# Solve One or Multi-Step Problems with Rational Numbers: TEAS

## 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**:

- Converting Among Non Negative Fractions, Decimals, and Percentages
- Arithmetic Operations with Rational Numbers
- Comparing and Ordering Rational Numbers
- Solve Equations with One Variable
**Solve One or Multi-Step Problems with Rational Numbers (Currently here)**- Solve Problems Involving Percentages
- Applying Estimation Strategies and Rounding Rules for Real-World Problems
- Solve Problems Involving Proportions
- Solve Problems Involving Ratios and Rates of Change
- Translating Phrases and Sentences into Expressions, Equations and Inequalities