Numbers and Algebra - Number Theory Concepts - Quiz 5

Which of the following numbers is neither prime nor composite?

1 One is neither a prime number nor a composite number.

In which of the following are the numbers ordered from greatest to least?

1, ½ , ¼ , -1 Since 1 is a positive, whole number, it's the largest. Since -1 is negative, it's the smallest number. With fractions, if the numerator (top) is the same, then the smaller denominator is a larger fraction; for example, 1 out of 2 is 50% but 1 out of 4 is 25%. Therefore, 1 > ½ > ¼ > -1.

When Bob eats a sandwich, Bob always eats only half his sandwich at lunch and saves the other half for a snack later in the day. If Bob eats a sandwich for 15 days in a row, what is the number of full sandwiches Bob ate during lunch in those 15 days? Which of the following equations should a student use to solve this word problem?

15 × ½ Bob eats ½ of a sandwich during lunch. To find how many sandwiches Bob ate during lunch during a given time period (x), the question is ½(x). Since the question is defining × as 15, the equation is ½(15) or 15 × ½.

Tom wants to mentally calculate a 20% tip on his bill of $40. Which of the following is best for Tom to use in the mental calculation of the tip?

40 × .1 × 2 Tom can quickly find 10% of 40 and then double it. In this case the answer is $8 because 10% of 40 is 4 and 4 × 2 is 8.

Which of the following has the least value?

483 ones This is the same as multiplying 483 × 1 which equals 483.

Below is an example of a student's work: 4/16 - 1/8 = 3/8 10/13 - 3/8 = 7/5 3/5 - 2/3 = 1/2 If the student continues making the same error, the student's most likely answer to the problem 9/16 - 3/4 would be:

6/12 In each example the student is subtracting both the numerators and denominators. When subtracting fractions, the student should find a common denominator and then subtract only the numerators. The student is not finding a common denominator but subtracting both the numerators from each other and the denominators from each other. Thus the most likely answer if the student performed (9/16) - (3/4) would be (6/12).

What is the value of the "8" in the number 17,436,825?

800 In a base 10 system, each place location for a number has a value that is a power of 10. Specifically, the ones place is properly understood to be 10⁰ (because any nonzero number raised to the zero power equals 1). The tens place is 10¹, the hundreds place is 10², the thousands place is 10³, etc. When a digit is in a specific position, its value is equal to the product of that digit and the power of 10 that is assigned to its position. Therefore, in the number 17,436,825, the 8 represents 8 × 10^2 = 8008×102=800.

Which numbers are divisible by 2, 3, 6, and 7? Select all answers that apply.

B 252 Using divisibility rules, it can be determined that 252 is factored by 2, 3, 6, and 7. C 2,772 Using divisibility rules, it can be determined that 2,772 is factored by 2, 3, 6, and 7. D 1,260 Using divisibility rules, it can be determined that 1,260 is factored by 2, 3, 6, and 7.

Which of the following is a correct factor tree for the prime factorization of the given number?

actor tree C This is the correct breakdown into prime numbers.

Which of the following represents 8,435.21 in written form?

eight thousand four hundred thirty-five and twenty-one hundredths This is the correct written form.