PREFACE
L
Exercises
Examples
N
Power-Up Math, is a new series applying Singapore Math strategies
aligned with the Department of Education’s K to 12 Curriculum.
This series follows the Concrete-Pictorial-Abstract Approach which
benefits all types of pupils in mastering the basic competencies in
S
Mathematics. The book uses
attractive illustrations, pictures, and
ES O
appropriate tools and manipulatives for an easier grasp and better
retention of the concepts.
The Power-Up Math Grade 5 textbook is composed of 15
chapters with guided examples and exercises for every lesson.
Lessons are presented in a direct and simple manner.
les Examples are explained in greater
p
m
a
x
E
detail, provided to give emphasis
and elaboration on concepts and
their applications.
Exercises are parallel to each example,
allowing the learners to practice and
reinforce what they have learned.
These are categorized into increasing
levels of difficulties.
Exercises
Combined with interesting and real-life situations, this book offers
the best possible start of mastering the basics. Learners are
expected to learn on their own with less guidance from the teacher.
iii
Table of Contents
CHAPTER
1
Whole Numbers Within 10 Million
Lesson 1Numbers to 10 Million
1
Lesson 2
6
Place Value and Value
S
ES O
N
L
Exercises Comparing and Ordering
Lesson 4
Rounding Off to the Nearest
s
Example
Thousands
and Millions
Lesson 3
2Number Sense
Lesson 1 Prime Factorization
23
Lesson 2 Greatest Common Factor
27
Lesson 3 Least Common Multiple
34
Lesson 4 Divisibility Rules for 2, 5, and 10
40
Lesson 5 Divisibility Rules for 3, 6, and 9
43
Lesson 6 Divisibility Rules for 4, 8, 11,
and 12
47
52
Enrichment
CHAPTER
3Fractions
Lesson 1 Equivalent Fractions
Lesson 2 Comparing and Ordering of
Fractions
iv
17
22
Enrichment
CHAPTER
10
53
60
Lesson 3 Simplifying Fractions
Enrichment
CHAPTER
4
68
74
Addition and Subtraction
Lesson 1 Adding Dissimilar Fractions
75
Lesson 2 Subtracting Dissimilar Fractions
82
Lesson 3 Adding Fractions and Mixed
Numbers
Lesson 4 88
Subtracting Fractions and
Mixed Numbers
94
Enrichment
98
CHAPTER
5
Multiplication of Fractions
Lesson 1 Multiplying Proper Fractions
Lesson 2 Multiplying Fractions and
Whole Numbers
Lesson 3 99
106
Multiplying Fractions and
Mixed Numbers
112
Enrichment
118
CHAPTER
6
Lesson 1 Division of Fractions
Dividing Proper and
Improper Fractions
Lesson 2 119
Dividing Fractions by a
Whole Number
124
v
Lesson 3 Dividing Mixed Numbers
136
Enrichment
CHAPTER
7Decimals
Lesson 1 Fractions and Decimals
137
Lesson 2 Place Value and Value
141
Lesson 3 Comparing and Ordering
146
Lesson 4 Rounding Off Decimals
153
160
Enrichment
CHAPTER
8Operations on Decimals
Lesson 1 Adding Decimals
161
Lesson 2 Subtracting Decimals
167
Lesson 3 Multiplying Decimals
174
Lesson 4 Dividing Decimals
180
186
Enrichment
CHAPTER
9Ratio and Proportion
Lesson 1 Ratio
187
Lesson 2 Proportion
195
Word Problems
205
Lesson 3 Enrichment
vi
130
210
CHAPTER
10 Polygons
Lesson 1 Polygons and Its Properties
211
Lesson 2 Congruent Polygons
220
Lesson 3 Similar Polygons
227
234
Enrichment
CHAPTER
11 Circle and Its Parts
Lesson 1 Circles
235
Lesson 2 Terms Related to a Circle
241
250
Enrichment
CHAPTER
12 Percent
Lesson 1 Percent
251
Lesson 2
Percentage, Rate, and Base
257
Lesson 3
Word Problems
263
268
Enrichment
CHAPTER
13 Lesson 1 Patterns and Algebra
Understanding Mathematical
Sentence
Lesson 2 Enrichment
Solving Simple Equations
269
272
278
vii
CHAPTER
14 Measurement
Lesson 1
Lesson 2 Units of Measure
284
Lesson 3 Area of a Circle
295
Lesson 4 Volume of a Cube and a
Circumference
Rectangular Prism
302
Lesson 5 Temperature
306
312
Enrichment
CHAPTER
15 Lesson 1 viii
279
Statistics and Probability
Tables and Line Graphs
313
Lesson 2 Probability
322
Enrichment
330
Chapter
Whole Numbers within
10 Million
ES
SO
1
N
L
1
Numbers to 10 Million
L
Observe these
numbers.
S
ES O
N
Exercises
Examples
Number of Enrollees SY 2015 – 2016
415 926
City Population
653 284
HOUSE FOR SALE
₱ 1 000 000
The numbers below are grouped in three digits starting from the right.
415 926
Millions
653 284
1 000 000
Hundred
Ten
Thousands Hundreds
Thousands Thousands
Tens
Ones
415 926
653 284
1 000 000
10 hundred thousands = 1 million
1
Observe these numbers.
The numbers below are grouped in three digits starting from the right.
1 254 503
Ten
Millions
5 089 111
10 000 000
Hundred
Ten
Thousands Hundreds Tens Ones
Thousands Thousands
Millions
1 254 503
5 089 111
10 000 000
10 millions = 1 ten million
Read these numbers.
A 415 926
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
4
1
5
9
2
6
First, read the thousands part: “four
hundred fifteen thousand”
Then, read the units part: “nine
hundred twenty-six”
In words, 415 926 is written as “four hundred fifteen thousand, nine hundred
twenty-six.”
2
B 4 950 080
Millions
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
4
9
5
0
0
8
0
First, read the
millions part:
“four million”
Lastly, read
the units part:
“eighty”
Then, read the thousands part:
“nine hundred fifty thousand”
In words, 4 950 080 is written as “four million, nine hundred fifty thousand,
eighty.”
C 8 653 284
Millions
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
8
6
5
3
2
8
4
First, read the
millions part:
“eight million”
Then, read the thousands
part: “six hundred fifty-three
thousand”
Lastly, read the units
part: “two hundred
eighty-four”
In words, 8 653 284 is written as “eight million, six hundred fifty-three thousand,
two hundred eighty-four.”
3
Examples
1 Write in words.
534 516
=
five hundred thirty-four thousand, five hundred
sixteen
7 034 579
=
seven million, thirty-four thousand, five hundred
seventy-nine
3 009 000
=
three million, nine thousand
9 999 999
=
nine million, nine hundred ninety-nine thousand,
nine hundred ninety-nine
653 104
=
six hundred fifty-three thousand, one hundred four
2 Write in number symbols.
four million, one hundred twenty-four thousand,
seven hundred ninety-five
ight million, ninety-seven thousand,
e
four hundred fifty-three
six million, seventy-five
4
4 124 795
8 097 453
6 000 075
one million, one hundred one thousand, eight
1 101 008
five million, five hundred fifty thousand
5 550 000
Exercises
1 Write in words.
629 745
=
2 331 789
=
9 885 000
=
8 660 044
=
5 300 407
=
2 Write in number symbols.
ine million, eight hundred thirty-nine
n
thousand, four hundred fifty-four
four million, two hundred nine
thousand, eleven
s even hundred twenty-three thousand,
ninety-nine
three million, three thousand, three
ight million, nine hundred forty
e
thousand
two million, three hundred sixty-nine
thousand, one hundred forty-six
5
L
SO
2
N
ES
Place Value and Value
Let us show the number 567 425 in the place value chart.
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
5
6
7
4
2
5
The digit 5 is in the hundred thousands place.
The digit 6 is in the ten thousands place.
The digit 7 is in the thousands place.
The digit 4 is in the hundreds place.
The digit 2 is in the tens place.
The digit 5 is in the ones place.
The digit 5 stands for 500 000.
The value of the digit 5 is 500 000.
Digit
Value
5
500 000
6
60 000
7
7000
4
2
5
400
20
5
The digit 6 stands for 60 000.
The value of the digit 6 is 60 000.
The digit 7 stands for 7000.
The value of the digit 7 is 7000.
The digit 4 stands for 400.
The value of the digit 4 is 400.
The digit 2 stands for 20.
The value of the digit 2 is 20.
The digit 5 stands for 5.
The value of the digit 5 is 5.
567 425 = 5 hundred thousands + 6 ten thousands + 7 thousands +
4 hundreds + 2 tens + 5 ones
= 500 000 + 60 000 + 7000 + 400 + 20 + 5
= 567 425
6
Let us show the number 4 398 781 in the place value chart.
Millions
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
4
3
9
8
7
8
1
The digit 4 is in the millions place.
Digit
Value
The digit 3 is in the hundred thousands place.
The digit 9 is in the ten thousands place.
The digit 8 is in the thousands place.
4
4 000 000
3
300 000
9
The digit 7 is in the hundreds place.
The digit 8 is in the tens place.
The digit 1 is in the ones place.
8
7
8
1
90 000
8000
700
80
1
The digit 4 stands for 4 000 000.
The value of the digit 4 is 4 000 000.
The digit 3 stands for 300 000.
The value of the digit 3 is 300 000.
The digit 9 stands for 90 000.
The value of the digit 9 is 90 000.
The digit 8 stands for 8000.
The value of the digit 8 is 8000.
The digit 7 stands for 700.
The value of the digit 7 is 700.
The digit 8 stands for 80.
The value of the digit 8 is 80.
The digit 1 stands of 1.
The value of the digit 1 is 1.
7
Examples
1 Identify the value of the digit 2 in each of the following numbers.
7 265 000
=
200 000
812 000
=
2000
2 093 711
=
2 000 000
1 020 137
=
20 000
5 300 427
=
20
2 Write the place value of the digit 5 in each of the following numbers.
6 568 681
=
hundred thousands
5 273 047
=
millions
231 590
=
hundreds
1 005 004
=
thousands
2 300 457
=
tens
3 Complete the following sentences.
In 8 622 776, the digit
8
is in the millions place.
6
In 1 367 931, the digit in the ten thousands place is
In 378 904, the digit 3 is in the
In 9 841 793, the digit 9 is in the
8
hundred thousands
million and tens
place.
place.
.
Exercises
1 Identify the value of the digit 2 in each of the following numbers.
2 975 001
=
788 200
=
3 102 731
=
7 820 911
=
2 907 300
=
2 Write the place value of the digit 6 in each of the following numbers.
6 392 524
=
113 060
=
4 961 085
=
1 006 004
=
7 650 002
=
3 Complete the following sentences by identifying the place value of the number
4 356 705.
The digit
is in the millions place.
The digit in the ten thousands place is
.
The value of the digit 4 is
The digit 3 is in the
.
place.
9
L
SO
3
N
ES
Comparing and Ordering
Comparing numbers within 10 Million
According to the 2010 Census, the population of the following cities in Metro
Manila are as follows:
City
Population
Caloocan
1 489 040
Las Piñas
552 573
Makati
529 039
Malabon
353 337
Mandaluyong
328 699
Manila
1 652 171
Marikina
424 150
Muntinlupa
459 941
Navotas
249 131
Paranaque
588 126
Pasay
392 869
Pasig
397 679
Quezon
2 761 720
San Juan
121 430
Taguig
644 473
Valenzuela
575 356
Between Mandaluyong and
Las Piñas City, which is more
populated?
10
City
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
Mandaluyong
3
2
8
6
9
9
Las Piñas
5
5
2
5
7
3
Compare the hundred thousands.
Digit 5 in hundred thousands place is greater than digit 3
in hundred thousands place.
FYI
So, 552 573 is greater than 328 699.
In symbols, 552 573 > 328 699.
Las Piñas is more populated than Mandaluyong.
CRISMonicaRachel
CRISMonicaRachel
CRISMonicaRachel



 



In comparing
numbers, look at
the value of each
digit starting from
the left.
Between Pasay and
Pasig, which city is more
populated?
City
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
Pasay
3
9
2
8
6
9
Pasig
3
9
7
6
7
9
Compare the hundred thousands.
The digits are the same.
Compare the ten thousands.
The digits are the same.
Compare the thousands.
The digits are not the same.
Digit 2 in thousands place is lesser than the digit in thousand in 7 thousands
place.
So, 392 869 is less than 397 679.
In symbols, 392 869 < 397 679.
Pasay is less populated than Pasig.
11
Which is more populated,
1 489 040 in Caloocan or
1 652 171 in Manila?
Hundred
Ten
Thousands Hundreds
Thousands Thousands
City
Millions
Caloocan
1
4
8
9
Manila
1
6
5
2
Tens
Ones
0
4
0
1
7
1
Compare the millions.
The digits are the same.
Compare the hundred thousands.
Digit 6 in hundred thousands place is greater than the digit 4 in hundred
thousands.
So, 1 652 171 is greater than 1 489 040.
In symbols, 1 652 171 > 1 489 040.
Manila is more populated than Caloocan.
12
Examples
1 Which is greater: 6 093 840 or 3 028 689? 6 093 840
2 Which is lesser: 7 283 026 or 7 204 392? 7 204 392
3 Arrange the numbers in increasing order.
849 268
974 024
261 056
261 056
849 268
974 024
1 983 638
1 925 835
935 098
935 098
1 925 835
1 983 638
4 Arrange the numbers in decreasing order.
496 926
950 725
527 938
950 725
527 938
496 926
3 914 021
3 937 926
939 106
3 937 926
3 914 021
939 106
5 Compare the value of the numbers below. Use greater than (>), less than (<) or
equal sign (=).
328 699
<
552 573
505 211
=
505 211
1 489 040
>
644 473
121 356
<
1 121 356
529 039
<
588 126
654 244
>
654 144
13
Exercises
1 Which is greater: 3 354 671 or 1 231 872?
2 Which is lesser: 820 346 or 820 416?
3 Arrange the numbers in increasing order.
325 140 7 080 923
476 190
8 923 070
231 760
7 090 823
345 765
7 023 980
4 Arrange the numbers in decreasing order.
324 455
561 715
452 916
971 436
247 896
2 478 961
776 541
7 765 412
5 Compare the value of the numbers below. Use greater than (>), less than (<) or
equal sign (=).
14
72 573
728 610
3 652 132
3 652 123
313 473
313 473
2 149 121
2 941 720
219 009
819 009
912 829
921 219
Ordering numbers within 10 Million
Population
Arrange the population
in increasing order.
1 489 040
1 529 039
1 353 337
1 424 150
1 644 473
Millions
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
1
4
8
9
0
4
0
5
2
9
0
3
9
3
5
3
3
3
7
4
2
4
1
5
0
6
4
4
4
7
3
First, compare all the digits in the millions place.
1 is the greatest. So, 1 489 040 is the greatest number.
Next, compare the digits in the hundred thousands place.
3 is the least. So, 353 337 is the least number.
4 is next to the least. So, 424 150 is next to the least number.
Then, compare the remaining digits in the hundred thousands place. 5 is less
than 6. So, 529 039 is less than 644 473.
Lastly, arrange the numbers in increasing order.
353 337
424 150
529 039
644 473
1 489 040
15
Arrange the population
in decreasing order.
Population
1 588 126
1 652 171
1 121 430
1 459 941
2 761 720
Millions
1
2
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
5
8
8
1
2
6
6
5
2
1
7
1
1
2
1
4
3
0
4
5
9
9
4
1
7
6
1
7
2
0
First, compare the millions.
2 is the greatest. So, 2 761 720 is the greatest number.
1 is next to the greatest. So, 1 652 171 is next to the greatest number.
Next, compare the hundred thousands of the remaining numbers.
5 is the greatest. So, 588 126 is third to the greatest number.
Then, compare the remaining digits in the hundred thousands place. 1 is less
than 4. So, 121 430 is less than 459 941.
Lastly, arrange the numbers in decreasing order.
2 761 720 1 652 171 588 126 459 941 121 430
16
L
SO
4
N
ES
Rounding off to the Nearest Thousands
and Millions
Round off 7525 to the
nearest thousand.
7525
7000
7500
8000
7525 is between 7000 and 8000.
7525 is nearer to 8000 than to 7000.
7525 is 8000 when rounded off to the nearest thousand.
We say 7525 is approximately equal to 8000.
We write 7525 ≈ 8000.
Round off 7264 to the
nearest thousands.
7264
7000
7500
8000
17
7264 is between 7000 and 8000.
7264 is nearer to 7000 than to 8000.
7264 is 7000 when rounded off to the nearest thousands.
We say 7264 is approximately equal to 7000.
We write 7264 ≈ 7000.
What is 125 934 rounded off to
the nearest hundred thousands?
125 934
100 000
150 000
200 000
125 934 is between 100 000 and 200 000.
125 934 is nearer to 100 000 than to 200 000.
125 934 is 100 000 when rounded off to the nearest hundred thousand.
We say 125 934 is approximately equal to 100 000.
We write 125 934 ≈ 100 000.
18
Round off 7 525 264 to the
nearest million.
7 525 264
7 000 000
7 500 000
8 000 000
7 525 264 is between 7 000 000 and 8 000 000.
7 525 264 is nearer to 8 000 000 than to 7 000 000.
7 525 264 is 8 000 000 when rounded off to the nearest million.
We say 7 525 266 is approximately equal to 8 000 000.
We write 7 525 266 ≈ 8 000 000.
19
Examples
1 Round off 1 281 255 to the nearest hundred thousand.
1 281 255
1 200 000
1 250 000
1 281 255 ≈
1 300 000
1 300 000
2 What is the rounded off value of 952 432 to the nearest ten thousands?
952 432
950 000
950 432 ≈
955 000
960 000
950 000
3 Round off these numbers to the nearest million.
8 721 120 ≈
9 000 000 3 532 446 ≈
4 000 000
1 213 325 ≈
1 000 000 6 623 219 ≈
7 000 000
4 Round off each number to the nearest place value as indicated.
20
Millions
Hundred
Thousands
Ten
Thousands
Thousands
1 234 567
1 000 000
1 200 000
1 230 000
1 235 000
3 250 865
3 000 000
3 300 000
3 250 000
3 251 000
6 624 400
7 000 000
6 600 000
6 620 000
6 624 000
9 756 715
10 000 000
9 800 000
9 760 000
9 757 000
Exercises
1 Round off 927 390 to the nearest ten thousand.
927 390 ≈
2 What is the rounded off value of 4 329 385 to the nearest hundred thousand?
4 329 385 ≈
3 Round off these numbers to the nearest million.
6 281 987 ≈
5 555 555 ≈
1 999 620 ≈
4 654 643 ≈
4 Round off each number to the nearest place value as indicated.
Millions
Hundred
Thousands
Ten
Thousands
Thousands
1 702 000
8 652 098
3 143 645
9 999 999
9 756 715
21
Enrichment
Population Alert!
The population of some provinces in the Philippines are shown below:
Province
Population
Province
Population
Batangas
2 377 395
Davao
3 781 368
Rizal
2 484 840
Laguna
2 669 847
Bacolod
511 820
Cebu
3 836 000
Camiguin
83 807
Aklan
535 725
Cagayan de Oro
602 088
Palawan
736 930
1 Which province has the largest population? What is its population in
numerals?
2 Which province has the least population? What is its population in words?
3 Which province has a larger population: Batangas or Laguna?
4 What provinces have more than 2 500 000 population?
5 Arrange the provinces in order, beginning with the province with the least
population.
6 What provinces have population of 500 000 when rounded off to the
nearest hundred thousand?
22