Boyet B. AluanBSE-Math, Teacher 1, MAED Mg’t

1/1/20142014

Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014Math 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.

Page

1 M

ath

Exer

cise

s for

Dai

ly U

se

Math Six Reviewer (RBEC) Boyet B. Aluan

ANSWERs DESCRIPTION/QUESTIONS/IDEAS/FACTS/EXPLANATION/DETAILSHISTORY 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

Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014

Page

2 M

ath

Exer

cise

s for

Dai

ly U

se

Math Six Reviewer (RBEC) 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 1 926.9049 Round 48.972 to the nearest ones.164 990 Round 164 985 to the nearest tens951 400 Round 951 357 to the nearest hundreds852 862 000 852 862 248 round to the nearest thousands729 814 000 000 729 813 624 984 round to the nearest million(3x104 ¿+ (5x 103 )+( 4 x102 )+( 1x101)+(2 x100)

Write 35 412 in expanded exponential form

(8 x109 )+(4 x108 )+( 6 x107 )+(3 x 106 )+(2 x105 )+( 3x 104 )+( 7x 103 )+( 9x 102 )+¿)+(3x100 ¿

Write 8 463 237 953 in expanded exponential form

7 864 382 Write (7 x106 )+(8 x105 )+ (6 x104 )+(4 x103 )+(3 x 102 )+(8 x101 )+( 2x 100 ) 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 0.879134.885 Find the answer when 587.065 is diminished by 452.188.73 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 operationsEst 377 Estimate the sum of 17.4, 8.32, 0.149 and 351.000 7Est 70 Estimate the sum of 0.487+0.698+12.462+55.3

Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014

Page

3 M

ath

Exer

cise

s for

Dai

ly U

se

Math Six Reviewer (RBEC) Est 2500 Estimate the sum of 157.3+194.23+2014.69+99.14Est 2 900 000 Estimate the sum of 684 896+412 563+954 632+751 953100 Estimate the difference of 845-746100 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 0.125.2805 Find the product of 89.5 and 0.05919.226982 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)=119,430 kgs 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=11,73035days=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=457,345Note: 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)=88 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 Operations9+12-1x2=21-2=19 9+4X3-3÷3x219+2 – 56 ÷ 4= 21- 14 =7 19+6÷3-8x7÷49 +3 X 2=9 +6 =15 (15-6)+(4-1) x 2

Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014

Page

4 M

ath

Exer

cise

s for

Dai

ly U

se

Math Six Reviewer (RBEC) 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=na. 99 723b. 99792c. 101 723d. 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. 165b. 180c. 170 d. 185

What is the estimated difference between 239 and 30?

a. 30b. 3 000c. 300 d. 30 300

Approximately, what is the quotient of 9 030 and 30?

a. 3 600b. 3 600 000c. 36 000 d. 36 000 000

What is the estimated product of 418 and 89?

a. 5 000 b. 6 000c. 5 500d. 5 100

What is the estimated difference between 9 755 and 4 651?

a. 1 800b. 180 000c. 18 000d. 1 800 000

What is the estimated answer if 6 140 is multiplied by 312?

a. 138b. 238c. 148 d. 248

What is 225 subtracted from the sum of 65, 78,89,96, and 45?

a. 1.250 b. 1.273c. 1.243d. 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. 2.56c. 8.92d. 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 522b. 4 284.2c. 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.oldMother =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?

b22

=51+1

(51x22)+1=1123

A certain number divided by 22 equals 51 with a remainder 1. What is the number?

Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014

Page

5 M

ath

Exer

cise

s for

Dai

ly U

se

Math Six Reviewer (RBEC) (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/y92=(88+90+92+x)/492x4=270+x368=270+x368-270=xX=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 FractionsDivisibility 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 34 If the last two digits of the number is divisible by 4 or if the number ends

with 05 If the last digit of the number is 0 and 56 If the number is divisible by 2 and 37 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 nine10 If the last digit of the number is zero11 If the difference between the sum of the odd and even places is a multiple

of eleven or equal to zero12 If the number is divisible by both 3 and 413 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 1817×3 5132 x22 36

24×3 48

32×23 72

34 81

22×17 6852×22 100

32×24 144

13×23×5 52011×52 275

32×61 54939×3×23 936

24×3×23 110434×26 5184

137×13×3 5343

Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014

Page

6 M

ath

Exer

cise

s for

Dai

ly U

se

Math Six Reviewer (RBEC) 1021×3×2 6126

Similar fraction Set of fraction with same denominatorNumerator Parts of the fraction that tells the number of parts taken or shaded?Unit fraction A proper fraction whose numerator is always 1Mixed fraction A combination of whole number and fractiondenominator 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 numeratorDissimilar fraction Set of fractions whose denominator is differentFraction bar. A line that separate the numerator and denominatorImproper fraction A kind of fraction whose denominator is smaller than or equal to the

numeratorEquivalent fraction Pair or set of fractions that names the same part

What is the equivalent of these fractions below2545 etc

59

1620 etc

810

414 etc

27

Compare the given fractions< 9

20¿

1720

< 6 310¿

7 810

< 1825¿

1415

> 1 23¿

412

Greatest Common Factor (GCf)

Is the largest factor common to given set of numbers it could also be defined as the greatest divisor?

36=2 x2 x3 x 348=2x 2x 3x 2x 22x2x3=⑫

What is the GCF of 36, and 48?

96 120 1564860 782430 398 1013

223

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 32046 Find the gcf of 24, 36, 544 96, 172, 1541 56, 63, 1208 88, 64, 1045 75, 15,1257 35,84,5610 160,100,7025 225,500,30012 204, 4569 603,9721539 1539,307837 1036, 13691045 13 585, 18 81080 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?

Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014

Page

7 M

ath

Exer

cise

s for

Dai

ly U

se

Math Six Reviewer (RBEC) 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?

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=7 x515=5 x3 gcf =5 l.term

7/3 or 2/1/3

Find the lowest term of these fraction 3515

Express the lowest term of the following

13

412

35

915

73∨2 1

33515

3515

6551

1 1451

3018

916

144256

6 14

30048

6 3382

52582

8 435

28435

13 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 15= 1 x 510= 5 x 2 3 x 1 x 5x2=30

Find the LCM of 3,5,and 10

224

2561286416

14472369

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

Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014

Page

8 M

ath

Exer

cise

s for

Dai

ly U

se

Math Six Reviewer (RBEC) 12 4,6

72 8,6,12

10 10,2,5

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?

Enhance Mathematics-Quiz Bee Review Materials by BOYET B. ALUAN S, 2014