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Algebraic fractions |
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CONTENTS |
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| Fractions in algebraic expressions |
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Workout |
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35 slides |
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| Algebraic fractions |
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Library |
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17 questions |
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Once you have registered, you can work through the slides one by one.
The workout comprises a series of sides that guide you systematically through the topic concept by concept, skill by skill. The slides may be used with or without the support of a tutor. The methodology is based on problem-solving that advances in logical succession by concept and difficulty. The student is presented with a problem or series of questions, and the next slide presents the fully-worked solution. To use the material you must sign-in or create an account.
blacksacademy.net comprises a complete course in mathematics with resources that are comprehensive.
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SAMPLE FROM THE WORKOUT |
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SLIDE 1 - QUESTION 1 |
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SLIDE 2 - SOLUTION |
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SAMPLE FROM THE LIBRARY |
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QUESTION [difficulty 0.1] |
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SOLUTION |
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DEPENDENCIES |
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CONCEPTS |
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LEV. |
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Algebraic rule for the addition of fractions
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646.5 |
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Addition of algebraic fractions
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646.7 |
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Algebraic rule for the multiplication of fractions
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646.9 |
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Multiplicaiton of algebraic fractions
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647.1 |
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Algebraic rule for the division of fractions
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647.3 |
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Division of algebraic fractions
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647.5 |
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Algebraic fractions with term in denominator
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648.0 |
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Negative signs in algebraic fractions
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648.2 |
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Linear equations with fractions
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648.8 |
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RAW CONTENT OF THE WORKOUT |
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| What is provided here is the raw text of the workout. Most of the information is contained in the image files, which are not included with this text. The text may appear deceptively short. (The content overall of blacksacademy.net is vast.) Any in-line questions appear as a question mark [?]. This text is provided only as an indication of the overall quantity of material contained in the chapter. To use the material you must sign-in or create an account. |
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SLIDE 1
Consolidation – operations on fractions
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SLIDE 2
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SLIDE 3
SLIDE 4
SLIDE 5
Addition of fractions
1. You find the common denominator of the two fractions. This is the lowest common multiple of the denominators of two fractions.
2. You find the equivalent fractions of the two fractions over their common denominator.
3. You add the numerators of the two equivalent fractions.
Task
Denoting two fractions by and find the algebraic rule for the addition of fractions
? where b and d are relatively prime
? where
SLIDE 6
Denoting two fractions by and find the algebraic rule for the addition of fractions
? where b and d are relatively prime
? where
Solution
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where
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where
SLIDE 7
Simplify the following
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SLIDE 8
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SLIDE 9
Multiplication of fractions
Multiply the numerators and multiply the denominators, cancelling down if possible.
Task
Denoting two fractions by and find the algebraic rule for the multiplication of fractions
SLIDE 10
Task
Denoting two fractions by and find the algebraic rule for the multiplication of fractions
Solution
SLIDE 11
Simplify
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SLIDE 12
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SLIDE 13
The rule for division of fractions is invert and multiply
? Invert the back fraction. This is the same as taking the reciprocal or flipping the two numbers.
? At the same time change the division to a multiplication.
? Multiply the numerators and denominators, just as for regular multiplication of fractions.
Task
Denoting two fractions by and find the algebraic rule for the division of fractions
SLIDE 14
Algebraic rule for the division of fractions
SLIDE 15
Simplify
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SLIDE 16
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SLIDE 17
Algebraic rule for the division of fractions
This is also
The numerator of the top fraction goes on the bottom. The denominator of the bottom fraction goes on the top.
“The bottom of the top goes on the bottom, and the bottom of the bottom goes on the top!”
SLIDE 18
Simplify
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SLIDE 19
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SLIDE 20
Example
Simplify
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SLIDE 21
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SLIDE 22
Example
Warning!
The minus sign in this question is in front of the entire fraction. It is a common error to conclude questions of this type with . This is an error.
The correct answer is .
Simplify
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SLIDE 23
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SLIDE 24
Example
Simplify
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SLIDE 25
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SLIDE 26
Example
Simplify
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SLIDE 27 CHECK THIS QUESITON AGAIN
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SLIDE 28
Linear equations with fractions
Solve
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SLIDE 29
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SLIDE 30
Solve
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SLIDE 31
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SLIDE 32
Solve
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SLIDE 33
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SLIDE 34
Solve
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SLIDE 35
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