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Exploring Basic Mathematics: Candy, Pencils, Prime Numbers, and Sequences

This document covers various mathematical concepts including division, divisibility rules, and prime factorization. It starts by evaluating whether Roger can evenly divide his 126 pieces of candy among his three friends and whether Bert has any leftover pencils when dividing 40 into different piles. It also explores finding the least common multiple (LCM) and greatest common factor (GCF) of numbers, creating factor trees, and writing in scientific notation. Finally, it delves into recognizing patterns in numerical sequences.

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Exploring Basic Mathematics: Candy, Pencils, Prime Numbers, and Sequences

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  1. Math LabNumber Theory Chapter 4

  2. Question 1 Roger has 126 pieces of candy. He has 3 friends. Can he divide the candy evenly between his friends?

  3. Question 2 Bert has 40 pencils. He divides him in to 2 piles. Are there any leftover pencils? What about 3 piles? What about 5 piles? What about 6 piles? What about 10 piles? Divisibility Rules 2: Ends in 0,2,4,6,8 3: Add digits  divisible by 3 5: Ends in 0,5 6: Yes for both 2 and 3 9: Add digits  divisible by 9 10: Ends in 0

  4. Question 3 Create a factor tree for 40:

  5. Question 4 Write 30 as 3 prime numbers multiplied together: 30 = _____ x _____ x _____

  6. Question 5 Find the LCM of 15 and 20: LCM: The smallest number that two numbers have as a common multiple. 6: 6 , 12 , 18 , 24 4: 4 , 8 , 12 , 16 , 20 , 24

  7. Question 6 Find the GCF of 15 and 20. GCF: The largest number that will divide both numbers in a pair. 15: 1 , 3 , 5 , 15 20: 1 , 2 , 4 , 5, 10, 20

  8. Question 7 Three miles is 16,000 ft. Re-write this in scientific notation. ______ x 10___

  9. Question 8 Re-write 4.5 x 106 as a normal number:

  10. Question 9 Find the next three numbers in this sequence: 4 , 8 , 12 , 16 , 20 , ___ , ___ , ___ What is the rule?

  11. Question 10 Find the next three numbers in this sequence: 1 , 2 , 4 , 8 , 16, ___ , ___ , ___ What is the rule?

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