Compare and Order Decimals
... Another way to compare decimals is to write them in a place value table. As you go from the left to the right, the decimal with the first digit that is greater is the greater of the two. So, the Tens ...
... Another way to compare decimals is to write them in a place value table. As you go from the left to the right, the decimal with the first digit that is greater is the greater of the two. So, the Tens ...
Measurement
... Only numbers that have the same unit can be added or subtracted. The sum or difference also has the same unit. Sometimes, it is useful to change a quantity to a different form in order to add or subtract quantities. o 4 teddy bears + 5 teddy bears = 9 teddy bears o 2 dogs + 3 cats is 2 dogs and 3 ca ...
... Only numbers that have the same unit can be added or subtracted. The sum or difference also has the same unit. Sometimes, it is useful to change a quantity to a different form in order to add or subtract quantities. o 4 teddy bears + 5 teddy bears = 9 teddy bears o 2 dogs + 3 cats is 2 dogs and 3 ca ...
There are no Coincidences
... last step, when we merge two lists of size 2k−1 . This merging requires an odd number of comparisons, thus the total is odd. Now suppose k is the largest integer such that 2k ≤ n: n = 2k + x, where x < 2k . At the last step we merge two lists of size 2k and x. Thus A003071(n) = A003071(2k ) + A00307 ...
... last step, when we merge two lists of size 2k−1 . This merging requires an odd number of comparisons, thus the total is odd. Now suppose k is the largest integer such that 2k ≤ n: n = 2k + x, where x < 2k . At the last step we merge two lists of size 2k and x. Thus A003071(n) = A003071(2k ) + A00307 ...
Representing Solutions to Inequalities
... An interval is a space between points, called endpoints. Interval notation represents a set of numbers using the endpoints and indicates whether the endpoints themselves are included in a set. An open interval does not include the endpoints. An open interval is indicated by parentheses: () ...
... An interval is a space between points, called endpoints. Interval notation represents a set of numbers using the endpoints and indicates whether the endpoints themselves are included in a set. An open interval does not include the endpoints. An open interval is indicated by parentheses: () ...
Situation 39: Summing Natural Numbers
... Another representation of the first n natural numbers is a staircase: a triangular array of unit squares, having n rows, in which the number of unit squares in the first row is 1, and the number of unit squares in each successive row increases by 1, so that in the nth row there are n unit squares. B ...
... Another representation of the first n natural numbers is a staircase: a triangular array of unit squares, having n rows, in which the number of unit squares in the first row is 1, and the number of unit squares in each successive row increases by 1, so that in the nth row there are n unit squares. B ...
EppDm4_04_02
... If you claim a property holds for all elements in a domain, then someone can challenge your claim by picking any element in the domain whatsoever and asking you to prove that that element satisfies the property. To prove your claim, you must be able to meet all such challenges. That is, you must hav ...
... If you claim a property holds for all elements in a domain, then someone can challenge your claim by picking any element in the domain whatsoever and asking you to prove that that element satisfies the property. To prove your claim, you must be able to meet all such challenges. That is, you must hav ...
