OBJECTIVE

• I will use the order of operations and rounding to find the exact and approximate solutions of equations that contain decimals.

Rounding for a Practical AnswerSix people buy some food to take to the lake. The

total cost for the food is $33.45. If each person pays the same amount, how much does each person owe?

6x = 33.45 Original equationx = 5.575 Exact answerx ≈ 5.58 Round to the nearest centEach person owes $5.58. The exact answer is not

practical because you cannot have a fraction of a cent, but six times the rounded answer does not correspond to the cost of the food. It is one cent too much due to round-off error.

Rounding for the Final Answer

Solve 7x + 32 = 128. Round to the nearest hundredth.7x + 32 = 128 Original equation7x = 96 Subtract 32 from each sidex = 13.714… Divide both sides by 7x ≈ 13.71 Round to nearest hundredthThe solution is approximately 13.71.

Guided Practice

1. Solve -12x - 13 = 37. Round to the nearest hundredth.

Original Equation Involving Decimals

• Solve using same methods used to solve equations without a decimal.

Solve 2.14x + 3.81 = 0.53x + 14.96. Round to the nearest hundredth.

2.14x + 3.81 = 0.53x + 14.961.61x = 11.15x = 6.925…x ≈ 6.93

Guided Practice

1. Solve 7.82x - 3.14 = 4.66x + 2.71. Round your answer to the nearest hundredth.

Changing Decimal Coefficients to Integers

• Change decimals to integers for easier calculationSolve 2.3x + 6.2 = 1.5x + 9.8. Round to the nearest tenth.2.3x + 6.2 = 1.5x + 9.7 Original Equation23x + 62 = 15x + 97 Multiply both sides by 108x = 35 Combine like termsx = 4.625x ≈ 4.6

Guided Practice

Re-write the coefficients as integers and solve. Round to the nearest tenth.

1. 5.7 - 3.4x = 2.2x - 7.1

Using a Verbal Model

You are shopping for roses. The total tax is 10%. You have a total of $27.79 to spend. What is your price limit for the roses?

Total cost is price limit and tax based on price limit.

Using a Verbal Model

Cost of Roses + Cost of Tax = Price Limitx + 0.10x = 27.79 Substitute1.10x = 27.79 Combine like termsx = 25.263… Divide both sides by 1.10x ≈ 25.26 Round downYou have a limited amount of money to spend,

so you must round down to $25.26. If you round up, the tax and total cost will increase and you will be a penny short.

Guided Practice

You are shopping for a bracelet. The sales tax is 5%. You have a total of $125.40 to spend. What is your price limit for the bracelet?

Independent Practice

Round answers to the nearest hundredth.1. 3x + 5 = 202. 2.51x - 4.27 = 1.13x + 2.153. Change the decimal coefficients to

integers to solve.3.4x - 2.3 = 1.7x + 5.4