Andhra Pradesh Secondary Board
Andhra Pradesh Secondary Board
'This session is developed for class v students of andhra pradesh board of secondary education. Andhra
Pradesh board of secondary education is a very renowned board which is continuously working to
provide quality education to the students of Andhra Pradesh.
Here we are going to study fractions. Fractions are the numbers which are expressed in form of a/b,
where a and b are whole numbers and b <> 0. We say that all the fractions can be marked on right
direction of the number line. The mid number of the number line is zero. On the right side of zero are
all positive numbers and so all fractions appear on the right side of the number line. We also must
remember that all the mathematical operators namely addition, subtraction, multiplication and division
can be performed on the fractions.
Also the number line extends endlessly and there can be uncountable fraction numbers. To get the
successor, we need to add 1 to the number. There are many fraction numbers which are equivalent, so
when we convert them to their lowest form, they appear to be same. Fraction numbers can be proper or
improper. Improper fraction numbers are always greater than 1 and proper fraction numbers are always
less than 1. Following are the properties of fractions:
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1. Closure property: Closure property holds true for the addition, division and multiplication of the
fractions but holds true for subtraction only if ( a1/b1 - a2/b2, if a1/b1 >a2/b2) which means that if we
have a1/b1 and a2/b2 as any two fractions, then their sum is also an fractions, their difference is not
necessary an fraction, their product is also an fractions but their quotient is also a fraction.
2. Commutative property of fractions holds true for the addition and multiplication of fractions but
does not hold true for the difference and the division of the fractions. It means that if a1/b1 and a2/b2
are any two integers, then
A1/b1 + a2/b2 = a2/b2 + a1/b1
A1/b1 * a2/b2 = a2/b2 * a1/b1
But A1/b1 - a2/b2 <> a2/b2 - a1/b1
A1/b1 / a2/b2 <> a2/b2 / a1/b1
3. Associative property of fractions holds true for the addition and multiplication of fractions but
does not hold true for the difference and the division of the fractions. It means that if a1/b1 ,a2/b2 and
a3/b3 are any three integers, then.
(a1/b1 + a2/b2 ) + a3/b3 = a1/b1 + [ a2/b2 + a3/b3 ]
(a1/b1 * a2/b2 ) * a3/b3 = a1/b1 * [ a2/b2 * a3/b3 ]
But
(a1/b1 - a2/b2 ) - a3/b3 <> a1/b1 - [ a2/b2 - a3/b3 ]
(a1/b1 / a2/b2 ) / a3/b3 <> a1/b1 / [ a2/b2 / a3/b3 ]
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