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Math six reviewer 2014 by aluan
Math six reviewer 2014 by aluan
Math six reviewer 2014 by aluan
Math six reviewer 2014 by aluan
Math six reviewer 2014 by aluan
Math six reviewer 2014 by aluan
Math six reviewer 2014 by aluan
Math six reviewer 2014 by aluan
Math six reviewer 2014 by aluan
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Math six reviewer 2014 by aluan

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  • 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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