1.
Enhance Mathematics-Quiz
Bee Review Materials by
BOYET B. ALUAN S, 2014
Math Exercises for Daily Use
This material covers the learning competencies for grade six . it simply aims to aid pupils to
comprehend and learn the concept to easily apply it in the real battle on the subjects.
2014
Boyet B. Aluan
BSE-Math, Teacher 1, MAED Mg’t
1/1/2014
2.
Math Six Reviewer (RBEC)
Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014
Page1MathExercisesforDailyUse
Boyet B. Aluan
ANSWERs DESCRIPTION/QUESTIONS/IDEAS/FACTS/EXPLANATION/DETAILS
HISTORY OF NUMBERS
NUMERALS Are written symbols for numbers and were probably develop first before
number words because it is easier to engrave marks that produce phrases
to identify a number.
NUMERATION SYSTEM Is a logical structured collection of numerals.
TALLY AND IMPROVE
TALLY NUMERATION
SYSTEM
Is one of the earliest systems of numeration. Though simple, it is difficult to
use for very large numbers as it requires many individual strokes.
EGYPTIAN NUMERATION
SYSTEM
By 3400 BC., it is the used of hieroglyphics or picture symbols in expressing
numbers. In this numeration there were seven symbols used. This system is
additive and can repeat symbols as many times as needed.
BABYLONIAN
NUMERATION SYSTEM
This numeration used only two symbols to express numbers. They took the
ideas of Egyptian adding system and brought new level. Symbol from 1-59
were formed by adding the value of each symbol. This system introduce
the used of place value system with places representing the different
multiples of 60.
GREEK NUMERATION
SYSTEM
They had two numeration system: Attic and Iconic numeration systems.
The attic used 6 symbols while the iconic used 27 symbols.
ATTIC NUMERATION
SYSTEM
I=1, ┌ -5, ∆= 10, χ= 1 000, Μ= 1 000 000.
ICONIC NUMERATION
SYSTEM
A=1, B=2, Γ=3, Δ=4, E=5, ς=6, Ζ=7, Η=8, Θ=9, Ι=10, Κ=20, Λ=30, M=40,
N=50,Ξ=60, O=70, Π=80, ϕ=90, P=100, Σ=200, T=300, Y=400, Φ=500,
X=600, Ψ=700, Ω=800, San=900.
CHINESE NUMERATION
SYSTEM
There are three schemes in this numeration, 1. The Standard or
Traditional,2 the Official and 3. Commercial or Mercantile. This is the
reason why this system of numeration is the most superior among than
that of Egyptians and Babylonian because it is based on 10 or decimal
which were similar to the system we used today but does not have place
value.. the numerals are written in vertical columns with powers of ten
placed in descending order from top to bottom. However can also be
written in horizontal form.
HSIAO-HSIEH Small or common is the traditional or standard numerals used by the early
Chinese. However, these numerals are often referred as modern form, they
are neither ancient nor medieval but were used during the third century
BC.
TA-HSIEH Means great writing, is the official numerals. These numerals are highly
ornamented to protect them from any falsification on bank notes, contract
and the likes. These were first used during the first century BC and are
occasionally found in mathematical texts.
MA-TZU OR AN MA TZU The commercial numerals of the Chinese, means confidential weight
numerals. These numerals are used by merchants or businessmen to write
numbers rapidly on less critical documents like price tags.
ARABIC OR HINDU-ARABIC This system is employed by the greater part of the world. It was developed
in India by the Hindus but it was the Arab who transmitted this system to
the west, thus the numerals have become called Arabic.
ROMAN NUMERATION
SYTEM
One of the most popular and similar system of numeration. It is widely
used until now in the book chapters, clock numerals and formal inscription.
It was developed because of peak civilization at around 100 AD. For record
keeping and accounting brought about taxes collection and exchange of
goods in the vast empire. It was based on Greek systems, just like Egyptian
numerals, additive system is applied with a few twists. These systems has
no place value and does not have zero (0) symbol. There are basically
seven-letter symbol used (I-1,V-5,X=10, L=50, C=100, D=500, M=1
000)please study charts on performing equation.
Place Value and e Value of Whole Numbers and Decimals
3.
Math Six Reviewer (RBEC)
Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014
Page2MathExercisesforDailyUse
384 422 016 987 648 Three hundred eighty-four trillion, four hundred twenty-two billion, sixteen
million, nine hundred eighty-seven thousand, six hundred forty-eight
written in standard form is?
0. 547 139 Read as five hundred forty-seven thousand, one hundred thirty- nine
millionths.
Note: decimal point is read as and.
trillion In 0.569 781 364 789 102, what is the place value of underline digit?
1 hundred millionths or
0.000 000 01
120 016. 547 896 16, what is the value of underlined digit?
975 135 478 Can be written as nine hundred seventy-five million one hundred thirty-five
thousand four hundred seventy- eight.
487 950 753 011. 099 Four hundred eighty-seven billion, nine hundred-fifty million, seven
hundred fifty-three thousand eleven and ninety-nine thousandths.
631. 000 487 678 Six hundred thirty-one and four hundred eighty seven hundred
thousandths six hundred seventy-eighty billionths.
= Compare 18.246 to 18. 246 000
> Compare 594.753 951 to 549. 352 000
< Compare 926.19 to 1 926.90
49 Round 48.972 to the nearest ones.
164 990 Round 164 985 to the nearest tens
951 400 Round 951 357 to the nearest hundreds
852 862 000 852 862 248 round to the nearest thousands
729 814 000 000 729 813 624 984 round to the nearest million
(3x104
) + (5𝑥103) +
(4𝑥102) + (1𝑥101) +
(2𝑥100
)
Write 35 412 in expanded exponential form
(8𝑥109) + (4𝑥108) +
(6𝑥107) + (3𝑥106) +
(2𝑥10 5) + (3𝑥104) +
(7𝑥103) + (9𝑥102) +
(5𝑥101
)+(3x100
)
Write 8 463 237 953 in expanded exponential form
7 864 382 Write (7𝑥106) + (8𝑥105) + (6𝑥104) + (4𝑥103) + (3𝑥102) + (8𝑥101) +
(2𝑥100) in standard form. Note any number raised to zero equal to one (1)
Operations Involving Whole Numbers and Decimals.
Notes
Addition is the process of putting things together or combining two or
more numbers which results to only one number called sum or total. They
used the phrases increase by, plus, sum up, added to, more than, the total
of., greater,
Subtraction on the other hand is an operation inverse to addition. It is a
process of taking away a number from another. Is has two parts (minuend
on the upper part, and subtrahend on the lower part). Words like minus, less, reduce by,
difference between, decreased by, and diminished by, negative and less
than denotes subtraction. Difference is the answer in subtraction.
362,975,375,629 What is the sum of 359 741 987 456, 745 987 201 and 369 852 increased
by 2 487 364 120?
874,371,689 What is 874 362 001 more than the results of 145 increased by 9 543?
7,548.320019 What is the sum of 48.236, 7125.168, 362.9 and 12.016019?
268.373 Find the results of 2.54 plus 68.95 added to the sum of 214.004 and 0.879
134.885 Find the answer when 587.065 is diminished by 452.18
8.73 Find the results of 74.6 decreased by 65.87.
197,879,904 What is 685 111 354 less than 487 231 450?
6650 What is 96 538 minus 89 888?
132,766 Find the result when the sum of 5 764 and 38 341 is added to the
difference of 997 236 and 908 575?
57.113 What is the difference between 11. 133 and the sum of 49.32 and 18. 926?
In estimating the sums and differences, simply round off the numbers to the highest place value before
proceeding the operations
4.
Math Six Reviewer (RBEC)
Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014
Page3MathExercisesforDailyUse
Est 377 Estimate the sum of 17.4, 8.32, 0.149 and 351.000 7
Est 70 Estimate the sum of 0.487+0.698+12.462+55.3
Est 2500 Estimate the sum of 157.3+194.23+2014.69+99.14
Est 2 900 000 Estimate the sum of 684 896+412 563+954 632+751 953
100 Estimate the difference of 845-746
100 000 Estimate the difference of 874 635-784 521
Note
Division id repeated subtraction the number we divide is called dividend
and divisor the answer is quotient. Some are words used, shared,
partitioning, divided equally, fraction of, each and quotient. The steps are:
divide, multiply, subtract, bring down, and repeat all the steps until you
reach zero or dividend is less than the divisor.
762.67 Find the quotient of 91.52 and 0.12
5.2805 Find the product of 89.5 and 0.059
19.226982 What is the product of 48.309 and 0.398?
31.5 or 31 r.12 What is the quotient of 756 and 24?
8233.333 What is the result when 24.7 is divided by 0.0003?
50,303 What is the quotient of 6456 and 24 times 187?
437.5092 What is the other factor if one of them is 8032 and their product is 3 514
074?
39766/59=674 What is the divisor if the dividend is 39 766 and the quotient is 59
Solving Worded Problems Involving the Four Operations.
GEORGE POLYA Hungarian Mathematician, brilliant teacher and expositor who contributed
the four steps in problem solving involves: understand, plan, solve, and
check.(UPSC)
(196+220)-78=
338 points
During the last game, Jay-R scored 196 points while Ringo scored 220
points. If Alfred’s score is 78 less than the combined scores of the two
boys, what is Alfred’s score
214+(18x3)=
214+54=268 points
In the game of scrabble, Jonjie made a word with a point value of 18. He
placed it such that it scored three times its value. If his current score is 214,
excluding the last word, around how many points will he have?
240 525- (120 750+345)=
119,430kgs weight of cargo
A truck and all its cargoes, including the drivers’ weigh 240 525 kgs. The
truck weighs 120 750 kgs when empty. The combined weight of the drivers
is 345kgs. What is the weight of the cargo?
Joey’s=82,041points
Misty’s= 77864 points
Boysee’s=51309 points
In a group contest, 100 000 points are needed in order to win the grand
prize. Joey’s group has earned 17 959 points, Misty’s group has 22 136
points, and Boysee’s group earned 48 691 points. About how many more
points are needed by each group in order to win?
1173x2x35days=11,730
35days=7daysx5weeks
The school organized a concert. Each pupil is expected to sell at least two
tickets a week. If there are 1173 pupils, how many tickets be sold in five
weeks?
6000x26= 156,000 average
people attended the last season
The average number of people attending a basketball game is 6 000. Last
season, there were 26 games. How many people attended the last season’s
game?
1253X365=457,345
Note: use the base of 1253 instead of population
at growth
The population of a certain microorganism is increasing at a rate of 1 253
per day. At this rate how much will the population increase in 365 days?Assume
it is not exponential
₱ 35,100.00/36=
₱ 975.00 each week
Tara saved ₱ 35,100.00 in 36 weeks. She save roughly the same amount
each week. Approximately how much did she save every week?
20-(4X3)=8
8 people are in the bus after the fourth stop
Twenty people are in a bus. Three people get off at each of the next four
stops. No one gets in the bus. How many people are in the bus after the
fourth stop?
18-6=12 needed passengers so
12/3=4, six stops or equals to 26 stops to
have 18 passenger inside the bus.
Six people are in the bus. At each of the next 6 stops 3 more people get in.
no one gets off. At which stop were there 18 people in the bus?
Sophia,William. Margaret, Harry
and Stephanie so, Harry is in the
fourth place.
Five people are in a line, Margaret is directly in front of Harry. Harry is just
in front of Stephanie. William is between Margaret and Sophia. What is
Harry’s position?
Order of Operations
9+12-1x2=21-2=19 9+4X3-3÷3x2
5.
Math Six Reviewer (RBEC)
Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014
Page4MathExercisesforDailyUse
19+2 – 56 ÷ 4= 21- 14 =7 19+6÷3-8x7÷4
9 +3 X 2=9 +6 =15 (15-6)+(4-1) x 2
14-2x(2+5)=0 14-2x{2+5x[7+3X(15-12)-15]}
3x(4-6)=6 3x[4-2x(10-8)+12 ÷ 6x1]
12+3x(6)=30 12+3x{3[4+(9-8)-2]-3}
{[92]x4}x7=2576 Evaluate {[(26-3)x(8-4)]x4}x7
{60-(47)+18}-[36-
33+5]=23
{60-(43-26+15+15)+18}-[36-(14+19)+5]
96-[9-11+8]-84=6 96-{32
− [7 + 5 − (42
− 7 + 3) + 5 + 23} − 84 = 𝑛
a. 99 723
b. 99792
c. 101 723
d. 101 723
What new number will be formed if in the number 96, 753, the thousands
digits is increase by five and tens digits is increased by 3?
a. 165
b. 180
c. 170
d. 185
What is the estimated difference between 239 and 30?
a. 30
b. 3 000
c. 300
d. 30 300
Approximately, what is the quotient of 9 030 and 30?
a. 3 600
b. 3 600 000
c. 36 000
d. 36 000 000
What is the estimated product of 418 and 89?
a. 5 000
b. 6 000
c. 5 500
d. 5 100
What is the estimated difference between 9 755 and 4 651?
a. 1 800
b. 180 000
c. 18 000
d. 1 800 000
What is the estimated answer if 6 140 is multiplied by 312?
a. 138
b. 238
c. 148
d. 248
What is 225 subtracted from the sum of 65, 78,89,96, and 45?
a. 1.250
b. 1.273
c. 1.243
d. 1.293
What is the difference between the sum of 1.248 and 0.025 and the
product of 0.01 and 2.3?
a. 11.48
b. 2.56
c. 8.92
d. 1.12
What is the sum of the product of 12.8 and 0.2 and the quotient of 178.4
and 20?
a. 4 522
b. 4 284.2
c. 4 252
d. 4 224.8
The quotient of 424.82 and 0.1 increased by 3.8 is what number?
168 Evaluate (27÷ 3 + 4 × 3 − 7) × (3 × 2 × 6 ÷ 4 + 5 − 2)
4+(9)-[(88)/(8)+(16-2)-
21]=9
Performs 4 + (
34+6×3
11
) − [(43
+ 23
× 3) ÷ (4 × 2) + (24
− 2) − 21]
Father=37 y.old
Mother =33y.old
Nina is 12 years old. Father is 25 years older than Nina. Mother is 4 years
younger than father. How old is her father? Her Mother?
487+76=563 Timmy sold 487 fruits this week. This was 76 less than last week. How
many fruits did she sell last week?
𝑏
22
= 51 + 1
A certain number divided by 22 equals 51 with a remainder 1. What is the
number?
6.
Math Six Reviewer (RBEC)
Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014
Page5MathExercisesforDailyUse
(51x22)+1=1123
(56 200-15
500)÷(12+8)=2035
Meagan bought a computer package for ₱ 56 200in an installment basis.
She gave a down payment of ₱ 15 500. How much will she pay in a month if
she has to pay the remaining balance in one year and eight months?
(7x245)+(5x380)+(3x275)=
₱ 4440
Mang Pepe is a fruit dealer. He has seven sacks of custard apple, five sacks
of mango and three sacks of avocado. If he is paid ₱ 245.00 per sack of
custard apple, ₱ 380.00 per sack of mango, and ₱ 275.00 per sack of
avocado, how much will he get from the fruits he sells?
A=Σx/y
92=(88+90+92+x)/4
92x4=270+x
368=270+x
368-270=x
X=98 her grade must be
Last year, Claudia got grades of 88,90, and 92 in the first three quarter in
Mathematics. What grade must she get in the fourth quarter to be able to
get an average of 92?
Number Theory and Fractions
Divisibility rule
2 If the Number is an even; ends with (0,2,4,6, and 8) the number is divisible
by
3 If the sum of the digits is divisible 3
4 If the last two digits of the number is divisible by 4 or if the number ends
with 0
5 If the last digit of the number is 0 and 5
6 If the number is divisible by 2 and 3
7 Double the last digit, then subtract it from the remaining digits. If the
difference is a multiple of seven, then it is divisible by seven. Repeat the
process if necessary.
8 If the last three digits of the number is divisible by eight or if the number
ends with zeros
9 If the sum of the digits of the number can be divided by nine
10 If the last digit of the number is zero
11 If the difference between the sum of the odd and even places is a multiple
of eleven or equal to zero
12 If the number is divisible by both 3 and 4
13 Delete the last digit from the number. Subtract nine times the deleted digit
from the remaining numbers. If the difference is divisible by thirteen, so is
the original number. Repeat process if necessary.
Prime Factorization It is the process of findings the prime factors of a number. There are two
methods the factor tree and continuous division or decomposition method.
Give the rime facto of the following.
52 25
32
× 2 18
17 × 3 51
32
𝑥 22 36
24
× 3 48
32
× 23 72
34 81
22
× 17 68
52
× 22 100
32
× 24 144
13 × 23
× 5 520
11 × 52 275
32
× 61 549
39 × 3 × 23 936
24
× 3 × 23 1104
34
× 26 5184
137 × 13 × 3 5343
1021 × 3 × 2 6126
7.
Math Six Reviewer (RBEC)
Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014
Page6MathExercisesforDailyUse
Similar fraction Set of fraction with same denominator
Numerator Parts of the fraction that tells the number of parts taken or shaded?
Unit fraction A proper fraction whose numerator is always 1
Mixed fraction A combination of whole number and fraction
denominator Part of a fraction that tells the number of equal parts the whole is divided.
Proper fraction A kind of fraction whose denominator is bigger than that of numerator
Dissimilar fraction Set of fractions whose denominator is different
Fraction bar. A line that separate the numerator and denominator
Improper fraction A kind of fraction whose denominator is smaller than or equal to the
numerator
Equivalent fraction Pair or set of fractions that names the same part
What is the equivalent of these fractions below
25
45
etc 5
9
16
20
etc 8
10
4
14
etc 2
7
Compare the given fractions
< 9
20
____
17
20
<
6
3
10
____7
8
10
< 18
25
____
14
15
>
1
2
3
____
4
12
Greatest Common Factor
(GCf)
Is the largest factor common to given set of numbers it could also be
defined as the greatest divisor?
36=2𝑥2𝑥3𝑥3
48=2𝑥2𝑥3𝑥2𝑥2
2x2x3=⑫ What is the GCF of 36, and 48?
96 120 156
48 60 78
24 30 39
8 10 13
2
2
3
so 2x2x3=12
Woody has three trees which he wishes to cut into logs of equal length. If
the trees are 96dm, 120dm, and 156 dm long, and are cut into longest
possible logs, what is the length of each?
267 Find the of 1335 and 3204
6 Find the gcf of 24, 36, 54
4 96, 172, 154
1 56, 63, 120
8 88, 64, 104
5 75, 15,125
7 35,84,56
10 160,100,70
25 225,500,300
12 204, 456
9 603,972
1539 1539,3078
37 1036, 1369
1045 13 585, 18 810
80 grams Lizzy has seven 720 grams of cashew nuts and 640 grams of almond nuts
which wishes to pack in small plastic bags. Each plastic bag should have
equal weight of cashew and almond nuts. And should hold the largest
number possible. How many grams of each can she put in each plastic bag?
5metres. Sally wishes to cut as many pieces of rope of equal length as she can from
four coils of ropes that are 45m, 60m, 75m, and 90m long. If she wishes the
pieces to be as long as possible and does not wish to waste any rope, how
long should she cut each?
8.
Math Six Reviewer (RBEC)
Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014
Page7MathExercisesforDailyUse
7 Minnie bought 35 apples, 49 oranges, and 28 mangoes to be given to small
children in the streets. If she will place these in baskets with the same
number of fruits, what is the greatest number of fruits each basket should
contain?
35= 7𝑥 5
15= 5𝑥3
gcf =5 l.term 7/3
or 2/1/3
Find the lowest term of these fraction
35
15
Express the lowest term of the following
1
3
4
12
3
5
9
15
7
3
𝑜𝑟 2
1
3
35
15
35
15
65
51
1
14
51
30
18
9
16
144
256
6
1
4
300
48
6
33
82
525
82
8
4
35
284
35
1
3
hours. Hapi spend 8 hours a day baking in the kitchen. What part of the day does
she spend in the kitchen?
26/2=13 hours ave. Every Saturday and Sunday, Minnie spends 26 hours cleaning the entire
house. How many hours in days she pend in cleaning the house?
Least Common
Multiple(LCM)
Is defined as the smallest non-zero multiple common to a set of numbers.
In some aspect, it is simple defined as the largest dividend. To get the this
simply find the prime factors, arrange all common in same column, bring
down all common and non-common, multiply the numbers to get LCM.
3= 3 x 1
5= 1 x 5
10= 5 x 2
3 x 1 x 5x2=30
Find the LCM of 3,5,and 10
2
2
4
256
128
64
16
144
72
36
9
So 2x2x4x16x9=2 304 lcm
What is the lcm of 256 and 144?
60 What is the lcm of ….
15,20
21 7,21
45 9,15
12 4,6
72 8,6,12
10 10,2,5
9.
Math Six Reviewer (RBEC)
Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014
Page8MathExercisesforDailyUse
60 10,12,15
18 3,9,2
18 Dennis the Menace is thinking of two numbers. Their greatest common
factor is 6. Their least common multiple is 36. One of the numbers is 12.
What is the other number?
70 mins Bugs Bunny and Lola Bunny are running in the same track. Bunny passes
Lola and then says Hi.Bunny goes around the course in 10 mins while Lola
goes 14 mins. they continue to jog until Bunny passes Lola. In how many
minutes Bunny pass Lola?
757 The number of apples in a bin if counted by 2s,3s,4s,7s,and 9s always give a
remainder of 1. What is the least number of apples in the bin?
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