Quiz 7

What is the prime factorization of 1,188?

A 2 squared x 3 cubed x 11 The prime factors of 1,188 are 2×2×3×3×3×11 Therefore 2 squared x 3 cubed x 11 is the prime factorization of 1,188.

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

A 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.

Which symbol most accurately reflects the relationship between the two numbers below? −2/7 □ −1/3

A > Fractions can be quickly compared once they have a common denominator. The smallest common denominator of both fractions is 21. Multiply −2/7 ​ by 3/3​ to get -6/21 Multiply −1/3 by 7/7 to get −7/21 The fraction −6/21 has the greater numerator, so its equivalent form −2/7 is the greater fraction.

If x is between 10 and 20, and y is between 100 and 200, x/y must be

A between 1/20 and 1/5 The least number will result from the smallest x value over the largest yvalue: 10/200, which equals 1/20. The greatest number will result from the largest x value over the smallest y value: 20/100, which equals 1/5.

Which of the following numbers is the product of one even number and two odd numbers, assuming the factors are greater than 1?

B 18 Eighteen can be written as the product of one even number and two odd numbers: 2×3×3=18. To find the prime factorization of a number, use a method such as a factor tree.

Which of the following is the product of 2 odd numbers and 1 even number, each of which is greater than 1?

B 30 The prime factorization of 30 is 2 × 3 × 5 which satisfies the need for 2 odd numbers and an even number.

What is the greatest odd factor of 5,824?

B 91 The prime factorization of 5,824 is 2 to the 6th power x 7 x 13 The greatest odd factor is given by the product of the two greatest odd prime factors: 13×7=91

Which symbol most accurately reflects the relationship between the two numbers below? −5/6 □ −9/12

C < Fractions can be quickly compared once they have a common denominator. The smallest common denominator of both fractions is 12. Multiply −5/6 by 2/2​ to get −10/12 The fraction −9/12 has the greater numerator, so it is the greater fraction.

Mr. Harris assigns his students to create a factor tree of the products of a number. One student turns in the product factor tree of 32 shown here. Which of the following best describes the error in this factor tree?

C The factor tree identifies the sums and not the product factors of many of numbers. The third level of factors is the sum of the second level numbers (4 + 4 = 8). The correct factors of eight would be either (4 and 2) or (1 and 8).

After a lesson on rounding and estimation, a teacher tells students that the football concession stand has purchased 590 candy bars to sell for the 6 football home games this year. The teacher asks the students to estimate the average number of candy bars that will be sold at each home game. Which of the following would be the correct estimation?

D 100 An estimate is finding an approximation of a value. Estimates are used to quickly find an answer that is close, but probably not precise. 590 can easily be rounded to 600 which is divisible by 6. This means that about 100 candy bars will be sold per game.