Math for Smart Kids Gr.5

Math for Smart Kids5

Math for Smart Kids Grade 5Textbook

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The Editorial BoardAuthorsDr. Estrella P. Mercado finished her PhD in Educational Management (with honor) and MA in Education at Manuel L. Quezon University. She also holds an MEd in Special Education degree and a BS in Elementary Education degree from the Philippine Normal University. She has been a classroom teacher, an Education supervisor, and assistant chief of the Elementary Division of the Department of Education, Culture and Sports (DECS-NCR). She was awarded as Outstanding Female Educator in 1998 by the Filipino Chinese Women Federation. She presently heads the Special Education Department at PNU.Bernardo R. Daquiz Jr. holds a Bachelor of Arts in Social Science degree, major in Behavioral Studies, from the University of the Philippines-Manila . He took units in BS Education at PNU. He was a former grade school teacher at PAREF-Northfield Private School for Boys. He is currently teaching grade school Mathematics at Xavier School. ConsultantMa. Portia Y. Dimabuyu holds an MA in Education degree, major in Mathematics, and a BS Education degree, major in Mathematics, from the University of the Philippines-Diliman. She was a recipient of the Excellence in Mathematics Teaching Award in 2007 from the UP College of Education. She is presently an Assistant Professor at the Mathematics Department of UP Integrated School and a lecturer of undergraduate and graduate courses in teaching Mathematics at the UP College of Education.ReviewerReina M. Rama has a bachelor’s degree in Mathematics from Silliman University and is currently pursuing her master’s degree in Mathematics from Ateneo de Manila University. Before teaching full time, she was a researcher/teacher-trainer at the University of the Philippines-National Institute of Science and Mathematics Education Development (UP-NISMED). She taught Mathematics at Colegio de San Lorenzo and Miriam College. She is the Subject Coordinator for Mathematics Area of Miriam College-High School Unit.

Preface

Math for Smart Kids is a series of textbooks in Mathematics for grade school, which is designed to help pupils develop appreciation and love for mathematics. This series also aims to help the learners acquire the skills they need to become computa-tionally literate.

The lessons in each textbook present mathematics concepts and principles that are anchored on the competencies prescribed by the Department of Education. Each lesson starts with Let’s Do Math, where mathematics concepts and principles are introduced through problems, stories, games, or puzzles. This section is followed by Let’s Look

Back, which lists questions that will help the pupils to think critically on what has been introduced in the lesson and will allow them to discover things on their own. For easy recall of important points or concepts taken up in a lesson, the section Let’s Remember

Our Learning has been included. Multilevel exercises are provided in Let’s Practice and Let’s Test Our Learning that will assess how much the pupils have learned from the lesson. The exercises will also determine if the pupils are ready to learn new mathematics skills. The development of the multiple intelligences of an individual is reflected in the different activities that the pupils will perform—from concrete to semi-concrete, and from semi-abstract to abstract kind of learning. Situations and real-life problems are provided in Let’s Look Forward to give the pupils opportunities to apply what they have learned to their daily life experiences.

This series of textbooks gives the learners the opportunity to explore and enjoy Mathematics. Let’s have fun learning together!

The Authors

Table of ContentsUnit 1 Whole Numbers, Number Theory, and Fractions

Chapter 1 Whole Numbers

Lesson 1 Place Values of Numbers ...................................................................2 2 Comparing and Ordering Numbers ....................................................8 3 Rounding off Numbers ..................................................................... 12 4 Adding Whole Numbers ................................................................... 15 5 Subtracting Whole Numbers ............................................................ 19 6 Multiplying Whole Numbers ............................................................ 22 7 Dividing Whole Numbers ................................................................. 28 8 Solving Word Problems Involving More than One Operation ........... 32 9 Roman Numerals ............................................................................. 38

Chapter 2 Number Theory

Lesson 1 Divisibility Rules ............................................................................. 41 2 Prime and Composite Numbers ........................................................ 46 3 Prime Factorization .......................................................................... 49 4 Greatest Common Factor .................................................................. 52 5 Least Common Multiple ................................................................... 57

Chapter 3 Fractions

Lesson 1 Reducing Fractions to Lowest Terms ................................................ 61 2 Changing Dissimilar Fractions to Similar Fractions ........................... 65 3 Equivalent Fractions ........................................................................ 70 4 Comparing and Ordering Fractions .................................................. 73

5 Estimating Fractions Close to 0, 12

, or 1 ........................................... 79

Unit 2 Operations on Fractions and Decimals

Chapter 4 Addition and Subtraction of Fractions

Lesson 1 Adding Similar Fractions ................................................................. 84 2 Adding Dissimilar Fractions ............................................................ 89 3 Adding Mixed Numbers ................................................................... 96 4 Mental Addition of Fractions .......................................................... 102 5 Subtracting Similar Fractions .......................................................... 105 6 Subtracting Dissimilar Fractions ..................................................... 115

Chapter 5 Multiplication and Division of Fractions

Lesson 1 Multiplying Fractions and Whole Numbers .................................... 124 2 Multiplying Mixed Numbers and Fractions ..................................... 128 3 Dividing Whole Numbers and Fractions ......................................... 135 4 Dividing Fractions .......................................................................... 140 5 Solving Multistep Word Problems ................................................. 144

Chapter 6 Decimals

Lesson 1 Place Values of Decimals ................................................................ 149 2 Reading and Writing Decimals ....................................................... 153 3 Comparing and Ordering Decimals ................................................ 156 4 Rounding off Decimals ................................................................... 160

Chapter 7 Operations on Decimals

Lesson 1 Adding Decimals ............................................................................ 164 2 Subtracting Decimals ..................................................................... 170 3 Multiplying Decimals ..................................................................... 176 4 Multiplying Mixed Decimals and Whole Numbers .......................... 179 5 Multiplying Mixed Decimals .......................................................... 182 6 Mental Multiplication Involving Decimals ...................................... 186 7 Dividing Decimals.......................................................................... 189 8 Dividing Decimals by Whole Numbers ........................................... 195

Unit 3 Ratio, Proportion, and Percent

Chapter 8 Ratio and Proportion

Lesson 1 Ratio .............................................................................................. 200 2 Proportion...................................................................................... 208 3 Direct and Indirect Proportions ...................................................... 211 4 Problem Solving on Proportion ....................................................... 215

Chapter 9 Percent

Lesson 1 Meaning of Percent ........................................................................ 219 2 Percents, Decimals, Fractions, and Ratios ....................................... 223 3 Finding the Percentage ................................................................... 228 4 Finding the Rate ............................................................................. 233 5 Finding the Base ............................................................................ 236

Unit 4 Geometry, Measurement, and Graphs

Chapter 10 Geometry

Lesson 1 Polygons: Quadrilaterals and Triangles ........................................... 240 2 Similar and Congruent Polygons ..................................................... 246 3 Circles ........................................................................................... 251 4 Space Figures ................................................................................. 254

Chapter 11 Measurement and Graph

Lesson 1 Perimeter and Circumference ......................................................... 258 2 Area ............................................................................................... 265 3 Volume of Space Figures ................................................................ 273 4 Temperature .................................................................................. 280 5 Line Graph .................................................................................... 284 6 Finding the Average ....................................................................... 290

Glossary .............................................................................................................. 293Bibliography ........................................................................................................ 296Index ................................................................................................................... 297

Whole Numbers, Number Theory, and Fractions 1

Unit

� MathforSmartKids5

Whole Numbers

Lesson 1 Place Values of Numbers

Pluto, once known as the coldest, smallest, and most distant planet from the sun, was discovered by an American astronomer named Clyde Tombaugh in 1930. Its distance from the sun is 5 906 380 000 kilometers (km). Its equatorial radius is 1 151 km, and its volume is 6 390 000 000 cubic kilometers (km³). It has a mass of 13 000 000 000 000 000 000 000 kilograms (kg).

On 24 August 2006, the International Astronomical Union (IAU) reclassified Pluto from one of the nine major planets of the solar system to a minor planet. The IAU said that Pluto does not meet the three criteria to be classified as a planet. One criterion is that a planet should have “cleared the neighborhood” around its orbit. Astronomers have observed that Pluto orbits among the icy debris in the asteroid belt.

What is Pluto’s distance from the sun? 5 906 380 000 kmWhat is its equatorial radius? 1 151 km To help you read these numbers, study the place-value chart below.

Place-value Chart

Billions Millions Thousands Units

Hundreds(H)

Tens(T)

Ones(O)

Hundreds(H)

Tens(T)

Ones(O)

Hundreds(H)

Tens(T)

Ones(O)

Hundreds(H)

Tens(T)

Ones(O)

1 1 5 1

5 9 0 6 3 8 0 0 0 0

You read 1 151 as “one thousand, one hundred fifty-one.”You read 5 906 380 000 as “five billion, nine hundred six million, three hundred

eighty thousand.”

Chapter 1

WholeNumbers,NumberTheory,andFractions �

Look at the place-value chart again. Each group of three digits in a number is a period. In numbers with four or more digits, the periods are separated by a single space.

Consider the number 1 426 725 400. This number can be written in three ways:

• Standard form: 1 426 725 400 • Expanded form: 1 000 000 000 + 400 000 000 + 20 000 000 + 6 000 000 +

700 000 + 20 000 + 5 000 + 400 • Word form: one billion, four hundred twenty-six million, seven hundred

twenty-five thousand, four hundred

Here are more examples:

1. Standard form: 57 909 175 Expanded form: 50 000 000 + 7 000 000 + 900 000 + 9 000 + 100 + 70 + 5 Word form: fifty-seven million, nine hundred nine thousand, one hundred

seventy-five

2. Standard form: 227 936 640 Expanded form: 200 000 000 + 20 000 000 + 7 000 000 + 900 000 + 30 000 +

6 000 + 600 + 40 Word form: two hundred twenty-seven million, nine hundred thirty-six

thousand, six hundred forty

3. Standard form: 778 412 020 Expanded form: 700 000 000 + 70 000 000 + 8 000 000 + 400 000 + 10 000 +

2 000 + 20 Word form: seven hundred seventy-eight million, four hundred twelve

thousand, twenty

4. Standard form: 1 426 725 400 Expanded form: 1 000 000 000 + 400 000 000 + 20 000 000 + 6 000 000 +

700 000 + 20 000 + 5 000 + 400 Word form: one billion, four hundred twenty-six million, seven hundred

twenty-five thousand, four hundred

5. Standard form: 2 870 972 201 Expanded form: 2 000 000 000 + 800 000 000 + 70 000 000 + 900 000 +

70 000 + 2 000 + 200 + 1 Word form: two billion, eight hundred seventy million, nine hundred

seventy-two thousand, two hundred one

6. Standard form: 4 498 252 900 Expanded form: 4 000 000 000 + 400 000 000 + 90 000 000 + 8 000 000 +

200 000 + 50 000 + 2 000 + 900 Word form: four billion, four hundred ninety-eight million, two hundred

fifty-two thousand, nine hundred


Examine the numbers in the place-value chart below.

Place-value Chart

Billions Millions Thousands Units

H T O H T O H T O H T O

6 2 0 0 1 7 9 5 0 8 0 0

7 0 1 0 3 0 8 7

1 5 9 6 0 5 6 3 8

4 1 2 0 7 3 1 5 0 0 4

period period period period

You read: six hundred twenty billion, seventeen million, nine hundred fifty thousand, eight hundred

You write: 620 017 950 800

You read: seventy million, one hundred three thousand, eighty-sevenYou write: 70 103 087

You read: one hundred fifty-nine million, six hundred five thousand, six hundred thirty-eight

You write: 159 605 638

You read: forty-one billion, two hundred seven million, three hundred fifteen thousand, four

You write: 41 207 315 004

Look at the numbers in the given place-value chart. 1. How are the digits in each number grouped? 2. How many digits are there in each period? 3. How are the digits in each period read? 4. How are the digits in each period written?


The place value of a digit depends on its place in the number. A place-value chart can be used to easily determine the place value of a digit. Zero is used as a place holder.

In reading a number, read first the leftmost digit, then the remaining digits going to the right.

Starting from the rightmost digit in a number, each group of three digits in a number is a period.

In writing the standard form of a number, leave a single space to separate each period.

A. Write the value of each underlined digit. 1. 4 396 _________________ 2. 59 485 _________________ 3. 104 629 _________________ 4. 3 495 829 _________________ 5. 46 829 405 _________________

6. 945 672 389 _________________ 7. 8 835 693 000 _________________ 8. 73 729 486 925 _________________ 9. 182 920 825 496 _________________ 10. 393 003 934 286 _________________

B. Write the numbers in standard form.

1. three million, two hundred twenty-four thousand, one hundred thirty-five _________________

2. four billion, four hundred million, nine hundred seventy-five thousand, three _________________

3. twenty-five billion, three million, one hundred twelve thousand, two hundred twenty-six _________________

4. one hundred three billion, thirty-four million, six hundred fifty-four thousand, seven hundred thirteen _________________

5. eight hundred billion, nine hundred forty-five million, five thousand, three hundred seventy-nine _________________

C. Write these numbers in words. 1. 6 922 436 ______________________________________________________ ______________________________________________________


2. 89 345 782 ______________________________________________________ ______________________________________________________ ______________________________________________________

3. 120 407 315 ______________________________________________________ ______________________________________________________ ______________________________________________________

4. 10 985 375 112 ______________________________________________________ ______________________________________________________ ______________________________________________________

5. 465 123 400 327 ______________________________________________________ ______________________________________________________ ______________________________________________________

You were asked to help in canvassing the number of votes during a presidential election. How would you read the following votes that each candidate received?

Presidential candidate A – 2 305 439 Presidential candidate B – 6 692 307

A. Write the place value of each underlined digit.

1. 825 _________________ 2. 9 262 _________________ 3. 34 827 _________________ 4. 505 948 _________________ 5. 6 828 725 _________________ 6. 73 263 827 _________________ 7. 825 684 936 _________________ 8. 9 836 825 000 _________________ 9. 63 527 043 924 _________________ 10. 425 682 426 135 _________________


B. Write the following numbers in standard form.

1. three million, five hundred twenty-three thousand, thirty-nine

2. seven billion, ninety-five million

3. eighty billion, three hundred twenty-seven million, three hundred fifteen thousand, one hundred twenty-one

4. one hundred five billion, three hundred two million, nine hundred thirty thousand, two hundred two

5. nine hundred two billion, three million, twenty-five thousand, seven

C. Write the following numbers in words.

1. 4 326 175

2. 35 002 872

3. 8 350 432 175

4. 92 001 426 127

5. 105 000 345 278


Lesson 2 Comparing and Ordering Numbers

Rita and Steve were discussing the results of the presidential elections. Find out how they were able to compare two numbers.

Steve: Who has the most number of votes?Rita: Let’s look at the figures.Steve: How do we find out who got the most number of votes just by looking at the

figures?Rita: Look at the digit in the highest place value of each number. In this case, the

highest place value of the numbers is ten billions. Are the digits the same? If they are, compare the digits in the next highest place value of the two numbers. Do this until you find different digits in the same place value of the numbers.

Steve: Since both numbers are more than 85 billion, we can compare the digits in the hundred millions place.

Rita: Right, Steve! One hundred million is less than 3 hundred million. So, 85 361 425 126 is greater than 85 136 395 427.

Here is another example. Compare 5 395 432 375 with 5 395 324 896.

First, compare the digits in the highest place value which is the billions place.

5 395 432 375 and 5 395 324 896 5 billion = 5 billion

Since the billions digits are the same, compare the digits in the next highest place value, which is the hundred millions place. Continue comparing until you find different digits in the same place value.

395 million = 395 million

Candidate AB

Number of Votes85 361 425 12685 136 395 427

Tally Board


Since all the digits in the millions period are the same, compare the digits in the hundred thousands period.

400 thousand > 300 thousand

Therefore, 5 395 432 375 is greater than 5 395 324 896.

You write 5 395 432 375 > 5 395 324 896.

Study this example.

Arrange these numbers in descending order.

17 432 187 19 807 453 18 476 389

Since the digits in the highest place value are the same, compare the digits in the next place value.

17 432 187 < 19 807 453 19 807 453 > 18 476 389 17 432 187 < 18 476 389

Arranged in descending order: 19 807 453, 18 476 389, 17 432 187

1. How do you compare numbers with the same number of digits? 2. How do you order numbers in a given set?

To compare two numbers, start comparing the digits in the highest place value. If the digits in the highest place value are the same, compare the digits in the next highest place value. Continue comparing until you find different digits in the same place value. After comparing numbers, order the numbers according to the indicated arrangement.

To order numbers means to arrange the numbers from least to greatest, or from greatest to least. Before you can order numbers, you have to compare the digits in the two numbers that belong to the same place value.

10 MathforSmartKids5

B. Arrange the numbers from least to greatest. Write 1 (least) to 3 (greatest) in the blanks.

1. 8 328 427 826 8 328 438 725 8 328 426 125

2. 75 639 628 73 789 009 77 836 133

3. 427 828 536 132 427 938 125 002 427 828 635 143

C. Arrange the numbers from greatest to least. Write 1 (greatest) to 3 (least) in the blanks.

1. 89 426 872 89 426 982 89 628 135

2. 5 825 326 143 5 825 145 009 5 825 427 182

3. 78 926 008 426 87 375 009 412 87 872 007 325

A. Compare the numbers. Write < or > in the box.

1. 28 350 425 27 475 986

2. 275 875 126 275 758 326

3. 8 925 627 829 7 978 735 926

4. 75 826 425 139 75 826 425 142

5. 182 373 003 146 182 373 003 164

WholeNumbers,NumberTheory,andFractions 11

The search for the World’s Top Singing Idol was launched in the highest rated television station. The top 5 singing idol hopefuls garnered the following text votes all over the world.

Fill in the blanks with a digit that will make the ranking of the idols correct. 1. Singing Idol A 92 3 __ __ 405 302 2. Singing Idol D 92 3 __ __ 139 406 3. Singing Idol E 87 __ __ 3 439 127 4. Singing Idol C 87 __ __ 3 203 725 5. Singing Idol B 87 __ __ 8 302 905

A. Compare the numbers. Write < or > in the box.

1. 39 426 104 39 462 139 4. 32 926 428 926 32 926 428 629 2. 526 927 324 526 927 423 5. 625 829 327 412 625 828 327 415 3. 9 825 326 008 9 825 326 800

B. Arrange the numbers from least to greatest. Write 1 (least) to 3 (greatest) in the blanks.

1. 8 723 142 7 829 602 7 826 342

2. 104 602 008 104 602 080 104 602 800

3. 92 829 523 92 826 439 92 838 426

4. 33 402 926 134 33 402 962 426 33 402 923 246

5. 825 302 411 321 832 412 142 008 894 142 602 000

1� MathforSmartKids5

Lesson 3 Rounding off Numbers

Look at the table below.

Top 10 Most Populated Countries in the World

Rank Country Population

1 China 1 330 044 605

2 India 1 147 995 898

3 United States 303 824 646

4 Indonesia 237 512 355

5 Brazil 191 908 598

6 Pakistan 167 762 040

7 Bangladesh 153 546 901

8 Russia 140 702 094

9 Nigeria 138 283 240

10 Japan 127 288 419

Source: Internet World Stats. http://www.internetworldstats.com/stats8.htm (accessed 20 May 2009)

What is China’s population rounded off to the nearest millions?

To answer this question, you need to round off the population of China. Study the figure below.

1 2 3 4 5 6 7 8 9 10 Round down if the digit to the right of the place value you are rounding off to is 4 or less.

1. Retain the digit in the place value you are rounding off to.

2. Replace the remaining digits to the right with zeros.

Round up if the digit to the right of the place value you are rounding off to is 5 or more.

1. Add 1 to the digit in the place value you are rounding off to.

2. Replace the remaining digits to the right with zeros.

0

WholeNumbers,NumberTheory,andFractions 1�

Round off 1 330 044 605 to the nearest

millions 1 3 3 0 0 4 4 6 0 5 1 330 000 000

ten millions 1 3 3 0 0 4 4 6 0 5 1 330 000 000

hundred millions 1 3 3 0 0 4 4 6 0 5 1 300 000 000

billions 1 3 3 0 0 4 4 6 0 5 1 000 000 000

Therefore, there are about 1 330 000 000 people living in China.

1. When do you round up? round down? 2. How do you round off numbers through millions?

In rounding off a number, look at the digit in the place value you are rounding off and identify the digit to its right. If the digit to its right is 5 or more, round up. Add 1 to the digit in the place value you are rounding off, then replace the remaining digits to the right with zeros. If the digit to the right is 4 or less, round down. When you round down a digit, retain the digit in the place value you are rounding off. Then, replace the remaining digits to the right with zeros.

Round off each number to the nearest place value indicated.

Number Millions Hundred Thousands Ten Thousands

1. 426 945 126

2. 824 136 621

3. 758 247 829

4. 566 729 124

5. 324 846 439


Number Millions Hundred Thousands Ten Thousands

6. 748 982 005

7. 834 193 448

8. 136 708 136

9. 493 625 278

10. 574 384 352

Round off each number to the indicated place value. 1. 9 805 thousands 2. 12 302 hundreds 3. 156 235 ten thousands 4. 3 845 364 millions 5. 36 081 426 ten millions 6. 785 320 437 ten millions 7. 8 829 009 621 billions 8. 15 826 435 085 ten billions 9. 159 927 390 713 hundred billions 10. 304 038 592 004 billions

A house owner, who is leaving for abroad, plans to sell his house including all his appliances. The selling price of the house is P 5 534 000. The appliances are marked as follows: refrigerator — P 16 700 television — P 24 300 aircon — P 11 500

Without using paper and pencil, or a calculator, how would you compute for the total amount instantly? What is the approximate total amount? Is it a good estimate?


Lesson 4 Adding Whole Numbers

Properties of Addition

Look at each set of equations below. Write down what you observe.

Set A Set B Set C

125 + 206 = 206 + 125 331 = 331

(583 + 926) + 428 = 583 + (926 + 428) 1 509 + 428 = 583 + 1 354 1 937 = 1 937

5 496 + 0 = 5 496 5 496 = 5 496

Look at set A. Focus on the order of the addends. What happened to the order of

the addends? Did the sum change? Set A illustrates the commutative property of addition. This property states that changing the order of the addends does not change the sum.

Look at set B. How are the addends grouped? Did the sum change? Another property of addition is illustrated here—the associative property of addition. The associative property of addition states that changing the grouping of the addends does not affect the sum.

Look at set C. What happens when zero is added to a number? Zero is known as the identity element for addition. When you add zero to a number, the identity property of addition is observed. This property states that the sum of a number and zero is the number itself.

Adding Numbers through Millions

In a combined effort of two organizations, a fund-raising project was launched to raise funds for typhoon victims. Organization A was able to raise P 4 362 890, while Organization B was able to raise P 5 471 008. How much money was raised by the two organizations?


Step 1. Align the digits of the addends according to their place values.

4 362 890+ 5 471 008 9 833 898

Step 2. Add the digits in the units period starting from the rightmost place value (ones). Write the sum below the digits being added. Regroup if needed.

Step 3. Add the digits from right to left in the thousands period. Regroup if needed.

Step 4. Add the digits from right to left in the millions period. Regroup if needed.

1

4 362 890+ 5 471 008 833 898

1 4 362 890+ 5 471 008

4 362 890+ 5 471 008 898

1. From what place value did you start adding? 2. What is the period of the digits that you added first? 3. If the sum of the digits is more than 9, what do you do?

The properties of addition are the commutative property, the associative property, and the identify property. Zero is known as the identity element of addition.

In adding numbers, align the digits of the addends according to their place values. Add the digits in the units period starting from the ones digit. Then, add the digits, from right to left, in the thousands and millions period. If the sum of the digits is more than 9, regroup to the next place value.

To find the answer, follow these steps in adding numbers.


A. Identify the property of addition shown in each equation. 1. 3 654 + 0 = 3 654 2. 4 351 + 3 610 = 3 610 + 4 351 3. (3 629 + 4 317) + 4 216 = 3 629 + (4 317 + 4 216) 4. 6 211 + (4 652 + 9 275) = (6 211 + 4 652) + 9 275 5. 0 + 1 295 602 408 = 1 295 602 408

B. Fill in the box with the correct number to show a property of addition. Then,

identify the property of addition illustrated in each.

1. 486 + 3 749 = + 486

2. 9 357 + = 9 357

3. + 5 982 = 5 982 + 9 285

4. 4 398 = 4 398 +

5. 6 743 + = 1 925 + 6 743

6. 982 + (697 + 528) = (982 + 697) +

7. 629 + (3 456 + 928) = (629 + ) + 928

8. ( + 8 299) + 4 673 = 4 664 + (8 299 + 4 673)

9. (9 465 + ) + 5 374 = 9 465 + (9 825 + 5 374)

10. 4 679 + (8 263 + 9 489) = (8 263 + 9 489) +

C. Find the sum.

1. 38 726 630 3. 12 743 981 5. 900 170 156 + 90 721 819 + 57 914 162 + 25 107 253

2. 210 725 351 4. 94 026 357 + 324 186 415 + 15 008 438


Solve the following problems.

1. In a nearby province, a landslide damaged a school building, a bridge, and a barangay center. The province needs P 1 512 650 to build another school building, P 3 421 540 to repair the bridge, and P 1 320 000 to rebuild the barangay center. How much money is needed to rebuild the structures that the landslide damaged?

2. Two teams of players are going to play volleyball. For the first game, team A has 10 players while team B has 11. For the second game, team A has 11 players while team B has 10. Considering both games, is the number of players fair to the two teams? Why?

A. Find the sum.

1. 194 281 3. 927 014 5. 57 263 455 + 625 132 + 356 820 + 18 900 516

2. 96 502 291 4. 658 166 800 + 12 816 589 + 132 823 918

B. Complete the addition equations below and identify the property shown.

1. 325 + 391 = + 325

2. 4 635 + 0 =

3. (928 + 425) + 391 = 982 + ( + 391)

4. + (7 928 + 9 284) = (8 276 + 7 928) + 9 284

5. 17 829 + 0 =


A country has 75 826 427 registered voters. Of this number, 64 936 316 exercised their right to vote during the presidential election. How many failed to vote?

Lesson 5 Subtracting Whole Numbers

Step 1. Write the subtrahend below the minuend. Align the digits with the same place value.

Step 2. Subtract the digits in the units period starting from the rightmost place value (ones). Write the difference under the digits being subtracted. Regroup if needed.

Step 3. Subtract the digits from right to left in the thousands period. Regroup if needed.

Step 4. Subtract the digits from right to left in the millions period. Regroup if needed.

75 826 427– 64 936 316 10 890 111

4 1712

75 826 427– 64 936 316 890 111

4 1712

75 826 427– 64 936 316 111

75 826 427– 64 936 316

Therefore, 10 890 111 failed to vote.

In the problem above, you need to subtract to find the answer. Study the following steps to perform subtraction.

�0 MathforSmartKids5

Here is another example.

Step 1: Step 2:

9 342 827– 7 213 925 2 128 902

31118

Hence, the difference is 2 128 902.

9 342 827– 7 213 925 128 902

311 18 9 342 827– 7 213 925

9 342 827– 7 213 925 902

1. What is the period of the digits that you subtracted first? 2. If the subtrahend is less than the minuend, what should you do?

In subtracting numbers, write the subtrahend below the minuend and align the digits with the same place value. Start subtracting from the ones digits in the units period. Then, continue subtracting the digits from right to left. If the subtrahend is greater than the minuend, rename the digit in the next higher place value and regroup.

A. Subtract.

1. 82 782 837 2. 738 000 136 3. 394 826 927 – 51 653 747 – 259 345 024 – 135 908 918

4. 92 343 983 5. 523 925 321 – 51 814 862 – 121 686 410

Step 3: Step 4:1 18

WholeNumbers,NumberTheory,andFractions �1

You are asked to prepare an inventory of unsold items in a boutique. How would you do this without counting the unsold items? Here are the data.

Items Total Number of Pieces Number of Pieces Sold

Dresses 375 892 286 391

Pants 469 527 358 792

Blouses 569 375 387 453

1. 6 0 0 0 3 –

5 6 3 5 2

2. 7 8 3 0 0 3 –

5 4 2 5 2 5

3. 3 2 4 8 9 6 – 3 2 5 6 7

4. – 8 2 9 6 2 5 1 3 5 2 1 6 8 9 9 8 6 3

5. 4 2 7 8 2 9 3 1 5 – 1 1 8 7 3 8 3 1 5

Find the difference.

1. 398 295 2. 87 926 425 3. 895 629 821 – 326 132 – 23 489 514 – 326 783 950

4. 826 713 5. 926 532 491 – 314 824 – 714 856 590

B. Find the missing numbers.

�� MathforSmartKids5

Properties of Multiplication

Look at the sets of multiplication equations below. Note what you observe.

Lesson 6 Multiplying Whole Numbers

Set A Set B Set C

392 × 685 = 685 ×392 268 520 = 268 520

(683 × 421) × 5 = 683 × (421 × 5) 287 543 × 5 = 683 × 2 105 1 437 715 = 1 437 715

8 620 × 0 = 0 0 × 8 620 = 0

Look at set A. How are the factors arranged on both sides of the equation? What happened to the product? In set A, you can observe one property of multiplication called the commutative property of multiplication. This property states that changing the order of the factors does not change the product.

Look at set B. How are the factors grouped on each side of the equation? What happened to the product? In set B, you see that changing the grouping of the factors does not change the product. This shows the associative property of multiplication.

Look at set C. What happens when a factor is multiplied by zero? This set shows the zero property of multiplication. This property states that when 0 is a factor, the product is 0.

How many operations are involved in set D? What are these operations? In set D, where the distributive property combines multiplication and addition, you can observe the distributive property of multiplication over addition. This property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding their products.

In set E, when 1 is multiplied by a number, the product is that number. This shows the identity property of multiplication. One (1) is known as the identity element for multiplication.

Set D Set E

942 × (8 +2) = (942 × 8) + (942 × 2) 942 × 10 = (942 × 8) + (942 × 2) = 7 536 + 1 884 9 420 = 9 420

90 420 ×1 = 90 420