of the submarine after 9 hours. (b) If the submarine ascends 150 m every hour from its new position, how many hours will it take to reach the surface of the sea?

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Whole Numbers (2)

otes Order of Operations 123

–

( 108 ÷ 6 )

123

–

123

2720

2843

–

2825

1. Carry out the operations in the brackets first. 2. Carry out multiplication and division from left to right. 3. Carry out addition and subtraction from left to right.

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Mathematics Primary 5 Unit 2 Whole Numbers (2)

xample 1 The table below shows the amount of calories burned in an hour of exercise based on different body masses.

Activity

Calories burned per hour 70 kg

90 kg

110 kg

Aerobics

365

456

545

Rollerblading

548

683

818

Rope skipping

861

1074

1286

Running

606

755

905

Swimming

590

704

817

Walking

314

390

469

(a)

Riley plays rollerblade for 30 min and rope skipping for 2 h every day. If Riley is 70 kg, how many calories does he burn in a day?

(b)

Edward’s body mass is 90 kg. He spends 30 min each doing aerobics, swimming and walking every day. How many calories does he burn in a day?

(c)

Does Riley or Edward burn more calories in a week? How many more?

olution (a)

60 min = 1 h

30 min =

Riley burns 1996 calories in a day.

1 h 2 274 1 × 548) + (2 × 861) = 274 + 1722 21 = 1996

(

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