producing fractions and mixed numbers in the proper form fractions and mixed numbers measure a...
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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
Common Fractions
• represent equal parts of a whole;
• consist of two numbers and a fraction bar.
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 5
1
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.”
Fraction Rule
Rule 1-1Rule 1-1 When the denominator is 1, the fraction equals the number in the numerator.
ExamplesExamples
Check these equations by treating each fraction as a division problem.
414 100
1100
Mixed Numbers
• Mixed numbers combine a whole number with a fraction.
Example Example
Fractions with a value greater than 1 are written as mixed numbers.
2 (two and two-thirds)
32
Rule 1-2Rule 1-2
1. If the numerator of the fraction is less than the denominator, the fraction has a value of < 1.
¾ < 1
2. If the numerator of the fraction is equal to the denominator, the fraction has a value =1.
Mixed Numbers (cont.)
144
Mixed Numbers (cont.)
Rule 1-2 Rule 1-2 (cont.)
3. If the numerator of the fraction is greater than the denominator, the fraction has a value > 1.
14
5
Rule 1-3Rule 1-3 To convert a fraction to a mixed number:
1. Divide the numerator by the denominator. The result will be a whole number plus a remainder.
2. Write the remainder as the number over the original denominator.
Mixed Numbers (cont.)
Mixed Numbers (cont.)
Rule 1-3 Rule 1-3 (cont.)
3.Combine the whole number and the fraction remainder. This mixed number equals the original fraction.
Mixed Numbers (con’t)
Convert to a mixed number:
1. Divide the numerator by the denominator.
2.
The result is the whole number 2 with a remainder of 3.
ExampleExample 411
3R2411
Mixed Numbers (cont.)
3. Write the remainder over the whole = ¾
4. Combine the whole number and the fraction = 2¾
ExampleExample
Rule 1-4Rule 1-4 To convert a mixed number ( ) to a fraction:
1. Multiply the whole number by the denominator of
the fraction.
5x3 = 15
2. Add the product to the numerator of the fraction.
15+1 = 16
31
5
Mixed Numbers (cont.)
Rule 1-4Rule 1-4 (cont.)
3. Write the sum from Step 2 over the original denominator.
4. The result is a fraction equal to original mixed number. Thus:
316
316
31
5
Mixed Numbers (cont.)
Practice
What is the numerator in ?
Answer = 17
Answer = 100
10017
What is the denominator in ? 1004
Practice
Twelve patients are in the hospital unit. Four have type A blood. What fraction does not have type A blood?
Answer = 128
Adding Fractions
Rule 1-11Rule 1-11 To add fractions:
1. Rewrite any mixed numbers as fractions.
2. Write equivalent fractions with common denominators. The LCD will be the denominator of your
answer.
Adding Fractions
Rule 1-11Rule 1-11 To add fractions:
1. Rewrite any mixed numbers as fractions.
2. Write equivalent fractions with common denominators. The LCD will be the denominator of your
answer.
Adding Fractions
Rule 1-11Rule 1-11 To add fractions:
3.Add the numerators. The sum will be the numerator of your answer.
Adding Fractions
2
5
4
13
2
12
4
13
4
35
4
23
4
10
4
13
Example Addition
Example Addition 2
12
4
13 Add:
4
10
4
13
2
5
4
13LCD is 4.
Rule 1-12Rule 1-12 To subtract fractions:
1. Rewrite any mixed numbers as fractions.
2. Write equivalent fractions with common denominators. The LCD will be the denominator of
your answer.
Subtracting Fractions
Subtracting Fractions
Rule 1-12Rule 1-12 To subtract fractions:
3.Subtract the numerators. The difference will be the numerator of your answer.
Adding and Subtracting Fractions
12
3
6
2Example
Subtraction
ExampleSubtraction
Subtract:
LCD is 12.
12
1
12
3
12
4
12
3
6
2
Rule 1-13Rule 1-13 To multiply fractions:1. Convert any mixed numbers or whole numbers to
fractions.
2. Multiply the numerators and then the denominators.
3. Reduce the product to its lowest terms.
Multiplying Fractions
Multiplying Fractions (cont.)
To multiply multiply the numerators and multiply the denominators:
167
x218
61
33656
33656
16 x 217 x 8
167
x218
Example Example
Practice
Find the following products:
9
4x
8
3
Answer6
1
5
47 x
6
51
Answer10
314
Practice
A bottle of liquid medication contains 24 doses. The hospital has 9 ¾ bottles of medication. How many doses are available?
43
9 x 24 Answer 234
Rule 1-15Rule 1-151. Convert any mixed or whole number to fractions.
2. Invert (flip) the divisor to find its reciprocal.
3. Multiply the dividend by the reciprocal of the divisor and reduce.
Dividing Fractions
Convert the following mixed numbers to fractions:
183
2 Answer 613
1839
Answer 109910
99
Apply Your Knowledge
Apply Your Knowledge
Add the following:
Subtract the following:
52
32 Answer:
151
1
52
32 Answer:
154
Apply Your Knowledge
Multiply:
Divide:
Answer: 52
31
x51
1
31
51
1 Answer: 53
3