Problem Solving: Guided Learning

Evaluating a mathematical expression means finding a numerical value for the expression. To evaluate expressions, the standard order of operations must be followed. This is abbreviated as PEMDAS.

PDo functions within Parentheses first.

EDo Exponents next.

MDMultiply and Divide from left to right.

ASLast is Adding and Subtracting from left to right.

Example:

(6-2) x (5+1)2 = (4) x (6)2 = (4) x (36) = 144

Practice:

Copy the problem onto another sheet of paper. Show all of your work.

1) (8 – 3) + 3 2) (6 + 12) ÷ 3 3) 6 + (12 ÷ 3) 4) (13 – 7)2 - 6

Isolating An Unknown

A mathematical equation is a statement that sets two expressions equal to each other. A solution to the equation gives a number that, when replaced for the variable, make the equation a true statement. The first step in solving an equation is to simplify the expression on both sides of the equal sign separately, using PEMDAS. Then, to solve equations and formulas, you must isolate the unknownvariable (or move the numbers to the opposite side of the equation as the variable). To do this you must often “undo” mathematical functions.

For example: 2x – 4 = 20First “undo” the subtraction by adding 4 to

each side of the equation.

2x – 4 + 4 = 20 + 4

2x = 24Then “undo” the multiplication of x by dividing

each side of the equation by 2.

x = 12Answer

Formula example:

Find °C if = 392

360 = To divide by a fraction, multiply by its reciprocal (turn the fraction upside-down)

(360) =

200 =

Practice:

Copy the problem onto another sheet of paper. Show all of your work.

Set up an equation to solve for the unknown.

5)3b + 4 = 11 6) 2(x + 5 – 3) = 8 7) 2n – 11 = 7 + n 8) °C = 50, find °F

Steps in Solving Word Problems

•Identify what is known or given.

•Identify the unknown.

•Plan a solution.

•Do the calculations.

•Check your answer.

Example:

The density of sulfur dioxide gas (SO2) is 2.87 kg per m3. What is the volume, in cubic meters (m3), of a sample of sulfur dioxide (SO2) that has a mass of 50.0 kilograms (kg)?

Solution:

Step 1: The known values are the mass (50.0 kg) and the density (2.87 kg per m3).

Step 2: The unknown is the volume, in cubic meters (m3).

Step 3: Set up an equation to solve for the unknown. Be sure that the UNITS of the known values are arranged so that the unknown will have correct units.

Step 4: Do the calculations.

The answer implies a high degree of accuracy, but this really is not appropriate. The answer should have only 3 significant figures as 50.0 kg has 3 sig figs. We must round the answer to 17.4 m3.

Step 5: Common-sense checking: is this number reasonable?

In Step 4, the value of the second fraction is close to, so the answer should be close to 17 (becauseof 50 is about 17).

Practice:

Copy the problem onto another sheet of paper. Show all of your work.

List the knowns. Set up an equation to solve for the unknown.

9)A sample of SO2 gas has a volume of 34 m3. Given that the density of the gas (SO2) is 2.87 kg per m3, what is the mass in kg?

revised 6/13/14 pe