Page 21 - Maths On the GO Class 7

¸
18 18 ¸2 9 18 18 3 6 2 5 6
Similarly, = = , = = etc. For example : , , etc. are irreducible
36 36 ¸2 18 36 36 3 12 3 7 11
¸
9 6 18 fractions.
Thus, , etc. are equivalent fractions of .
18 12 36 a
If HCF of a and b is other than 1, then is said
5. Unit fractions : Fractions having 1 as b
numerator are called unit fractions. to be reducible.
1 1 1 1 1 9. Complex fractions : Fractions having a
For example : , , , , etc. all are unit
2 4 9 18 37 fraction or a mixed fraction either in numerator
fractions. or denominator or in both are called complex
fractions.
6. Like fractions : Fractions having same
2 1
denominator are called like fractions. 1
2 7 5 6
5 6 7 11 For example : , , , etc. are complex
For example : , , , etc. are like 1 6 2 2
13 13 13 13 3 1
3 5 3 3
fractions.
fractions.
7. Unlike fractions : Fractions having different
To simplify a complex fraction, we convert the
denominators are called unlike fractions.
complex fraction into a division sum i.e., we
3 5 2 4
For example : , , , etc. are unlike divide the numerator by the denominator.
7 9 11 13 4 3 2 8
fractions. For example : = ¸4 2 = ´4 3 =
3
3
2
Comparison of Fractions
û To convert unlike fractions into like
To compare two unlike fractions, first convert each
fractions, first find the LCM of the
fraction into equivalent fraction having denominator
denominators of the given fractions and
then convert each fraction into equivalent equal to LCM of denominators of the given fractions,
then compare the numerators of the equivalent
like fraction with the denominator equal
fractions. The fraction with the greater numerator is
to LCM.
3 4 greater.
For example : Let us convert __ ,__ and
4
3
5 4 7 For example : Let us compare and .
into like fractions.
12 7 8
Q LCM of 4, 7 and 12 = 84 Q LCM of 7 and 8 = 56
4 4 × 12 48
3 3 × 21 63
´
\ = 4 4 ´8 32 3 3 7 21
,
=
=
=
4 4 × 21 84 7 7 × 12 84 Now, = = and = =
´
5 5 × 7 35 7 7 ´8 56 8 8 7 56
and = =
12 12 × 7 84 32 21 4 3
Clearly, > or >
35
Hence, , and are like fractions. 56 56 7 8
63 48
84 84 84
Inserting a Fraction between Two Given Fractions
To get the numerator of the required fraction, add
a
8. Irreducible fraction : A fraction is said to be the numerators of two given fractions. Similarly, add
b
the denominators of the given fractions to get the
irreducible or in lowest term, if HCF of a and b
denominator of the required fraction and simplify.
is 1.
Fractions 21