Page 15 - SM inner class 7.cdr

(5 ¸ ) Sec ond Method
5
=
(10 ¸ ) 21 21
5
2 ´ + 3 ´
2 3 3 7 14 + 9 23
[Divide the numerator and denominator by + = = =
their HCF (highest common factor) 5, to 3 7 21 21 21
convert the fraction into lowest term.
Note :
1
= An swer. a c
2 ±
b d
Addition and Subtraction of Unlike Fractions a ´ LCMof band d c ´ LCM of b and d
±
In addition and subtraction of unlike fractions, = b d
we first convert them into corresponding LCMof band d
equivalent like fractions and then they are
added or subtracted. 1 3
Ex am ple 4. +
Following steps are used to do the same : 6 8
Step I : Obtain the fractions and their So lu tion : The LCM (least com mon mul ti ple)
de nom i na tors. of the de nom i na tors 6 and 8 is 24.
Step II : Find the LCM (least common So, we convert the given fractions into
mul ti ple) of the de nom i na tors. equivalent fractions with denominator 24.
Step III : Convert each fraction into an We have,
equiv a lent frac tion hav ing its de nom i na tor 1 1 ( ´ 4) 4
equal to the LCM (least common multiple) = = = [since 24 ¸ 6 = 4]
ob tained in Step II. 6 6 ( ´ 4) 24
Step IV : Add or subtract like fractions and, 3 = ( 3 ´ 3) = 9 [since 24 ¸ 8 = 3]
ob tained in Step III. 8 ( 8 ´ 3) 24
2 3 1 3 4 9
Ex am ple 3. Add and . Thus, + = +
3 7 6 8 24 24
9
So lu tion : First Method : The LCM (least (4 + )
=
com mon mul ti ple) of the de nom i na tors 3 and 7 24
is 21. 13
=
So, we convert the given fractions into 24
equivalent fractions with denominator 21. 4 5
Ex am ple 5. Add 2 and 3 .
We have, 5 6
2 3 So lu tion : First we convert mixed fractions
+
3 7 into improper frac tions
7
3
(2 ´ ) (3 ´ ) 4 ( 2 ´ 5 + 4)
= + 2 =
3
(3 ´ ) (7 ´ ) 5 5
7
(10 + ) 14
4
¸
[since 21 3¸ = 7 and 21 7 = 3] = =
5 5
14 9
= + 5 ( 3 ´ 6 + 5)
21 21 and, 3 =
6 6
(14 + )
9
= 23
21 =
6
23 2
= =1 An swer 14 23
21 21 Now, we will compute +
5 6
15
Mathematics In Focus - 7