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In Exercises 1-8, find a counterexample to show that each of the statements is false. Adding the same number to both the numerator and the denominator (top and bottom) of a fraction does not change the fraction's value.

In Exercises 1-8, find a counterexample to show that each of the statements is false. If a number is added to itself, the sum is greater than the original number.

In Exercises 5-8, one more piece of information is given than is necessary for solving the problem. Identify this unnecessary piece of information. Then solve the problem. An architect is designing a house. The scale on the plan is 1 inch - 6 feet. If the house is to have a length of 90 feet and a width of 30 feet, how long will the line representing the house's length be on the blueprint?

In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) \(8,12,16,20,24\),_____

In Exercises 9-22, obtain an estimate for each computation by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to the actual answer? \(359+596\)

Use Polya's four-step method in problem solving to solve Exercises 9-44. a. Which is the better value: a \(15.3\)-ounce box of cereal for \(\$ 3.37\) or a 24 -ounce box of cereal for \(\$ 4.59\) ? b. The supermarket displays the unit price for the 15.3-ounce box in terms of cost per ounce, but displays the unit price for the 24-ounce box in terms of cost per pound. What are the unit prices, to the nearest cent, given by the supermarket? c. Based on your work in parts (a) and (b), does the better value always have the lower displayed unit price? Explain your answer.

A television sells for \(\$ 750\). Instead of paying the total amount at the time of the purchase, the same television can be bought by paying \(\$ 100\) down and \(\$ 50\) a month for 14 months. How much is saved by paying the total amount at the time of the purchase?

Calculators were purchased at \(\$ 65\) per dozen and sold at \(\$ 20\) for three calculators. Find the profit on six dozen calculators.

In Exercises 23-34, determine each estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? Estimate the total cost of six grocery items if their prices are \(\$ 3.47, \$ 5.89, \$ 19.98, \$ 2.03, \$ 11.85\), and \(\$ 0.23\).

A college graduate receives a salary of \(\$ 2750\) a month for her first job. During the year she plans to spend \(\$ 4800\) for rent, \(\$ 8200\) for food, \(\$ 3750\) for clothing, \(\$ 4250\) for household expenses, and \(\$ 3000\) for other expenses. With the money that is left, she expects to buy as many shares of stock at \(\$ 375\) per share as possible. How many shares will she be able to buy?