Division and Multiplication of Fractions, Curriculum and Pedagogical Issues

1. Presented By:
Ghanshyam Joshi
The British Model College
Kathmandu, Nepal
Presented in the National Conference of
History of Mathematics in Nepal 2017
Fraction Multiplication and Division:
A Model Of Quantitative Reasoning for
School Mathematics

2. Presentation Outline
➢Introduction of Fraction
➢History of Fraction
➢Fraction Multiplication and Division in Nepalese School
Curriculum
➢ Multiplication of Fraction and Quantitative Reasoning
Model on Fraction Multiplication
➢Fraction Division and Quantitative Reasoning Model
On Fraction division
➢Recommendations
➢References
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3. Introduction of Fraction in a Number
3.50.5-4.2
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4. Introduction of Fraction as a Quantity
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6. Concept of Fraction
➢A fraction (from Latin fractus, "broken") represents a
part of a whole or, more generally, any number of equal
parts.
➢A fraction describes how many parts of a certain size
there are, for example, one-half, eight-fifths, three-
quarters.
➢The numerator represents a number of equal parts, and
the denominator, which cannot be zero, indicates how
many of those parts make up a unit or a whole.
➢ For example, in the fraction 3/4, the numerator, 3, tells
us that the fraction represents 3 equal parts, and the
denominator, 4, tells us that 4 parts make up a whole.7/26/20196 GD Joshi

7. ➢Other forms of Fractions: decimals, percent, or negative
exponents (as in 0.01, 1%, and 10−2 respectively, all of
which are equivalent to 1/100).
➢ An integer such as the number 7 can be thought of as
having an implicit denominator of one: 7 equals 7/1.
➢A fraction is part of a whole. It's less than 1 whole thing,
but more than 0. [Unless it is negative fraction]
➢We use fractions all the time in real life.
➢Have you ever ordered a quarter-pound burger? Or
noticed that your gas tank is half full? Both of these are
fractions of the whole amount—a whole pound of meat,
or a whole tank of gas.
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8. History of Fraction
➢The history: began with human observations of nature.
➢The divisions of the day, the month, the seasons and the
patterns in nature.
➢The use of fractions increased as growing societies
needed ways to measure goods and merchandise.
➢Numbers representing parts of a whole are called
rational numbers or fractions. Fractions can be
expressed as the quotients of two integers (a and b).
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9. ➢The Egyptians-- the first groups to study fractions.
➢The Egyptians– used sums of unit fractions, fractions
with one in the numerator. For example, the fraction 3/4
was written in hieroglyphic as 1/2 + 1/4.
➢This method did not allow numbers such as 2/7 to be
represented except as sums of unit fractions and so they
kept prepared tables for such fractions.
➢The Egyptians -- calculated the areas of geometric shapes
and volume including the planning and building of the
pyramids and kept detailed accounting of land and goods.
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10. ➢"Euclid's (300 BC) Algorithm used continuous
fractions to help solve mathematical equations that
contained fractions in the problem.
➢For example this is used to find the greatest common
denominator of two numbers which, if the sequence is
continued, the remainder will end in zero.
➢ Fractions were used in Greek astronomy, architecture
and music theory for describing musical intervals and
the harmonic progression of string lengths.
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11. Fraction Multiplication
Multiplication of fraction by fraction
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12. Multiplication of a Fraction by Whole
Numbers
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13. Multiplication of Fraction by a Mixed
Fraction
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14. Fraction Division
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16. Division of Fraction by Whole
Number
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17. Division of Mixed Numbers.
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18. Dividing a Fraction by a Fraction
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19. Recommendations
➢Include modeling of fraction multiplication and
division in curriculum
➢Include modeling of fraction multiplication and
division in textbook
➢Use real life examples and practical models for
teaching fraction problems
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22. References
JEMC, Sanothimi, Bhaktapur, Nepal
Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
"Fraction". Encyclopedia of Mathematics. 2012-04-
06. Retrieved 2012-08-15.
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