Basic Terms and Terminology Relating to Solving One or Multi Step Problems with Rational Numbers

  • Rational numbers: Any number that can be expressed as a fraction or as a ratio. Rational numbers include whole numbers, zero, positive numbers, negative numbers, and decimal numbers.
  • Irrational Numbers: All numbers except rational numbers. An example of an irrational number is the square root of a number.
  • Necessary information in a word mathematical problem: That information in a word problem that is essential and necessary to understand, set up and calculate the word problem
  • Extraneous information in a word mathematical problem: That information in a word problem that is unnecessary and only extra information that is not relevant in a word problem and which can confuse you and NOT necessary to understand, set up and calculate the word problem
  • Erroneous information in a word mathematical problem: That information in a word problem that is false, inaccurate, incorrect and faulty information in a mathematical word problem.

Necessary, Extraneous and Erroneous Information in Word Problems

All word problems can have possible and potential extraneous and erroneous information in them. You should, therefore, discard and ignore all extraneous and erroneous information and focus on the necessary information in the word problem that is needed to successfully understand, set up and calculate the word problem. This requires careful reading of word problems found on your TEAS.

Simply defined, necessary information is that information in a word problem that is essential and necessary to understand, set up and calculate the word problem; extraneous information, simply defined, is unnecessary and extra information that is not relevant in a word problem that can confuse you and that is NOT necessary to understand, set up and calculate the word problem; and, lastly, erroneous and inaccurate information is incorrect and faulty information that can be included in a mathematical word problem.

It is wise to anticipate that your TEAS will include erroneous and extraneous information as you solve and calculate real world word problems in the Mathematics section of your TEAS.

Here are some word problems that include necessary information, erroneous information and extraneous information.

You are coordinating a holiday party for children in your church. Based on the ages of the children, you should plan for a cup of milk for each of the 32 children who will be attending. The children will have this milk with their cookies, after their main meal of spaghetti and meatballs. Because there are 5 cups per quart, how many quarts of milk should you purchase for this church holiday party?

Now, let's read this word problem very carefully and identify all necessary information, all extraneous information and all erroneous information.

The same word problem is repeated below with all necessary information highlighted in red, all extraneous information highlighted in green and all erroneous information is highlighted in turquoise.

You are coordinating a holiday party for children in your church. Based on the ages of the children, you should plan for a cup of milk for each of the 32 children who will be attending. The children will have this milk with their cookies, after their main meal of spaghetti and meatballs. Because there are 5 cups per quart, how many quarts of milk should you purchase for this church holiday party?

When all the erroneous and extraneous information in the above word problem are eliminated, you are left with only the information that you will need to successfully understand, set up and calculate the word problem.

The only necessary and relevant information in this problem is:

  • How much milk will be consumed by each child
  • How many children will be attending
  • How many quarts of milk should you buy

The calculation of this word problem is then done, as shown below:

  • The amount of milk for each child x The number of children who will attend
  • 1 cup of milk per child x 32 children = 32 cups
  • 32 cups/4 cups = x quarts
  • 32/4 = 8 quarts will be needed for this party

Answer: You will have to buy 8 quarts of milk for the church holiday party when each of 32 children will get one cup of milk.

Here is another word problem with necessary, erroneous and extraneous information.

A nurse is taking care of your mother in the hospital because she has a fever and pneumonia. She is getting an injection of an antibiotic every 8 hours. The nurse adds 1.5 mLs of sterile water into a vial with powdered antibiotic and this mixture now yields 0.5 grams of the medication in each mL of solution. How much solution should this nurse give your mother if the doctor has ordered 1 gram of the medication?

The same word problem is repeated below with all necessary information highlighted in red, all extraneous information highlighted in green and all erroneous information is highlighted in turquoise.

A nurse is taking care of your mother in the hospital because she has a fever and pneumonia. She is getting an injection of an antibiotic every 8 hours. The nurse adds 1.5 mLs of sterile water into a vial with powdered antibiotic and this mixture now yields 0.5 grams of the medication in each mL of solution and there are 1,000 mg in 0.5 grams. How much solution should this nurse give your mother if the doctor has ordered 1 gram of the medication?

The only necessary and relevant information in this problem is:

  • The yield in terms of the number of grams per mL
  • The number of grams that your mother should be getting

The calculation of this word problem is then done, as shown below:

  • The yield in terms of the number of grams per mL x number of grams that your mother should be getting
  • 0.5 grams /1 mL = 1 gram/x mL
  • 0.5 grams = 2 mLs

Answer: Your mother should be getting 2 mLs of this antibiotic when the nurse adds 1.5 mLs of sterile water into a vial with powdered antibiotic and this mixture yields 0.5 grams of the medication in each mL of solution and the doctor has ordered 1 gram of the medication.

RELATED TEAS NUMBERS & ALGEBRA CONTENT:

Alene Burke

Alene Burke

Alene Burke RN, MSN is a nationally recognized nursing educator. She began her work career as an elementary school teacher in New York City and later attended Queensborough Community College for her associate degree in nursing. She worked as a registered nurse in the critical care area of a local community hospital and, at this time, she was committed to become a nursing educator. She got her bachelor’s of science in nursing with Excelsior College, a part of the New York State University and immediately upon graduation she began graduate school at Adelphi University on Long Island, New York. She graduated Summa Cum Laude from Adelphi with a double masters degree in both Nursing Education and Nursing Administration and immediately began the PhD in nursing coursework at the same university. She has authored hundreds of courses for healthcare professionals including nurses, she serves as a nurse consultant for healthcare facilities and private corporations, she is also an approved provider of continuing education for nurses and other disciplines and has also served as a member of the American Nurses Association’s task force on competency and education for the nursing team members.
Alene Burke

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