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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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**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.

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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.

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**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.

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**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.

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**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.

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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.

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**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.

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**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

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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.)

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**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.

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**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.

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**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.

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**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?

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**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.

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**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.

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**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?

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**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.

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**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?

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**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?

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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?

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**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.

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**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

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**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:

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**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:

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