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Unit 3.Operating with fractions
Look through the table and try to memorize it.
Examples
written read
Rules
1/2 One second; or: a half
1/3 one third; a third
2/3 Two thirds
1/4
One fourth; or: a fourth;
or: a quarter
1/100 A hundredth
5/16 Five sixteenths
½; 1/3; ¼; 2/3; 1/100; and 5/16 are
proper fractions.
A proper fraction is one whose
numerator is less than denominator
23/6
9/9
Twenty three six
Nine ninths
23/6 and 9/9 are improper fractions. An
improper fraction is a fraction, whose
numerator is equal to or larger than the
denominator
7
5
3
Three and five sevenths
Three and five seventh is a mixed
number. A mixed number is a number
and a fraction written together
b
a
br
ar
=
ar over br equals a over
b
To reduce a fraction to its lowest terms,
divide the numerator and the
denominator by their highest common
factor (or: measure, or: divisor)
br
ar
b
a
=
a over b equals ar over
br
To reduce a fraction to higher terms,
multiply the numerator and the
denominator by the same number.
bd
bcad
d
c
b
a ±
=±
a over b, this fraction
followed by plus or
minus c over d equals ad
plus or minus bc this
sum or difference over
bd
To find the sum (the difference) of two
unlike fractions, change them to like
fractions (fractions having their least
common denominator) and combine the
numerators.
bd
ac
d
c
b
a
=×
a over b, this fraction
multiplied by c over d
equals ac over bd
To find the product of two fractions,
multiply the numerators together and the
denominators together
9
Unit 3.Operating with fractions Look through the table and try to memorize it. Examples Rules written read 1/2 One second; or: a half 1/3 one third; a third ½; 1/3; ¼; 2/3; 1/100; and 5/16 are 2/3 Two thirds proper fractions. One fourth; or: a fourth; A proper fraction is one whose 1/4 or: a quarter numerator is less than denominator 1/100 A hundredth 5/16 Five sixteenths 23/6 and 9/9 are improper fractions. An 23/6 Twenty three six improper fraction is a fraction, whose 9/9 Nine ninths numerator is equal to or larger than the denominator Three and five seventh is a mixed 5 3 Three and five sevenths number. A mixed number is a number 7 and a fraction written together To reduce a fraction to its lowest terms, ar a = ar over br equals a over divide the numerator and the br b b denominator by their highest common factor (or: measure, or: divisor) a over b equals ar over To reduce a fraction to higher terms, a ar = br multiply the numerator and the b br denominator by the same number. a over b, this fraction To find the sum (the difference) of two followed by plus or unlike fractions, change them to like a c ad ± bc minus c over d equals ad ± = fractions (fractions having their least b d bd plus or minus bc this common denominator) and combine the sum or difference over numerators. bd a over b, this fraction To find the product of two fractions, a c ac × = multiplied by c over d multiply the numerators together and the b d bd equals ac over bd denominators together 9
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