1. Producing Fractions and Mixed Numbers In the Proper Form
Fractions and mixed numbers measure a portion or part of a whole amount.
They are written in two ways:
as common fractions
as decimals
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.

2. Common Fractions represent equal parts of a whole;
consist of two numbers and a fraction bar.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
In the example of 1/5 the 1 represents one part of the whole while the 5 represents the whole.

3. Common Fractions Common fractions are written in the form:
Numerator (top part of the fraction) = part of whole
Denominator (bottom part of the fraction) represents the whole
one part of the whole
the whole
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.

4. Common Fractions (cont.)
With a scored (marked) tablet for 2 parts, you:
administer 1 part of that tablet each day;
show this as 1 part of 2 wholes or ½;
read it as “one half.”
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
If the physician has ordered a half tablet per dose of medication:
make sure the tablet is scored;
properly break the tablet;
administer ½ of the tablet.

5. Check these equations by treating each fraction as a division problem.
Fraction Rule
Rule When the denominator is 1, the fraction equals the number in the numerator.
Examples
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Check by dividing the denominator into the numerator: 4 divided by 1 = 4.
Check these equations by treating each fraction as a division problem.

6. Mixed Numbers Mixed numbers combine a whole number with a fraction.
2 (two and two-thirds)
Example
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Fractions with a value greater than 1 are written as mixed numbers.

7. Mixed Numbers (cont.) Rule 1-2
If the numerator of the fraction is less than the denominator, the fraction has a value of < 1.
¾ < 1
If the numerator of the fraction is equal to the denominator, the fraction has a value =1.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Example of 1: ¾ - The numerator of 3 is less than the denominator of 4; therefore the value of the fraction is less than 1.
Example of 2: 4/4 – The numerator equals the denominator; therefore the value of the fraction is 1.

8. Mixed Numbers (cont.) Rule 1-2 (cont.)
If the numerator of the fraction is greater than the denominator, the fraction has a value > 1.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Example of 3: 5/4 – The numerator is larger than the denominator; therefore the value of the fraction is greater than 1.

9. Mixed Numbers (cont.)
Rule 1-3 To convert a fraction to a mixed number:
Divide the numerator by the denominator. The result will be a whole number plus a remainder.
Write the remainder as the number over the original denominator.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
See example
This rule is applied only if the numerator is greater than the denominator.

10. Mixed Numbers (cont.) Rule 1-3 (cont.)
Combine the whole number and the fraction remainder. This mixed number equals the original fraction.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
This rule is applied only if the numerator is greater than the denominator.

11. Mixed Numbers (con’t) Convert to a mixed number:
Divide the numerator by the denominator.
The result is the whole number 2 with a remainder of 3.
Example
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
R3 means a remainder of 3.

12. Mixed Numbers (cont.) Write the remainder over the whole = ¾
Combine the whole number and the fraction = 2¾
Example
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.

13. Mixed Numbers (cont.)
Rule 1-4 To convert a mixed number ( ) to a fraction:
Multiply the whole number by the denominator of the fraction.
5x3 = 15
Add the product to the numerator of the fraction.
15+1 = 16
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.

14. Mixed Numbers (cont.) Rule 1-4 (cont.)
Write the sum from Step 2 over the original denominator.
The result is a fraction equal to original mixed number. Thus:
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.

15. Practice What is the numerator in ? What is the denominator in ?
Answer = 17
What is the denominator in ?
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Answer = 100

16. Practice
Twelve patients are in the hospital unit. Four have type A blood. What fraction does not have type A blood?
Answer =
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Practice problem 3:
12 patients represents the whole unit. Only 4 of the patients on the unit have type A blood. 12 – 4 = 8, so 8 of the 12 patients do not have type A blood. (The fraction is not reduced to lowest form because this has not been covered at this point.)

17. Adding Fractions Rule 1-11 To add fractions:
Rewrite any mixed numbers as fractions.
Write equivalent fractions with common denominators.
The LCD will be the denominator of your answer.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-2 Produce and identify equivalent fractions.
Learning Outcome: 1-4 Find the least common denominator.
Learning Outcome: 1-6 Add fractions.

18. Adding Fractions Rule 1-11 To add fractions:
Rewrite any mixed numbers as fractions.
Write equivalent fractions with common denominators.
The LCD will be the denominator of your answer.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-2 Produce and identify equivalent fractions.
Learning Outcome: 1-4 Find the least common denominator.
Learning Outcome: 1-6 Add fractions.

19. Adding Fractions Rule 1-11 To add fractions:
Add the numerators. The sum will be the numerator of your answer.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-2 Produce and identify equivalent fractions.
Learning Outcome: 1-4 Find the least common denominator.
Learning Outcome: 1-6 Add fractions.

20. Adding Fractions Add: LCD is 4. Example Addition
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-2 Produce and identify equivalent fractions.
Learning Outcome: 1-4 Find the least common denominator.
Learning Outcome: 1-6 Add fractions.
Learning Outcome: 1-7 Subtract fractions.
Think!…Is It Reasonable?

21. Subtracting Fractions
Rule To subtract fractions:
Rewrite any mixed numbers as fractions.
Write equivalent fractions with common denominators.
The LCD will be the denominator of your answer.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-2 Produce and identify equivalent fractions.
Learning Outcome: 1-4 Find the least common denominator.
Learning Outcome: 1-7 Subtract fractions.

22. Subtracting Fractions
Rule To subtract fractions:
Subtract the numerators. The difference will be the numerator of your answer.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-2 Produce and identify equivalent fractions.
Learning Outcome: 1-4 Find the least common denominator.
Learning Outcome: 1-7 Subtract fractions.

23. Adding and Subtracting Fractions
Example
Subtraction
Subtract:
LCD is 12.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-2 Produce and identify equivalent fractions.
Learning Outcome: 1-4 Find the least common denominator.
Learning Outcome: 1-6 Add fractions.
Learning Outcome: 1-7 Subtract fractions.
Think!…Is It Reasonable?

24. Multiplying Fractions
Rule 1-13 To multiply fractions:
Convert any mixed numbers or whole numbers to fractions.
Multiply the numerators and then the denominators.
Reduce the product to its lowest terms.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-3 Determine the simplest form of a fraction.
Learning Outcome: 1-8 Multiply fractions.
Multiplying fractions can be performed even when the fractions do NOT have a common denominator.

25. Multiplying Fractions (cont.)
To multiply multiply the numerators and multiply the denominators:
Example
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-3 Determine the simplest form of a fraction.
Learning Outcome: 1-8 Multiply fractions.
56 and 336 can both be evenly divided by 56.
Think!…Is It Reasonable?

26. Practice Find the following products: Answer Answer
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-3 Determine the simplest form of a fraction.
Learning Outcome: 1-8 Multiply fractions.
Problem 1
3/8 x 4/9 = 12/72 = 1/6
Problem 2
1 5/6 x 7 4/5 = 11/6 x 39/5 = 429/30 = 14 9/30 = 14 3/10
Think!…Is It Reasonable?

27. Practice
A bottle of liquid medication contains 24 doses. The hospital has 9 ¾ bottles of medication. How many doses are available?
Answer 234
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-3 Determine the simplest form of a fraction.
Learning Outcome: 1-8 Multiply fractions.
Problem 3
24 x 9 ¾ = 24/1 x 39/4 = 936/4 = 234
Think!…Is It Reasonable?

28. Dividing Fractions Rule 1-15
Convert any mixed or whole number to fractions.
Invert (flip) the divisor to find its reciprocal.
Multiply the dividend by the reciprocal of the divisor and reduce.
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-9 Divide fractions.
Dividing of fractions can be performed even when the fractions do NOT have a common denominator.

29. Apply Your Knowledge Answer
Convert the following mixed numbers to fractions:
Answer
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Problem 1
2 3/18 = 2 x = 39/18 = 13/6
Problem 2
9 9/10 = 9 x = 99/10
Think!…Is It Reasonable?
Answer

30. Apply Your Knowledge Add the following: Subtract the following:
Answer:
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-4 Find the least common denominator.
Learning Outcome: 1-6 Add fractions.
Learning Outcome: 1-7 Subtract fractions.
Problem 1
LCD = 15
2/3 + 2/5 = 10/15 + 6/15 = 16/15 = 1 1/15
Problem 2
2/3 – 2/5 = 10/15 – 6/15 = 4/15
Think!…Is It Reasonable?
Answer:

31. Apply Your Knowledge Multiply: Divide: Answer: Answer:
Learning Outcome: 1-1 Produce fractions and mixed numbers in the proper form.
Learning Outcome: 1-8 Multiply fractions.
Learning Outcome: 1-9 Divide fractions.
Problem 1
1 1/5 x 1/3 = 6/5 x 1/3 = 6/15 = 2/5
Problem 2
Divide 1 1/5 by 1/3 = 6/5 divided by 1/3 =
6/5 x 3/1 =18/5 = 3 3/5
Think!…Is It Reasonable?
Answer: