# Producing Fractions and Mixed Numbers In the Proper Form

## Presentation on theme: "Producing Fractions and Mixed Numbers In the Proper Form"— Presentation transcript:

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.)

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.

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.

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.

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?

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.

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.

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?

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.

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?

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?

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?

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.

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