Fractions

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Fraction

part of a whole

numerator

Top number representing the part(s) of the whole number.

Denominator

Bottom number representing the whole number.

Types of fractions

• Proper fraction - numerator is smaller than the denominator. EX: 1/2

• Improper fraction - numerator is larger than the denominator. EX: 6/4 if the numerator is equal to the denominator, this indicates the quantity equals 1. EX: 3/3

• Mixed number fraction - whole number with a fraction EX: 2 ¾

• Complex Fraction - numerator and or the denominator is a fraction. EX: ½ / ¾

Equivalent fractions

fractions with different numerators and denominators but have the same value.

EX: ½ and 2/4

Greatest Common Factor (GCF)

the largest number that divides into both the numerator and denominator to give a whole number

Factor

a number that can be multiplied by another number to equal a specific number.

• they can be found by dividing the number with a specific number that results in a whole number

• EX: Factors of 10: 10 ÷ 1 = 10, 10 ÷ 2 = 5, 10 ÷ 3 = 3.3333 → A factor must result in a whole number. This indicates 3 is not a factor of 10, 10 ÷ 5 = 2

  • Therefore, factors of 10 are 1, 2, 5

lowest terms

when a fraction’s numerator and denominator cannot be divided into a smaller number.

What is the greatest common factor for the following fraction?

12/18

6

Step 1:  List the factors for the numerator.

Factors of 12 – 1, 2, 3, 4, 6, 12

Step 2: List the factors for the denominator.

Factors of 18 – 1, 2, 3, 6, 9, 18

Step 3: Find the common factor between the numerator and denominator.

The greatest common factor is 6.

Reduce the following fraction to its lowest terms.

12/18

2/3

Step 1: Find the greatest common factor.

Greatest common factor is 6.

Step 2: Divide the numerator by the greatest common factor.

12÷6=2​​​​​

This is the new numerator.

Step 3: Divide the denominator by the greatest common factor.18÷6=3 This is the new denominator.

Step 4: Final answer with new numerator and denominator

2/3​

Common denominator

same number in the denominator of each fraction

EX: 5/12 and 9/11

• Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156

• Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154

• The lowest common denominator is 132.

What is the lowest common denominator for both fractions:

5/8 and 7/10?

40

Step 1: List multiples of the denominators.

Multiples of 8: 8, 16, 24, 32, 40, 48, 56

Multiples of 10: 10, 20, 30, 40, 50, 60

Step 2: Compare lists and find the lowest number both fractions have in common.

The common denominator is 40.

Steps on how to Covert Mixed Numbers to Improper Fractions

Step 1: Multiply the denominator by the whole number.

Step 2: Add the numerator.

Step 3: Place new number over the denominator.

3 ¼ ​=4(4×3)+1​ / 4 = 13/4

Convert the mixed number to an improper fraction. 

3 5/7

26/7

Step 1: Multiply the denominator by the whole number.

• 7×3=21​​​​​​​

Step 2: Add the numerator.

• (7×3)+5=21 + 5 = 26​​​​​​

Step 3: Place new number over the denominator.

• 26/7 ​​​​​​​​

Steps to Convert Improper Fractions to Mixed Numbers

Step 1: Divide the numerator by the denominator.

Step 2: Write down the whole number.

Step 3: Write down the remainder above the denominator.

EX: 19/5

step 1: 19÷5=3.8

Step 2: whole number is 3

Step 3: what’s left is the .8 and 4/5 is is equalivent to that.

Answer: 3 4/5

Convert the improper fraction to a mixed number. (Practice these) :

46/12

3 5/6

Step 1: Divide the numerator by the denominator.

46÷12=3 remainder 10​​​​​​​

Step 2: Write down the whole number.

The whole number is 3.

Step 3: Write the remainder over the denominator.

10/12

​​​​​​​​Step 4: Reduce the fraction.

5/6​​​​​​​​

Final answer: 3 5/6​

Steps to Add Fractions with Common Denominators

Step 1: Add the numerators together.

Step 2: Keep the denominators the same.

Step 3: Reduce the final answer to its lowest terms if needed.

EX: 6/10 + 1/10 = 6 + 1 / 10

• 7/10

EX#2: 7/10 + 1/10 = 7+1 / 10

• 8/10 → reduce to lowest terms

  • Final Answer: 4/5

Steps to Adding Fractions Without Common Denominators

Step 1: Find the common denominator.

Step 2: Convert the fraction.

Step 3: Add the numerators together.

Step 4: Keep the denominators the same.

Step 5: Reduce the final answer to its lowest terms if needed.

EX: 1/5 + 6/10

• The lowest common denominator is 10

• Convert the fraction to the lowest common denominator

  • 1/5 → 1/ 5 (x2) {on top and bottom} = 2 / 10

• Add the numerators, keep the denominators

  • 2/10 + 6/10 = 8/10

• Reduce to the lowest terms

  • 8/10 = 4/5

• Final Answer : 4/5

Steps to Adding Mixed Fractions

Step 1: Reduce the fractions if needed.

Step 2: Convert the fractions to common denominators.

Step 3: Add the whole numbers.

Step 4: Add the numerators.

Step 5: Keep the denominators the same.

Step 6: Reduce the fractions if needed.

EX: 1 ¾ + 3 1/8

• The lowest common denominator is 8.

• Convert the fraction to the lowest common denominator

  • ¾ → ¾ x2(on top and bottom) = 6/8

• Add the whole numbers

  • 1 + 3 = 4

• Add the numerators, keep the denominators

  • 6/8 + 1/8 = 7/8

• Final Answer:

  • 4 7/8

Case Study: The nurse discusses the importance of daily water intake with the client.

Nurse: How much water did you drink yesterday?

Client: I drank 3 ½ ​​​​​​​​ cups in the morning and 2 ¾ ​​​​​​​​ cups in the evening.

How many cups of water did the client drink yesterday?

6 ¼

The nurse should determine the total amount of water the client consumed in one day. The nurse should use the addition calculation to combine the amounts reported by the client.

Step 1: Are the denominators the same?

No; convert the fractions to common denominators.

Step 2: Convert the fractions to common denominators.

Multiples of 2: 2, 4, 6, 8, 10

Multiples of 4: 4, 8, 12, 16, 20

4 is the lowest common denominator.

½   ×  2 { on top and bottom}  +  ¾   =  2/4   +  3/4 ​​​​​​​

Step 3: Add the new numerators and keep the denominator the same.

2/4  +  3/4  =  5/4​​​​​​​​

Step 4: Convert the improper fraction to a mixed number.

5÷4=1 remainder 1​​​​​​​

1 ¼ ​

Step 5: Add the new mixed fraction to whole numbers.

3  +  2  +  1 ¼   =  6 1/4​​​​​​​​

The nurse should calculate that the client consumed a total of 6 ¼ cups of water in one day.

4/5 + 3/5

1 2/5

Step 1: Are the denominators the same?

Yes; keep the denominators the same.

Step 2: Add the numerators.

4  +  3  =  7

​​​​​Step 3: Place the new numerator over the denominator.

7/5

​​​​​​​​Step 4: Convert the improper fraction to a mixed number.

7  ÷  5  =  1  remainder  2

Final Answer:

1 2/5 ​

Steps to Subtracting Fractions With Common Denominators

Step 1: Subtract the numerators.

Step 2: Keep the denominators the same.

Step 3: Reduce the final answer to its lowest terms if needed.

EX: 6/10 - 1/10

Subtract the numerators, keep the denominators

• 6/10 - 1/10 = 5/10

Reduce the final answer

• 5/10 = 1/2

Steps to Subtracting Fractions Without Common Denominators

Step 1: Find the common denominator.

Step 2: Convert the fraction.

Step 3: Subtract the numerators.

Step 4: Keep the denominators the same.

Step 5: Reduce the final answer to its lowest terms if needed.

EX: 5/12 - ¼

The lowest common denominator is 12.

Convert the fraction to the lowest common denominator

• ¼ → ¼ x 3 {on top and bottom} = 3/12

Subtract the numerators, keep the denominators.

• 5/12 - 3/12 = 2/12

Reduce

2/12 = 1/6

Final Answer

1/6

Steps to Subtracting Mixed Fractions

Step 1: Reduce the fractions if needed.

Step 2: Convert the fractions to common denominators.

Step 3: Subtract the whole numbers.

Step 4: Subtract the numerators.

Step 5: Keep the denominators the same.

Step 6: Reduce the fraction if needed.

EX: 4 ¼ - 3 1/8

The lowest common denominator is 8

Convert the fraction to the lowest common denominator

• ¼ → ¼ x2 {on top and bottom} = 2/8

Subtract the whole numbers

• 4-3 = 1

Subtract the numerators, keep the denominators

• 2/8 - 1/8 = 1/8

Final Answer

• 1 1/8

A nurse gathers information about a client’s work environment. The client reports that they work at a factory and that their line of work is physically demanding. The client reports recently reducing their work per week.

Nurse: How much did you reduce your work week to?

Client: I used to work a full week, but I reduced it by ¼ ​​​​​​​​ of the time.

How much of the work week does the client work now?

¾

The nurse should determine the amount of time the client works per week. The nurse should subtract the reduced amount of time the client worked from the original amount.  

Step 1: Are the denominators the same?

No; convert the fractions to common denominators.

Step 2: Convert the fractions to common denominators.

Multiples of 1: 1, 2, 3, 4, 5

Multiples of 4: 4, 8, 12, 16

4 is the lowest common denominator.

1  ×  4 / 1  ×  4  −  1/4  =  4/4  −  1/4​​​

Step 3: Subtract the new numerators and keep the denominator the same.

4/4  −  1/4  =  3/4​​​​​​​​

The nurse should calculate that the client now works ¾ ​​​​​​​​ of the week instead of a full week. 

Steps to Multiplying Fractions

Step 1: Convert the whole number or mixed number to an improper fraction if needed.

Step 2: Reduce the fraction to its lowest terms if needed.

Step 3: Multiply numerators.

Step 4: Multiply denominators.

Step 5: Reduce the fraction to its lowest terms again if needed.

Step 6: Convert the improper fraction to a mixed number if needed.

A nurse discusses dietary intake with the client. The nurse asks the client if they finish all of their dinners. The client reports eating 3443​​​​​​​​ of their dinner each day, 7 days a week.

What total number of dinners does the client consume in 7 days?

5 ¼

The nurse should determine the total amount of dinners consumed in 7 days. The nurse should multiply the number of dinners consumed by 7 days a week.

Step 1: Convert the whole number or mixed number to an improper fraction, if needed.

7 days needs to be converted to: ​​​​​​​7​ / 1​​​​​​​

¾   ×7/1 ​​​​​​​​

Step 2: Reduce the fraction to its lowest terms, if needed.

None of the fractions can be reduced to lower terms.

Step 3: Multiply the numerators.

3  ×  7  =  21​​​​​​​

Step 4: Multiply the denominators.

4  ×  1  =  4​​​​​​​

Step 5: Put the new numerator and denominator together.

21/4​​​​​​​

Step 6: Convert the improper fraction to a mixed number.

21/4  =  21  ÷  4  =  5  remainder 1​​​​​​

5 ¼ ​​​​​​​​

The nurse should calculate that the client consumes 5 ¼ ​​​​​​​​ full dinners in 7 days.

Steps to Divide Fractions

Step 1: Convert the whole number or mixed number to an improper fraction if needed.

Step 2: Keep the dividend as it is written.

Step 3: Reverse the divisor’s numerator and denominator (put the numerator on the bottom and denominator on the top).

Step 4: Multiply the dividend and divisor together.

Step 5: Cancel numbers if needed.

Step 6: Reduce the fraction to its lowest terms.

Step 7: Convert the improper fractions to mixed numbers if needed.

Dividend

first fraction in the division equation

divisor

second fraction in the division equation

Quotient

final answer obtained by the division of the dividend and divisor

A nurse discusses the importance of exercise with the client. The nurse asks the client how much they exercise in a week. The client reports running 4 ½ ​​​​​​​​ miles over 5 days a week.

How many miles does the client run each day?

The nurse should determine the distance the client runs per day. The nurse should divide the total amount of miles ran by 5 days a week.

Step 1: Convert the whole number or mixed number to an improper fraction, if needed.

Convert 4 ½ ​​​​​​​​miles to an improper fraction 9/2 ​​​​​​​​

Convert 5 days a week to an improper fraction ​​​​​​​5/1 ​​​​​​​​

Step 2: Keep dividend as it is written.

9/2​​​​​​​

Step 3: Reverse the divisor’s numerator and denominator (put the numerator on the bottom and denominator on the top).

​​​​​​​1/5​​​​​​​

Step 4: Multiply the dividend and divisor together.

9/2  ×  1/5  =  9/109​​​​​​​

Step 5: Cancel numbers if needed.

None of the numbers can be canceled.

Step 6: Reduce the fraction to its lowest terms.

9/10​​​​​​​ cannot be reduced to lower terms.

The nurse should calculate that the client runs 9/10​​​​​​​​ of a mile every day over 5 days. 

Summary

In conclusion:

• The ability to understand fractions and apply basic math principles to them plays an important role in nursing.

• Calculating dosages, comparing quantities, and converting between metric and household measurements may require the use of fractions.

• Fractions in nursing can be used in a variety of ways, including calculating fluid and food intake, determining amount of exercise, and calculating changes in caffeine consumption and reduction in work time).

• It is important to remember the components of a fraction to calculate basic math problems accurately. Basic conversions between different types of fractions might also be necessary.

• Nurses use fractions in addition, subtraction, multiplication, and division calculations.

A nurse is documenting the client's intake of 3 ¹/₂ cups of water. What type of fraction is being used?

mixed number

A nurse is reviewing a client's electronic health record. The client reports taking ¹/₄ of a tablet once a day for 7 days. How many tablets total has the client taken in 7 days?

1 ¾

The nurse should determine the total amount of medication taken in 7 days. The nurse should use the multiplication calculation to multiply the amount of medication taken by the client 7 days per week.

Step 1: Convert whole number or mixed number to an improper fraction, if needed.

7 days needs to be converted to ⁷/₁

1		7
	×
4		1

Step 2: Reduce fraction to lowest terms, if needed.

None of the fractions can be reduced to lower terms.

Step 3: Multiply numerators.

1 × 7 = 7

Step 4: Multiply denominators.

4 × 1 = 4

Step 5: Put new numerator and denominator together.

⁷/₄

Step 6: Convert improper fraction to a mixed number.

⁷/₄ = 7 ÷ 4 = 1 remainder 3

Final answer:

1 ³/₄

Using the calculation, the nurse should understand the client has taken 1³/₄ tablets total in 7 days.

A nurse is preparing to administer ⁵/₂ tablets of a medication to a client. How many tablets should the nurse administer using a mixed number fraction?

Step 1: Divide the numerator by the denominator.

5 ÷ 2 = 2 remainder 1

Step 2: Write down the whole number.

Whole number is 2.

Step 3: Write the remainder over the denominator.

¹/₂

Step 4: Reduce the fraction to its lowest terms.

¹/₂ is already reduced to its lowest terms.

Final answer:

2 ¹/₂ tablets

Using the calculation, the nurse should administer 2 ¹/₂ tablets.

A nurse is reviewing a client's electronic health record. The client reports exercising 4 ¹/₂ hr over 4 days per week. How many hours per day does the client exercise?

1 ¹/₈ hr

The nurse should determine the amount of time the client exercises each day. The nurse should use the division calculation to divide the total amount of time exercising by 4 days per week.

Step 1: Convert whole number or mixed number to an improper fraction, if needed.

Convert 4 ¹/₂ hr to an improper fraction: ⁹/₂

Convert 4 days a week to an improper fraction: ⁴/₁

Step 2: Keep dividend as written.

⁹/₂

Step 3: Reverse divisor’s numerator and denominator (put the numerator on the bottom and denominator on the top).

¹/₄

Step 4: Multiply the dividend and divisor together.

9		1		9
	×		=
2		4		8

Step 5: Cancel numbers, if needed.

None of the numbers can be canceled.

Step 6: Reduce fraction to the lowest terms.

⁹/₈ cannot be reduced to lower terms

Step 7: Convert improper fraction to mixed number fraction.

1 ¹/₈

Final answer:

Using the calculation, the nurse should understand that the client exercises 1¹/₈ hr per day over 4 days.

A nurse calculates a client's total intake. The client drank 2 ¹/₂ cups of water for breakfast and 1 ³/₄ cups of juice for lunch. How many total cups of liquid did the client drink?

4 ¼ cups

The nurse should determine the client’s total intake for the day. The nurse should use the addition calculation to add the amount of intake during breakfast and lunch.

Step 1: Are the denominators the same?

No, convert fractions with common denominators.

Step 2: Convert fractions with common denominators.

Multiples of 2: 2, 4, 6, 8, 10

Multiples of 4: 4, 8, 12, 16

4 is the lowest common denominator

(1 × 2)		3		2		3
	+		=		+
(2 × 2)		4		4		4

Step 3: Add the new numerators, keep the denominator the same.

2		3		5
	+		=
4		4		4

Step 4: Convert to a mixed number if an improper fraction.

5 ÷ 4 = 1 remainder 1 = 1¹/₄

Step 5: Add to whole numbers.

2 + 1 + 1¹/₄

Final answer:

4 ¹/₄

Using the calculation, the nurse should understand the client has consumed 4¹/₄ cups total.