Division and Fractions | Practical Mathematics

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The Fractions, Rational Numbers and Real Numbers

Introduction

Introduction (6:26)

Discover the fractions of integers

Division and Fractions (2:11)
The example of the decimal numbers (5:57)
Equality of fractions (6:14)
Simplify fractions (5:18)
Simplify fractions in Python (9:45)
The fractions exploration and simplification (pdf)
Test Section 2

Construct and order the rational numbers set

The rational numbers as equivalence classes of fractions (4:06)
Compare two fractions (8:34)
Compare two rational numbers (5:41)
The totally ordered set (Q,≤) (5:16)
Construction and comparison of the rational numbers (pdf)
Test Section 3

Add and subtract rational numbers

Exploration of the addition of fractions (4:43)
Addition of rational numbers (5:24)
Exploration of the subtraction of fractions (10:31)
Subtraction of Rational numbers (4:50)
Fractions and Rational Numbers Addition and Subtraction (pdf)
Test Section 4

The rational numbers additive group

Addition and subtraction mutual reciprocity in Q (3:18)
Solving additive and subtractive equations in Q (11:42)
The commutative group (Q,+) (6:17)
The Indexed Sums in Q (6:23)
The rational numbers additive group (pdf)
Test Section 5

Multiply and divide rational numbers

Multiply Fractions and Integers (11:38)
Multiply two Rational Numbers (5:50)
The Signs Rules for the Multiplication of Rationals (4:27)
Divide Fractions and Integers (16:53)
Divide two Rational Numbers (8:23)
The Signs Rules for the Division of Rationals (5:25)
Fractions and Rational Numbers Multiplication and Division (pdf)
Test Section 6

The non-zero Rational Numbers Multiplicative Group

The Division and Multiplication Mutual Reciprocity in Q* (4:37)
Solve Linear Equations in Q (7:02)
Properties of the Multiplication in Q (9:45)
Solve Proportionality Problems (3:50)
The Multiplicative Group of non-zero Rational Numbers (pdf)
Test Section 7

Master Computation in Q

The Commutative Field (Q,+,x) (6:28)
Application: The Percentages Definition and Manipulation (23:07)
More Properties of the Four Operations in Q (6:18)
Solve Affine Equations in Q (6:01)
Compute in the Commutative Field (Q,+,x) (pdf)
Test Section 8

Exponentiation by an Integer of any Sign

Exponentiation by a non-negative Integer (9:22)
Exponentiation by a negative Integer (5:27)
Exponentiation on a Product and a Quotient (8:17)
Homomorphism of Groups from (Q*,x) to (Z,+) (9:03)
Exponentiation of Rational Numbers by Signed Integers (pdf)
Test Section 9

Draw Straight Lines and Curves in Python

Draw Straight Lines (12:59)
Draw Parabolas (6:21)
Draw Hyperbolas (10:07)
Draw straight lines and curves in Python (pdf)
Test Section 10

The Rational Numbers Ordered Field (Q,+,x,≤)

Order with Addition and Subtraction (11:02)
Order with Multiplication and Division (23:05)
Solve Linear and Affine Inequations (14:38)
The Density of the Rational Numbers Set (1:37)
Direction of Variation of Affine Functions and Hyperbolas (10:19)
Comparison between two Positive Powers of a Positive Rational Number (7:17)
Direction of Variation and Convexity of a Parabola (7:51)
The Rational Numbers Ordered Field (Q,+,x,≤) (pdf)
Test Section 11

The Real Numbers

About the Real Numbers (4:19)
The Square Roots of Non Negative Real Numbers (5:04)
The Quadratic Equations (15:17)
Discover the Trigonometric Functions (3:21)
The Sine and Cosine in the Unit Circle (11:20)
Properties of the Cosine and Sine Functions (17:20)
Draw the Sine and Cosine Functions (9:23)
Quadratic Equations and Trigonometry in R (pdf)

Final Assessment: The Decimal Expansion of Rational Numbers

The Assessment Subject

Conclusion

Conclusion (2:03)

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Division and Fractions

Let's discover how division between integers lead to fractions.

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