Chapter 4: Problem Solving

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Chapter 4 Problem Solving

• A. Word Problems
• Dont let word problems scare you!
• Follow these steps, and youll ACE all word
  problems
• Analyze
• Calculate
• Evaluate

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• Analyze
• Read the problem first!
• Identify the known(s) What do you know?
• Identify the unknown What is the question
  asking you to find?
• Box the numbers and units
• Underline the variable you want to find
• Think about a possible formula to use that
  contains the variables (known and unknown) in the
  problem

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• Calculate
• Show all work (formula, substitution, and answer
  with units)!
• Start with a formula
• Do you only have one variable left to solve for?
• Plug in the numbers (show the substitution)
• Do the units make sense for each variable?
• Does your answer match the question that was
  asked in the problem?

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• Evaluate
• Does your answer make sense?
• In terms of the value of your number?
• In terms of the units?
• Correct number of sig figs?
• If not
• Check the formula
• Check the numbers in the problem
• Check your work (substitution)
• Check your math (calculation)

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• Density Calculations
• Formula Density mass / Volume
• ( D m / V )
• ex. What is the density of an object that has
  a mass of 25.36g and a volume of 12.74mL?
• D ? , m 25.36g , V 12.74mL
• D m / V (write on top/bottom)
• D 25.36g / 12.74mL
• D 1.99 g/mL

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• Density Calculations (cont.)
• ex. What is the mass of a piece of lead,
  when its density is 11.4g/cm3 and has a
  volume of 19.84cm3?
• D 11.4g/cm3 , m ? , V 19.84cm3
• D m / V ? m D x V (How?!)
• m D x V
• m 11.4g/cm3 x 19.84cm3
• m 226.2 g (note cm3 cancels out)

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• Density Calculations (cont.)
• ex. What is the volume, in cm3, of cough
  syrup that has a mass of 50.0g and has a
  density of 0.950g/cm3?
• D 0.950g/cm3, m 50.0g , V ?
• D m / V ? V m / D (How?!)
• V m / D
• V 50.0g / 0.950g/cm3
• V 52.6 cm3 (note g cancels out)

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• Density Calculations (cont.)
• ex. The mass of a gasoline sample is .81g
  and with a volume of 1.21mL. What is the
  samples density?
• Will gasoline float or sink in H2O?
• D m / V
• D .81g / 1.21mL
• D .67 g/mL
• Float in H2O (D lt 1.0 g/mL)

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• B. Unit Conversions
• Conversion factor a ratio (or fraction) of
  equivalent measurements of different
  units

ex. 1 m 100 cm Conversion factor 1
m or 100 cm 100 cm 1 m ?
? larger smaller smaller unit larger
unit
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• Methods to convert units
• Proportions
• Factor-Label (Dimensional Analysis)
• Either method is accepted, as long as you show
  all work (do not just write an answer)
• Answers should use the of sig figs that are
  in the given (not the of decimals)

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• Proportions Method
• ex. Convert 0.5m into cm

0.5m 1 m ? cm 100cm
cross-multiply (the 2 s that are diagonal from
each other), then divide
(0.5m) x (100cm) 1.0m
50 cm
m cancels out
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• Proportions Method (cont.)
• ex. Convert 750mL into L

750mL 1000mL ? L 1L
(750mL) x (1L) 1000mL
0.75 L
mL cancels out
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• Factor-Label Method
• Start with the given ( in the problem)
• Multiply the given () by the conversion factor
  used
• The unit of the given is put in the denominator
  (bottom) of the conversion factor
• Cross-out units that are the same on top and
  bottom (diagonal from each other)
• Going left-right, multiply the top s, then
  divide by the bottom

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• Factor-Label Method (cont.)
• ex. Convert 750mL into L

750mL x 1L 1000mL
0.75 L
(750mL) x (1L) 1000mL mL cancels out

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• Factor-Label Method (cont.)
• ex. Convert 247.5g into cg

247.5g x 100cg 1g
24750 cg
g cancels out
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• Practice these
• (use either method proportion or factor-label)
• ex. 1. Convert 0.044km to m
• 2. Convert 4.6mg to g
• 3. Convert 15cm3 to L
• Answers 1. 44 m
• 2. 0.0046 g
• 3. 0.015 L

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• Multi-step conversions
• Factor-label method works best
• Can easily see what unit (conversion factor) to
  use next
• Goal cross-out units on the diagonal
• ex. How many seconds are in 1 day?

1 day x 24 hrs x 60 min x 60 sec 1
day 1 hr 1 min
86400 sec
days, hrs, and min all cancel out
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• Multi-step conversions (cont.)
• ex. What is the mass (in grams) of 8 bushels
  of apples if
• 1 bushel 20 apples
• 12 apples 1 dozen apples
• 1 dozen apples 2.0 kg

8 bushels x 20 apples x 1 dozen x 2.0
kg x 1000 g 1 bushel 12
apples 1 dozen 1 kg
26666.7 g
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• Multi-step conversions (cont.)
• ex. How many snoots are in a snod if
• 8 snods 4.3 pilks
• 2 pilks 0.5 mook
• 1 mook 14.9 snoots

1 snod x 4.3 pilks x 0.5 mook x 14.9
snoots 8 snods 2 pilks 1 mook
2 snoots