Fractions

Fractions

A number that is a factor of two or more numbers.

The number of equal parts in a whole. It is the bottom number of a fraction.

Equivalent Fraction

Fractions that represent the same relationship of part to the whole. The fractions are equal even though there are variations in the size of the pieces or the number of parts of the total.

The number being multiplied.

A ratio that represents part of something in comparison to the total number of parts.

Fractions with Common Denominators

Fractions that have the same denominator.

Greatest Common Factor (GCF)

The largest factor of two or more numbers.

Improper Fraction

A fraction in which the numerator is greater than the denominator.

Least Common Denominator (LCD)

The smallest common multiple of the denominators of two or more fractions.

A number expression that consists of a whole number and a fraction.

The number of parts to which the problem is referring. It is the top number of a fraction.

Proper Fraction

A fraction in which the denominator is greater than the numerator.

Reduce or Simplify Fractions

Finding the lowest equivalent fraction by dividing the numerator into the denominator. This is done by finding the greatest common factor of the numerator and the denominator.

Part of a mixed number that is not in fractional form.

Objective 1

Health care professionals perform a variety of mathematical computations during the course of the day. Professionals involved in the clinical side of health care frequently encounter fractions while performing the following duties:

• Medical assistant: preparing medications, measuring height and weight, measuring for the length of a cast or splint

• Pharmacy technician: assisting in the preparation of medication

• Physical therapy assistant: supervising rehabilitation exercises involving weights, documenting endurance in minutes or hours

• Nurse: administering medication, IV therapy, and blood transfusions

• Dietician: calculating dietary intake or calorie needs

• Paramedic: preparing medication doses based on weight, calculating length of time for transport from a scene

However, there is more to health care than just the clinical application. Many careers fall under the administrative aspect of health care. Anyone who deals with money, payroll, time sheets, or ordering of supplies will probably manipulate fractions or at least convert the fractions into decimals.

Like most people, you have probably used fractions since grade school. However, your confidence in your ability to manipulate fractions may be weak. In this chapter, we will assess your knowledge level and provide strategies for properly manipulating fractions.

Objective 2

Understanding fractions

“Fractions—I just don’t understand them and never could.” “I can’t do math because of fractions.” “I’m fine with math, except for fractions, but that doesn’t matter because I never use them.” Do these statements sound familiar? Is this how you feel about fractions? Why do people become so anxious when they just hear the word fractions? People use fractions every day, whether they realize it or not. Here are a few examples:

• Who left 14 of a tank of gas in the car?

• About 34 of the students in the class are girls.

• We have 12 an hour for lunch.

• You need to add 23 cup of sugar to the recipe.

See more examples in Box 3-1.

Box 3-1 FRACTIONS IN THE REAL WORLD

• Cooking: measuring ingredients

• Carpentry: measuring materials

• Plumbing: measuring the length and diameter of pipes

• Health care: measuring height, weight, and medications

• Science: establishing the amount of each chemical in a compound

• Payroll: determining the amount of pay for a fractional part of an hour

• Music: reading a time signature to find out what fraction of the beats in a measure each note is

• Interior design: figuring out wallpaper and fabric measurements

Objective 1

To understand fractions, we need to review their purpose. Let’s get down to basics by answering the following questions:

1. What is a fraction?

2. Why do we use fractions?

3. Can fractions be equivalent?

I’m sure you know the answers. Now it is a matter of taking that knowledge and applying it in a different manner.

What Is a Fraction?

A fraction is a mathematical way to describe a part or unit used in relation to the total quantity. The numerator represents the total number of units being used, and the denominator represents the total number of pieces.

Example: Figure of a fraction:

Many people learned fractions by visualizing a pizza pie. So, let’s take what we know and apply it.

Example:

Three friends have ordered a pizza. The pizza comes in eight slices. Each friend has two slices (Figure 3-1).

Describe what fraction of the pizza has been eaten:

3 friends × 2 slices each = 6 slices of pizza eaten.

The pizza had a total of 8 slices.

The fraction 68 represents how much of the pizza has been consumed. Did you automatically reduce 68 to 34? If so, great! If you are unsure how to reduce a fraction, that is all right because we will address this in the next few paragraphs.

What is the fractional expression for the amount of pizza that has not been consumed?

8 total slices – 6 slices already eaten = 2 slices left.

So, the fraction of the pizza has not been consumed is 28, or 14.

Now let’s apply this concept to the real world. You work a 12-hour shift. You needed to leave 4 hours early. What fraction of the shift did you work? What fraction of the shift did you not work?

You worked 8 out of the 12 hours. The 8 hours you worked is the part or unit that you worked out of the total scheduled 12 hours. So, the fraction of the shift you did work is 812 (or 23 if you automatically reduce the fraction).

You left 4 hours early; this represents the part or unit that you did not work out of the total scheduled 12 hours. Therefore, the fraction of the shift you did not work is 412 (or 13 if you automatically reduce the fraction).

Objective 2

Why Do We Use Fractions?

As we have learned, fractions are a descriptive way to identify a portion, either used or remaining, of the total. For the visual learners and kinesthetic learners of the world, however, fractions can be hard to visualize. If you are having problems in determining the size of a series of fractions, try drawing a box into the number of sections indicated in the denominator and then shading the sections indicated in the numerator (Figure 3-2).

Figure 3-1 Reflection of fractions with pizza pie.

If you are having difficulty determining the order of a series of fractions, try this method:

1. Draw a rectangular box.

2. Divide the box into equal portions as determined by the denominator.

3. Shade the total portions used as determined by the numerator.

4. Finally, answer the question.

Objective 3

Can Fractions Be Equivalent?

Yes, equivalent fractions are fractions that represent the same relationship of a part to the whole. The fractions are equal even though there are variations in the size of the pieces or parts of the total. Many times we refer to equivalent fractions when we reduce a fraction to its lowest form. When we reduce or simplify fractions, we are finding the lowest equivalent fraction by dividing the numerator and the denominator by the greatest common factor (GCF). Remember the example discussed above regarding the pizza pie: 68 slices were eaten. We need to find a common factor that can be divided into both 6 and 8. In other words, what is the highest number that can be divided into both 6 and 8? In this case, the GCF is 2.

Thus, 68 is equivalent to 34. The fractions involved have different denominators; however, they represent the same number of pieces.

Why Does It Matter How We Express the Fraction?

Many people reduce fractions automatically either on paper or in their heads. Why? Because it is how they were taught: “Express your answer in its lowest form.” Let’s just say it is math etiquette.

Refer to the bulleted list of statements in the first section of this chapter. People describe fractions in their lowest form. People do not say 416 gallon of gas was left in the tank. It sounds awkward. However, 416 and 14 are equivalent fractions. Your instructor will most likely deduct points from your test scores if you do not reduce answers to their lowest form.

HUMAN ERROR 3-1

Most people do not like dealing with large numbers. The larger the number, the greater the chance for an error. By reducing your fractions to their smallest form, you will have less chance of error.

BUILDING CONFIDENCE WITH THE SKILL 3-1

Is the series of fractions equivalent? Answer “True” or “False.”

1. 12, 2550, 50100 _________________________________

2. 13, 39, 26 _________________________________

3. 14, 45, 312 _________________________________

4. 110, 880, 990 _________________________________

5. 115, 630, 945 _________________________________

6. 118, 318, 29 _________________________________

7. 612, 2448, 981 _________________________________

8. 318, 710, 643 _________________________________

9. 2346, 57114, 78156 _________________________________

10. 23, 46, 69 _________________________________

Reduce the following fractions

11. 1224 _________________________________

12. 618 _________________________________

13. 2436 ________________________________

14. 3048 ________________________________

15. 915 ________________________________

16. 575 ________________________________

17. 1248 ________________________________

18. 721 ________________________________

19. 7296 ________________________________

20. 1545 ________________________________

Solve the following word problems

21. Mary and Joe both are scheduled to work a 12-hour shift at the hospital. Mary receives a phone call and must leave the hospital after working only 3 hours. Joe becomes ill after working 8 hours and must leave.

a. What fraction of the work day did Mary work? ______________________

b. What fraction of the work day did Joe not work? ________________________

22. You are ordering pizza for everyone at the fire station. A large pizza has 12 slices. Your order includes one large supreme pizza, one large pepperoni pizza, and one large cheese pizza. The firefighters consume the following:

Ryan eats two slices of supreme and three slices of pepperoni.

Shawn eats one slice of supreme and three slices of pepperoni.

Kevin eats four slices of pepperoni and two slices of cheese.

Ben eats three slices of cheese.

Gerry eats six slices of supreme and two slices of pepperoni.

a. What fraction of each type of pizza is eaten? ________________________

b. What fraction of each pizza is left? ________________________

Objective 4

Different Types of Fractions

Have you ever received a lower grade on a math paper because your answer was correct but not written in the correct form? Your teacher might have deducted points because you left your answer as an improper fraction. In many occupations, it is acceptable to work with improper fractions; however, it is common practice for health care professionals to reduce fractions to their lowest form when recording results.

MATH ETIQUETTE 3-1

Proper Fraction: A fraction in which the denominator is greater than the numerator.

Examples:35, 34, 18, 310, 12

Improper Fraction: A fraction in which the numerator is greater than the denominator.

Examples:1210, 95, 1514, 2725

Mixed Number: Number expression that consists of a whole number and a fraction.

Examples: 115, 145, 1114, 1225

Whole Number: Any fraction with the same numerator and denominator can be rewritten as a whole number.

Examples:3232 = 1, 1515 = 1, 33 = 1, 22 = 1, 44 = 1

Many mathematical operations involve converting an improper fraction to a mixed number or vice versa. To convert an improper fraction into a proper fraction, you must divide the denominator into the numerator. Sometimes this will result in a whole number.

6 divided by 3 = 2

Most improper fractions will not divide evenly to create a whole number. Most improper fractions will have a whole number and a fraction.

29 divided by 7 = 4 with a remainder of 1; the remainder is placed in the numerator and the denominator remains unchanged, so the answer is written as 417

HUMAN ERROR 3-2

Mixed numbers must also be reduced to the lowest form.

MATH ETIQUETTE 3-2

The only time we do not change an improper fraction to a mixed number is when the fraction is being used in an operation involving multiplication or division.

Now that you remember how to reduce improper fractions, can you change a mixed number into an improper fraction?

Multiply the denominator by the whole number: 10 × 3 = 30.

Then add the numerator: 30 + 7 = 37.

The number 37 is your new numerator and will go over the existing denominator.

is your improper fraction.

Denominator × Whole Number + Numerator ÷ Denominator = Improper Fraction

Denominator/Numerator = Mixed Number

PRACTICE THE SKILL 3-2

Change the following improper fractions into mixed numbers. Record all answers in their lowest form

1. 274 ______________________________

2. 358 ______________________________

3. 1210 ______________________________

4. 478 ______________________________

5. 636 ______________________________

6. 2511 ______________________________

7. 457 ______________________________

8. 569 ______________________________

9. 232 ______________________________

10. 819 ________________________

PRACTICE THE SKILL 3-3

Convert the following mixed numbers to improper fractions

1. 334 ______________________________

2. 816 ______________________________

3. 512 ______________________________

4. 734 ______________________________

5. 1158 ______________________________

6. 9316 ______________________________

7. 1223 ______________________________

8. 1512 ______________________________

9. 478 ______________________________

10. 959 ______________________________

People use fractions every day. In this section, we have reviewed the different properties of fractions as well as how to manipulate fractions. In the following sections, we will build on these concepts to perform mathematical operations. As a reminder, all fractions should be stated in their lowest form.

BUILDING CONFIDENCE WITH THE SKILL 3-2

In the following series, place the fractions in order from least to greatest

1. 112, 116, 124 ______________________________

2. 25, 79, 316 ______________________________

3. 524, 536, 515 ______________________________

4. 110, 250, 75100 ______________________________

5. 23, 34, 18 ______________________________

Convert the following improper fractions into either whole numbers or mixed numbers. Write all answers in their lowest form

6. 183 ______________________________

7. 154 ______________________________

8. 245 ______________________________

9. 4536 ______________________________

10. 237 ______________________________

Reduce the following fractions to their lowest form

11. 721 ______________________________

12. 1632 ______________________________

13. 2472 ______________________________

14. 424 ______________________________

15. 648 ______________________________

Convert the mixed numbers into improper fractions

16. 658 ______________________________

17. 9310 ______________________________

18. 4711 ______________________________

19. 7910 ______________________________

20. 512 ______________________________

Match the fractions that are equivalent

21. 23 _____________ 1260

22. 12 _____________ 1218

23. 34 _____________ 1632

24. 15 _____________ 948

25. 316 _____________ 1520

26. 1224 _____________ 15

27. 525 _____________ 12

Answer the following word problems

28. Mr. James drank 12 cup of milk, 23 cup of orange juice, and 34 cup of coffee. Mr. James drank the most of which type of fluid? ______________________

29. Stacey submitted the following time sheet: Monday—512 hours, Tuesday—634 hours, Wednesday—334 hours, Thursday—512 hours, and Friday—7 hours. What is the total number of hours that Stacey worked during the week? ______________________

30. Janie used 1218 of her plaster to form a cast. Mary used 36 of her plaster to form a different cast. Who used more casting material? ______________________

HUMAN ERROR 3-3

Did you add correctly?

Did you subtract correctly?

Is your answer in its lowest form?

Does your answer make sense?

Objective 5

Addition and subtraction of fractions

As much as we would like to compare, reduce, and measure fractions, the most common operation performed with fractions is manipulation. In this section, we will refresh our knowledge of how to properly add and subtract with fractions.

Ryan’s time sheet for work:
Monday	614 hours
Thursday	414 hours
Saturday	5 hours

You may feel compelled to convert the mixed numbers into decimals before you add, and that is an acceptable way to figure this problem. Fractions can be user friendly, however, so let’s work this problem using the fractions.

When adding fractions, it is essential to have common denominators. In our example above, the common denominator is 4.

614	Add the numerators.
414	The denominators will remain the same, since they are common.
+5152/4	Add the whole numbers.

Once you have calculated the sum of the problem, you still need to reduce the fractions to the lowest form. In this case, 24 can be reduced to 12. So your final answer is 1512 hours.

For many people, it is easier to set up addition and subtraction problems in a vertical fashion. Either method is acceptable.

PRACTICE THE SKILL 3-4

Perform the following operations

1. 25+15=____________________

2. 316+916=____________________

3. 413+713=____________________

4. 524+1524=____________________

5. 23+13=____________________

6. 38+58=____________________

7. 314+814=____________________

8. 78+58=____________________

9. 435+835=____________________

10. 4560+1560=____________________

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Tags: Saunders Math Skills for Health Professionals

Apr 17, 2017 | Posted by admin in NURSING | Comments Off

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