Question

1. find the prime factorization of 900.
2. what is ( 6 \frac{10}{12} ) reduced?
3. norton read 4 books during his vacation. the first book had 326 pages, the second had 288 pages, the third had 349 pages, and the fourth had 401 pages. the 4 books he read had an average of how many pages per book?
4. the dog show has 8 small dogs, 4 medium - sized dogs, and 16 large dogs. what is the probability that a dog chosen at random is a medium - sized dog?

Explanation:

Question 1: Find the prime factorization of 900.

Step1: Start with dividing by 2

$900 \div 2 = 450$

Step2: Divide 450 by 2 again

$450 \div 2 = 225$

Step3: Divide 225 by 3

$225 \div 3 = 75$

Step4: Divide 75 by 3 again

$75 \div 3 = 25$

Step5: Divide 25 by 5

$25 \div 5 = 5$

Step6: Divide 5 by 5

$5 \div 5 = 1$

Step7: Write the prime factors

So the prime factors are $2 \times 2 \times 3 \times 3 \times 5 \times 5$ or $2^2 \times 3^2 \times 5^2$

Step1: Simplify the fraction part

Find the GCD of 10 and 12. GCD(10,12) = 2. Divide numerator and denominator by 2: $\frac{10\div2}{12\div2}=\frac{5}{6}$

Step2: Combine with the whole number

So $6\frac{10}{12}=6\frac{5}{6}$

Step1: Find the total number of pages

Total pages = $326 + 288 + 349 + 401$
$326+288 = 614$; $349 + 401 = 750$; Then $614+750 = 1364$

Step2: Calculate the average

Average = $\frac{\text{Total pages}}{\text{Number of books}}=\frac{1364}{4}=341$

Answer:

$2^2 \times 3^2 \times 5^2$ (or $2 \times 2 \times 3 \times 3 \times 5 \times 5$)

Question 2: What is $6\frac{10}{12}$ reduced?