Answer all the following problems in the text. Be sure to show your work for each problem.
1. Analyze the following computations. Explain what is wrong in each case
a. 135+47 =172 b. 87+25 =1012 c. 57-38 = 21 D. 56-18 =48
2. George is cooking an elaborate meal for Thankgiving. He can cook only one thing at a time in his microwave oven. His turkey takes 75 min; the pumpkin pie takes 18 min; rolls take 45, sec; and a cup of coffee takes 30 sec to heat. How much time does he need to cook the meal?
3. Give reasons for each of the following step:
4. Place parentheses, if needed, to make each of the following equations true:
5. Jonah has a large collection of marbles. He notices that if he borrows 5 marbles from a friend, he can arrange the marbles in rows of 13 each. What is the remainder when he divides his original number of marbles by 13?
6. Can 0 be the identity for multiplication? Explain why or why not.
7. Xuan saved $5340 in 3 years. If he saved $95 per month in the first year and a fixed amount per month for the next 2 years, how much did he save per month during the last 2 years?
8. Give reason for each of the following steps:
9. Use front –end estimation with adjustment to estimate each of the following:
10. Give several examples from real world situations where an estimate, rather than an exact answer is sufficient.
11 A Student asks why he has to learn about any estimation strategy other than rounding. What is your response?
12. Show that the distributive property of multiplication over addition a(b+c)=ab+ac, is true for each of the following values of a, b, and, c.
13. Compute each of the following:
14. Identify the property of integers being illustrated in each of the following:
15. Kahlil said that using the equation (a+b)^2=a^2+2ab+b^2 he can find a similar equation for a(-b)^2
Examine his argument. If it is correct, supply any missing steps or justifications; if it is incorrect, point out why.
16. Without using a calculator, test each of the following numbers for divisibility by 2, 3, 4, 5, 6, 8, 9, and 11:
17. Devise a test for divisibility by each of the following numbers:
18. Jim uses his calculator to see if a number n having eight or fewer digits is divisible by a number d. He finds that n d has a display of 32. Does d ∣n? Why?
19. Can you find three consecutive natural numbers none of which is divisible y 3? Explain your answer.
20. Find the prime factorization of the following:
20. Explain why the product of any four consecutive integers is divisible by 24.
21. A movie rental sore gives free popcorn to every fourth customer and a free movie rental to every sixth customer. Use the number line method to find which customer was the first to win both prizes.
22.The principal of Valley elementary school wants to divide each of the three fourth grade classes into small same size groups whit at least 2 students in each. If the classes have 18, 24, 36 students, respectively, what size groups are possible?