Download Algebraic Problem

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.
P
E
MD
AS
Do functions within Parentheses first.
Do Exponents next.
Multiply and Divide from left to right.
Last 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.
1) (8 – 3) + 3
2) (6 + 12) ÷ 3
Show all of your work.
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 unknown variable (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 = 20
First “undo” the subtraction by adding 4 to
each side of the equation.
2x – 4 + 4 = 20 + 4
2x = 24
Then “undo” the multiplication of x by dividing
each side of the equation by 2.
2 x 24
=
2
2
x = 12
Answer
revised 6/13/14 pe
Formula example:
æ9ö
° F = ç ÷°C + 32
è5ø
Find °C if ° F = 392
æ9ö
392 = ç ÷°C + 32
è5ø
æ9ö
392 - 32 = ç ÷°C + 32 - 32
è5ø
æ9ö
360 = ç ÷°C To divide by a fraction, multiply by its reciprocal (turn the fraction
è5ø
upside-down)
æ5ö
ç ÷ (360) =
è9ø
200 = °C
æ5ö æ9ö
ç ÷ ç ÷°C
è9ø è5ø
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).
revised 6/13/14 pe
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.
æ 50.0 kgöæ 1 m3 ö
3
ç
֍
÷=? m
è 1 øè 2.87 kgø
Step 4:
50.0 kg 1 m 3
 ? m3
1
2.87 kg
Do the calculations.
æ 50.0 kgöæ 1 m3 ö
3
ç
֍
÷ = 17.42 m
è 1 øè 2.87 kgø
50.0 kg 1 m 3
 17.42 m 3
1
2.87 kg
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?
1
In Step 4, the value of the second fraction is close to , so the answer should be
3
1
close to 17 (because of 50 is about 17).
3
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