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Section Topics
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| 4 5 |
th's means or equals | 4 times | 1 5 |
th of an object |
In symbols or shorthand notation (with a × meaning times)
| 4 5 |
= | 4 × | 1 5 |
Here
| 1 5 |
is unit fraction. All fractions are multiples of unit fractions
Another Example:
| 3 4 |
= | 3 × | 1 4 |
Think of a unit fraction like a third
1
3
as unit for counting not whole objects, but parts of them. With that viewpoint, can count 2 thirds, 5 thirds and 7 thirds of an object. We also have
2 thirds + 5 thirds = 7 thirds.
or in fraction notation
| 2 3 |
+ | 5 3 |
= | 7 3 |
Whole numbers like 20 will be regarded as 20×1. Below we have to add whole numbers to fractions.
for reading as part of algebra skill development - optional reading for now
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Algebraic Shorthand Description of Ideas: |
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| A unit fraction has the form |
1 |
where N is a whole number. For example 2, 3, 4, 5. ... | |||
| A simple fraction has the form | M N |
= | M × | 1 N |
where both M and N are whole numbers. |
Remark: Explanations of (simple) fractions begin with the idea that a fraction is given by a pair of numbers a/b. Then the meaning or meanings of that pair of numbers written in fraction form is explained. The development above takes a different route starting with unit fractions as a unit of measure (or division) and leading to simple fractions as multiples of that unit of measure.
Notational Convenience: We will let
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1 |
= 1 and | |
| M 1 |
= M |
With this convenience or convention, our discussion of unit and simple fractions extends with no difficulty nor trouble to the case where the denominator N has the value 1.
Instructors and Tutors: Fractions appear in many situations involving weights, measures and divisions. For example the measure of a continuous quantity such as mass, weight, length, time will be expressed in terms of a integral and fractional multiples of a unit. Such multiples can be added and subtracted from each other, and also multiplied by mixed numbers - a natural number plus a fraction. That is besides and beyond the division of pies (a unit of food) into fractions and the division of groups of objects (money) into fractions etc. In essence rules for adding and subtracting fractions are drawn the description in terms of whole numbers and fractions of sums and differences of continuous quantities starting say with lengths and then being extended to further quantities. The ability to multiply a continuous quantity by a mixed number in principle or in practice leads to a multiplication of coefficients when and where continuous quantities are all expressed in terms of a unit quantity. Whence addition, subtraction, multiplication and division of mixed numbers may be drawn from the description of sums, difference, products and divisions of continuous in terms of divisible and repeatable or reproducible units of measure - length, time, mass and unit counts.
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Road
Safety Message Do not walk on a road with your back to the
traffic - rule of thumb
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