Discussion
... exploration of the sum of the first n natural numbers. For example, suppose that n = 16. One could begin by adding the numbers (i.e. 1 + 2 + 3 + … + 16). However, one way to add the numbers, using the both the commutative and associative laws of addition, could be to change the order and groupings o ...
... exploration of the sum of the first n natural numbers. For example, suppose that n = 16. One could begin by adding the numbers (i.e. 1 + 2 + 3 + … + 16). However, one way to add the numbers, using the both the commutative and associative laws of addition, could be to change the order and groupings o ...
Miscellaneous Exercises 10
... The diagram shows some of the results of a survey to find out which household tasks are done by women only, which are done by men only, and which are shared. Tasks done by men only ...
... The diagram shows some of the results of a survey to find out which household tasks are done by women only, which are done by men only, and which are shared. Tasks done by men only ...
Maths
... Year 5 Fractions, decimals and percentage I can read, write, order and compare numbers with up to 3 decimal places. ...
... Year 5 Fractions, decimals and percentage I can read, write, order and compare numbers with up to 3 decimal places. ...
Year 5 Autumn Term
... To add and subtract whole numbers with more than 4 digits ● To add and subtract numbers mentally with increasingly large numbers. ● To solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why. ● To identify multiples and factors, including ...
... To add and subtract whole numbers with more than 4 digits ● To add and subtract numbers mentally with increasingly large numbers. ● To solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why. ● To identify multiples and factors, including ...
Numbers: Fun and Challenge
... Write n = 2f · n1 · n2 , where every prime divisor of n1 (resp. n2 ) is ≡ 1 (mod 4) (resp. ≡ 3 (mod 4)). Fermat showed that r2 (n) > 0 (i.e. n is a sum of two squares) if and only if every prime divisor p of n2 occurs in n2 to an even power. Assume this is the case, Jacobi obtained the following clo ...
... Write n = 2f · n1 · n2 , where every prime divisor of n1 (resp. n2 ) is ≡ 1 (mod 4) (resp. ≡ 3 (mod 4)). Fermat showed that r2 (n) > 0 (i.e. n is a sum of two squares) if and only if every prime divisor p of n2 occurs in n2 to an even power. Assume this is the case, Jacobi obtained the following clo ...
Handout
... Numbers that have a whole number square root. The first ten perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Is zero a perfect square? There is a debate about this in the mathematics community – some believe zero is a perfect square because 0 times 0 = 0; some disagree because they say ...
... Numbers that have a whole number square root. The first ten perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Is zero a perfect square? There is a debate about this in the mathematics community – some believe zero is a perfect square because 0 times 0 = 0; some disagree because they say ...
Hints for Warm
... 8. An integer is reduced to 1/9 of its value when a certain one of its digits is deleted, and the resulting number is again divisible by 9. (a) Prove that division of this resulting integer by 9 results in deleting an additional digit. Hint. Prove that the number can be reduced to 1/9 of its value o ...
... 8. An integer is reduced to 1/9 of its value when a certain one of its digits is deleted, and the resulting number is again divisible by 9. (a) Prove that division of this resulting integer by 9 results in deleting an additional digit. Hint. Prove that the number can be reduced to 1/9 of its value o ...
2008 = 251(2+5+1): Properties of a New Number
... Then, if x = Ab n + Bb n−1 + Cb n−2 + L + Pb + Q the corresponding EP (x ) number can be generated using the expression (1). It is straightforward to realize that the numbers X define an integer sequence. The first numbers of this sequence for the base b = 10 are given below: ...
... Then, if x = Ab n + Bb n−1 + Cb n−2 + L + Pb + Q the corresponding EP (x ) number can be generated using the expression (1). It is straightforward to realize that the numbers X define an integer sequence. The first numbers of this sequence for the base b = 10 are given below: ...
Parent Page L26 - Hempfield Curriculum
... You can use compatible numbers to estimate quotients. Compatible numbers are numbers that are easy to compute with mentally. To find two estimates with compatible numbers, first round the divisor. Then list multiples of the rounded divisor until you find the two multiples that are closest to the div ...
... You can use compatible numbers to estimate quotients. Compatible numbers are numbers that are easy to compute with mentally. To find two estimates with compatible numbers, first round the divisor. Then list multiples of the rounded divisor until you find the two multiples that are closest to the div ...
Lesson1 - Purdue Math
... the expression involves a fraction, treat the numerator and denominator as if they were each a group. Grouping can include parentheses, brackets, a root, or absolute value bars. 2. Evaluate all exponential expressions. 3. Perform multiplication and/or division as they occur, working from left to rig ...
... the expression involves a fraction, treat the numerator and denominator as if they were each a group. Grouping can include parentheses, brackets, a root, or absolute value bars. 2. Evaluate all exponential expressions. 3. Perform multiplication and/or division as they occur, working from left to rig ...
Study Guide Review Study Guide Review
... the measurements taken by a climatologist of the width of tree rings of a particular tree for different years. List the years in order of increasing ring width. Which year was the hottest? How do you know? Which year was the coldest? How do you know? ...
... the measurements taken by a climatologist of the width of tree rings of a particular tree for different years. List the years in order of increasing ring width. Which year was the hottest? How do you know? Which year was the coldest? How do you know? ...
2016-17 Factors and Multiples
... If ab=c, where a,b,c belongs to N then a and b are called factors of c. The product c is called multiple of a and b. A natural number greater than 1, which has exactly two factors, namely 1 and itself, is called a prime number. A natural number having at least one factor, besides 1 and itself ...
... If ab=c, where a,b,c belongs to N then a and b are called factors of c. The product c is called multiple of a and b. A natural number greater than 1, which has exactly two factors, namely 1 and itself, is called a prime number. A natural number having at least one factor, besides 1 and itself ...
Some Very Interesting Sequences
... ending in a given digit, we get a triangular table that starts out 1 (row 1), 0, 1 (row 2), 1, 1, 0 (row 3), 0, 1, 2, 2, . . . . Look familiar? That’s right, it’s precisely the first four rows of the zigzag triangle! Indeed, the pattern continues, and in general, the kth entry of row n of the zigzag ...
... ending in a given digit, we get a triangular table that starts out 1 (row 1), 0, 1 (row 2), 1, 1, 0 (row 3), 0, 1, 2, 2, . . . . Look familiar? That’s right, it’s precisely the first four rows of the zigzag triangle! Indeed, the pattern continues, and in general, the kth entry of row n of the zigzag ...