A Problem Solving Approach to Mathematics for Elementary School Teachers (13th Edition)

Chapter 3

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8By using order of operations, result of the given... more

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The number 46,902 can be written as forty-six ... more

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Both the number names have only two 2 periods.The ... more

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The numbers can be written in expanded form or in ... more

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The place values ones, tens, and hundreds are ... more

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; Divide the given number by 5. ; Write the ... more

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1922 ; Write the face value of the numerals given ... more

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15 ; Simplify the exponent in the given expression... more

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; Write   at the tens place and   at the ones ... more

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; The first block is a cube in the first row of ... more

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20 ; Since each number less than 20 has base ... more

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142 ; Use the place value concept of each digit.... more

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; Draw the base-five blocks diagrams that are ... more

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; The number of digits in thegiven numeral is 4. ... more

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seven ; The numbers of digits in all the numerals ... more

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1 prize of , 2 prizes of , 1 prize of   ; To ... more

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 B TeB TwB FiB Se             ; For part (a), ... more

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; Take 2 groups of 4 units for 2 longs. There are... more

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; Drawa table that shows the Roman number ... more

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19 ; The number   implies that 10 is multiplied 15... more

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; Let the two-digit number be XY, where X is the ... more

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; The value of 1 dot in the 1st column is 27, so... more

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; It is clear that 3 units are equal to 1 long, 3... more

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18 digits ; Converting a number from one base ... more

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; As the number is given in base three notation, ... more

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; It is clear that 2 units are equal to 1 long, 2... more

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; As the given number is in base eight notations... more

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Base seven ; Write the given expression in ... more

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4 ; If one would take power of 2 as 10 then number... more

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9876 ; Since 9 is the greatest number in the ... more

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; To convert 54 in base 3.Divide 54 successively ... more

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; In the figure, there is 1 flat, 4 longs and 5 ... more

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A number is expressed in digits, whereas a numeral... more

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A place value in a system is the actual value of a... more

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Zero is a number that has a numerical value of 0. ... more

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In China, Singapore, Malaysia, Japan, and Sri ... more

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Increase the value of the bead to one in each row.... more

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From to , at least 4 weights are required.From ... more

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The rekenrek was designed by Individual A.T, an ... more

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It follows that the first century AD in the ... more

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Both the 3s are different because their place ... more

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No, R system is not a base ten system as R ... more

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No, the bar symbol over the symbol   cannot be ... more

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Tens and ten thousand values are missing in the ... more

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It is clear that 10 units are equal to 1 long, 10 ... more

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Since hundred-thousands position has no symbol in ... more

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642 ; Placing the digit 6 such that its value is ... more

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Start checking the positional values of number ... more

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If the sets in the addition of whole numbers are ... more

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A number line represents the numbers starting from... more

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; The expanded algorithm involves adding the ... more

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By moving 1 counter from 4 to 9 because 1 more ... more

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;Add 1 to 19 and subtract 1 from 26 to rewrite the... more

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, so . ; Draw a diagram showing 7 counters in red ... more

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so ; Draw a diagram showing 8 counters in red and... more

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Associative property of addition, Commutative ... more

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Numbers can be added by two methods, they are:... more

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The numbers can be rounded with the help of place ... more

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Rounding method compatible numbers can be used for... more

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For associative property, consider the instance... more

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Entire Proof Answer: Add 228 and 171 to determine ... more

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Individual S' Number: 452Other Numbers: 462, 472, ... more

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The front-end estimation is used to calculate the ... more

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Add 3 and 17 and subtract 3 from 9 to rewrite the ... more

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Subtract 3 from 23 and add 3 and 12 to rewrite the... more

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Subtract 3 from 25 and add 3 and 47 to rewrite the... more

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Subtract 1 from 33. Add 1 and 19 to rewrite the ... more

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Add 2 and 28. Subtract 2 from 8 to rewrite the ... more

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Add 3 and 27. Subtract 3 from 36 to rewrite the ... more

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A compensation number is a number that is added to... more

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Entire Proof Answer: Add 3 and 17 and subtract 3 ... more

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; For the given two sets, find the value of.By ... more

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Entire Proof Answer:Assume two sets and to be ... more

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The number line model represents the sum of the ... more

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13 and 4 ; The given strategy involves adding two ... more

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; The given expression has 7 and 8 as addends.... more

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Even numbers are 4, 6, and 8, while the odd ... more

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The first step is the expanded form of the two ... more

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; Draw the number of blocks with base 10 for 20 ... more

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410 ; The given algorithm involves adding the ... more

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2911 ; The given algorithm involves adjusting one ... more

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The sum obtained in the given problem has 5 as its... more

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; To find the balance left the check amounts of... more

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834159672 ; Consider the elements given in the ... more

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; Each domino is a rectangular tile. A line ... more

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; The sum of the given addends is 9059, and the ... more

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; For the two given sets, find the value of .  By... more

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Number line model represents the sum of the ... more

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15 and 3 ; The given strategy involves adding two ... more

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Closed; sum of any two elements of the set is also... more

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The first step is the expanded form of the two ... more

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The first step is obtained by applying the ... more

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; Draw the number of blocks with base for and 6... more

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533 ; The given algorithm involves adding the ... more

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531 ; The given algorithm involves adjusting one ... more

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The sum obtained in the given problem has 6 as its... more

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432,000 ; Approximate 71,150 to the nearest ... more

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; Calculate the sum of the digits in Column 1. ; ... more

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1 hour 34 minutes 15 seconds2: 25: 45 PM ; Add the... more

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; The largest number less than 100 is 99.Add 8, 7... more

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  ; Start solving from the right side.Add 4 and 5 ... more

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No, the set of students who take Subject A and the... more

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Associative property of addition ; The individual ... more

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As , for some counting number , . On adding , . So... more

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126489573An unmagic square is obtained by randomly... more

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Colored counters can be used to teach addition.If ... more

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This algorithm uses the concept of place values ... more

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No, it is not necessary for the front-end ... more

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Mental computations can be helpful in quickly ... more

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The algorithm has the following rules:Rule 1: ... more

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Donating money to the needy, making budget for ... more

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Using the commutative property and associative ... more

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The student should be appreciated for solving the ... more

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Person R’s answer is incorrect as, on rounding ... more

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Person A’s answer is incorrect as, on rounding 345... more

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For associative property, ; For commutative ... more

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,; ,; ,; ,; ,; ,; ,; ,; ; Compensation number is a... more

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Trading off:Making compatible numbers:Trading off ... more

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The number could be ,  ,  ,  , or .  The front-end... more

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; The given number can be expanded by using the ... more

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; The face value of Roman numeral is 500, which ... more

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; The digits of base 10 or the decimal base are 0... more

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Yes, the students should be encouraged to develop ... more

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The list with price in dollars consists of Milk - ... more

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Team A draws the cards 1, 3, 6, 5, and 9 and ... more

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Each small square box represents 1 unit.The number... more

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On the given number line, it can be clearly seen ... more

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Assess the first number in the given pattern, that... more

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; Subtract the number of visitors who went to the... more

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Let be a non-empty set and be a subset of, that ... more

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If and are two whole numbers such that , is ... more

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Person R currently has a total of 58 Object T and ... more

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Write 44 in the form of base ten blocks.To ... more

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Compensation number is a number that is added to ... more

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Equation: ; Total number of Object T: 31 ; Form ... more

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Equation: ; Total amount:   ; Form the equation of... more

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Yes; 27 ; Write 35 in form of base ten blocks. ; ... more

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No; 43 ; Write 46 in the form of base ten blocks... more

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Yes; 58 ; Write 62 in the form of base ten blocks... more

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Yes; 43 ; Write 50 in the form of base ten blocks... more

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Yes; 79 ; Write 81 in the form of base ten blocks... more

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No; 28 ; Write 29 in the form of base ten blocks... more

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Yes; 56 ; Write 60 in the form of base ten blocks... more

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Yes; 15 ; Write 24 in the form of base ten blocks... more

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No; 72 ; Write 75 in the form of base ten blocks... more

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Yes; 38 ; Write 43 in the form of base ten blocks... more

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The required operation can be performed on all ... more

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; Compensation number is a number that is added ... more

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; Compensation number is a number that is added ... more

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; Compensation number is a number that is added ... more

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; Compensation number is a number that is added ... more

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; Compensation number is a number that is added ... more

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; Compensation number is a number that is added ... more

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; Compensation number is a number that is added ... more

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; Compensation number is a number that is added ... more

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; Compensation number is a number that is added ... more

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; Compensation number is a number that is added ... more

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Compensation number is a number that is added to ... more

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One can subtract numbers by using trading-off ... more

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The method in which the compensation number is ... more

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; If and are the whole numbers, then a whole ... more

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; Add the number of marbles that individual G and... more

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Add the calories of all the food items that ... more

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 Numbers in the form of Base-Ten ... more

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HTO Write 146 in terms of hundreds, tens, and ones... more

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; Create the greatest three-digit number using ... more

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1 hr 39 min 40 sec ;  HoursMinutesSeconds  Write 5... more

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; In the first quarter, team H scored 14 points ... more

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; Subtract 30 from 997. ; Subtract 2 from 967. ; more

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; It is known that the operation can only be ... more

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The given number sentence is an addition problem ... more

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, , , , ; Combine the first two inequalities ... more

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HTO     Represent 115 as base ten blocks.    Break... more

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; Write 128 as 1 hundred, 2 tens and 8 ones.Trade... more

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 Q1Q2Q3Q4TotalTeam H15324033120Team E20254739131... more

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 Yes, learning how to do subtraction using more ... more

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If the student type wrong key, for instance, in ... more

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Addition and subtraction are the inverse ... more

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Yes. The subset   is closed under subtraction. ; ... more

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Regrouping is the process of making groups of tens... more

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Regrouping is used to regroup numbers in tens and ... more

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The approximation is greater than the original ... more

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As   for all , so 0 cannot be the identity. ; The ... more

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When comparison happens between two things then ... more

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As   is not a whole number, so the set is not ... more

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In a whole number system, 0 is the least number. ... more

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It is incorrect, as in subtraction turning the ... more

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It is wrong. The given calculation will not follow... more

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It is a wrong calculation because the difference ... more

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Though the answer is correct, it is a wrong way of... more

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The answer is wrong. It is 49. Since ones place ... more

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The process used for subtraction is wrong. The ... more

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Student O did the subtraction correct but she got ... more

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Student P obtained the right answer after ... more

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Student M has a good thinking skill but got ... more

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Estimation is very helpful in making right ... more

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Doing homework using calculator will not help the ... more

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; To find number of toys Person R bought, ... more

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            The subtraction can be done easily ... more

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Compensation of numbers is used to make ... more

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Equal-Additions algorithm. ; As in equal-addition ... more

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2017 ; MM in MMXVII represents 2000 as value of M ... more

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Set is said to be closed under addition when any ... more

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; As associative property of addition of whole ... more

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Three friends in a group read book of grade 4, ... more

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The given method is a difficult way to subtract ... more

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; Assume the blank as .Add 8 on both sides of the... more

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Add   into 4895 ; Equal addition algorithm for ... more

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; The difference of the digits selected should be... more

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; Add 25 and 16 to obtain the total vehicle C. ; ... more

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The individual L can start walking at any time. To... more

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One can find the total number of objects by using ... more

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An array is a representation of multiplication. In... more

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One can use the given property by breaking the ... more

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; Make a bar and make 5 partitions in it.The ... more

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.Individual J has more Object M than Individual D... more

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The distributive property of multiplication over ... more

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; Front end multiplying ; The total amount (in ... more

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72 ;  In the given problem, there are 6 choices ... more

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 12 ;  Let the colors which can be used on outer ... more

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In the given figure, the area of shaded region can... more

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; Represent 42 by using 4 long strips of 10 units... more

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  ; Write 323 horizontally and 42 vertically on ... more

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5; 7The value of   is always greater than equal to... more

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There are two steps observed in the given pattern... more

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In the first step, the first factor is written in ... more

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; Let Coin P in box3 be, then Coin P in box1 will... more

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496 miles ; The given number of miles per hour can... more

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1000; Estimate the number of rows and the seats ... more

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and and Both the expressions contains factors in ... more

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; Find the square of 25, 35, 45 and 55 by using ... more

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21, 2105 ; Rewrite the given number in the form of... more

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15 ;  Let be the set of all exterior colors and ... more

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40 ;  Let be the set of all flavors and be the ... more

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Entire Proof Answer: Find the area of the shaded ... more

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In the given figure, the area of leftover region ... more

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; The set of 13 blocks is repeated 4 times, which... more

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; Write 423 horizontally and 23 vertically on the... more

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5; 17The value of   is always greater than equal ... more

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In the first step, the first factor is written in ... more

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; Let Coin D in box 2 be , then Coin D in box 1 ... more

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; When 4 at units place in the multiplicand is ... more

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390 miles ; As total distance travelled is given ... more

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21000 calories ; To find the estimation of the ... more

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Multiply the 2-digit number by 100 and then ... more

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62, 43 ; To estimate the product as 2400, consider... more

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The product of two whole numbers can be written as... more

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The multiplication identity is that number by ... more

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Use the distributive property of multiplication ... more

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Yes, can be equal to . Substitute 1 for into the... more

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; Let and be whole numbers.For and , calculate... more

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By using the distributive property, the given ... more

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Person P bought a book for and 6 units of another... more

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The multiplication can be obtained by writing the ... more

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Any two-digit number of the form on multiplying ... more

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An algorithm is correct if it always produces the ... more

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The calculations are performed like this:  This ... more

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The claim of person S is false since according to ... more

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The claim of person A is false since the finite ... more

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Person L's conclusion is not true for all whole ... more

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Person W might not know the rule of exponents.The ... more

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3 is regrouped with the 3 at fives place of the ... more

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; Make the area model to multiply and add the ... more

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; Consider the set , which is clearly an infinite... more

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No. ; Apply the given operations for two whole ... more

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The number ‘two’ does not exist in base two system... more

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; Write 81 as a multiple of 3. ; Write the ... more

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4,598 is very far from the estimated product 13,... more

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2025 ; The total number of buttons can be obtained... more

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Twice of 15 cups means cups.Add the cups sold on ... more

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; The blanks can be filled by using the rules of ... more

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Add 4 to the first number, 2 in the pattern.Second... more

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The division problem can be solved by using the ... more

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; Take 3 empty boxes and start putting one Object... more

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The division problem can be solved using partial ... more

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Individual J can distribute among 2 people only ... more

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Multiply the result obtained by the division and ... more

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Multiply the result obtained by the division and ... more

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Number of Object B: 2 ; Use the repeated ... more

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; Draw a diagram of 16 boxes and give each box a ... more

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; Draw a diagram with 28 blocks and assign a ... more

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; Take 4 empty boxes and start putting one Object... more

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; Take 2 empty boxes and start putting one Fruit ... more

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; Take 4 empty boxes and start putting one Object... more

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; Take 7 empty boxes and start putting one ... more

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; Take 5 empty boxes and start putting one Object... more

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; Take 2 empty boxes and start putting one Object... more

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; Take 3 empty boxes and start putting one person... more

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The algorithm is better than the base-ten blocks ... more

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Solved division problem by estimating how many 45 ... more

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; Use estimation to find the approximate answer.... more

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; Assume that .Rewrite   and   in the form... more

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; Rewrite the given equation as .According to the... more

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The given equation holds true as it can be proved ... more

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Check for whole numbers less than 100 which have ... more

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3 ; As division and multiplication are inverse of ... more

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; 132 can be represented by 1 flat, 3 longs, and ... more

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; Number 15 can be counted 100 times and then ... more

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Five ; As the greatest digit used in the given ... more

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15 ; Multiply 10 by 12 to get the total number of ... more

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; If a number is divided by 4 and remainder 1 is ... more

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; Divide 50,000 by 1000. ; Multiply 30 by 50 to ... more

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Equal; Yes, because the number has been increased ... more

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; Assume that .Rewrite   and   in the form... more

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; Rewrite the given equation as .According to the... more

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The given equation holds true as it can be proved ... more

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; Assume the original number of Object M to be . ... more

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10 ; As division and multiplication are inverse of... more

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; 256 can be represented by 2 flats, 5 longs, and... more

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; Number 24 can be counted 100 times, and then ... more

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Base two or any base greater than two ; As the ... more

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12 ; Multiply 8 by 9 to get the total number of ... more

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; If a number is divided by 5 and a remainder 3 ... more

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; Divide 30,000 by 1000. ; Multiply 24 by 30 to ... more

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Let be equal to 0, and perform the division . is ... more

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2,  ,   ; Use the order of operations in the ... more

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Word Problems are as follows: In a garden, there ... more

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Yes; The result will be the same irrespective of ... more

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Yes, one may face difficulty using one particular ... more

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An individual cannot agree with the given ... more

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Use the definition of division, that is,  if and ... more

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Use the definition of division, that is,  if and ... more

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Let   be any whole number. Calculate .  does not ... more

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The repeated subtraction method gives correct and ... more

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It seems like the student does not completely ... more

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Press   on the prescribed device, and then keep on... more

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This method will always be true only when the unit... more

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Each person will get 4 toys, and one toy will be ... more

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2247 ; Use the repeated subtraction method to find... more

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If , then the product of 21 and 3 must be 63. ; ... more

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For instance, ; For any whole number , the ... more

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6979 miles ; The starting point is 52,281 and the ... more

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This method is just like the standard long ... more

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This method is based on the standard long division... more

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Addition, Subtraction, Multiplication, Division... more

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There are 24 students in each class and 12 Object ... more

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Individual EWhen the dividend is the same, the ... more

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According to the question, each of the 6 students ... more

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Use the order of operations to add all the numbers... more

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Perform subtraction using the standard method.  ; ... more

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; The given base three blocks can be converted ... more

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1 block, 2 flats, 2 longs and 0 units so 5 blocks... more

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Base 12 has real life applications. Items like ... more

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; Convert   into base ten numeral by multiplying ... more

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40 ; Multiply 60 by 8. ; Divide 48 by 12. ; ... more

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12 ; Individual H has two pairs of slacks and ... more

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26 ; Let the imagined number be .Divide   by 13, ... more

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for 80 people ; Divide 6000 by 80.The package of... more

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; Find the total number of extra hours Individual... more

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; Let the winning prize of the first question be... more

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; Add the units place digits of the numbers.If ... more

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; Multiply 613 by 98 using the traditional method... more

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; Multiply 912 by 5.Add 243 to the product.... more

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; The required income (in dollars) can be ... more

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2600 ; Find the total number of Object C ... more

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; 1 dozen is equal to 12 units.Find the total ... more

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Vehicle B: 36; Vehicle T: 18 ; Let the owner have... more

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; Write   as a sum of   and , which is same as 4... more

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; Divide   by .Subtract   hundred times from . ; ... more

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; Write the estimated average of the numbers. ; ... more

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Entire Proof Answer: Let , where .Considerbecause... more

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; In the first 30 second, the PTA reached out to ... more

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13 children ; Find the number of Item C that the ... more

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Yes, ;;; ; Apply the order of operations to the ... more

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; The maximum value with all the digits is 8 and ... more

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