Page 73 - classs 6 a_Neat

36 = 36 ÷ 7 = 4 SIMPLEST FORM OF A FRACTION Afraction is said to be in the simplest form if the HCF of its
63 63 ÷ 7 7 numerator and denominator is 1.

4 REDUCING A GIVEN FRACTION TO ITS SIMPLEST FORM
Hence, the required fraction is ·
7
20 METHOD Let the given fraction be a and let the HCF of a and b be h.
EXAMPLE 5: Write ajraction equivalent to with denominator 9. b
36 a (a ÷ h )
20 Then, = is in the simplest form.
SOLUTION: Let = b (b ÷ h )
36 9 7
EXAMPLE 8: Show that is in the simplest form.
Clearly, 9 = 36 ÷ 4. 10
So, we divide the numerator also by 4. SOLUTION: Here, numerator = 7 and denominator = 1 0.

20 = 20 ÷ 4 = 5 Factors of 7 are 1, 7.
36 36 ÷ 4 9 Factors of 10 are 1, 2, 5, 10.
Hence, the required fraction is 5 Common factor of 7 and 1 0 is 1 only.
9 :. HCF of 7 and 10 is 1.
TO TEST WHETHER TWO GIVEN FRACTIONS ARE EQUIVALENT OR NOT 7
Hence, is in the simplest form.
10

TEST Let a and c be two given fractions. 21
b d EXAMPLE 9: Reduce to the simplest form.
Cross multiply as shown, a c 35
b d SOLUTION: Here, numerator= 21 and denominator= 35.
a c Factors of 21 are 1, 3, 7, 21.
If ad = bc, say that and are equivalent, otherwise not. Factors of 35 are 1. 5, 7, 35.
b d Common factors of 21 and 35 are 1, 7.

5 20 HCF of 21 and 35 is 7.
EXAMPLE 5: Show that and are equivalent fractions.
8 32 :. 21 (21 ÷ 7 ) 3
SOLUTION : The given fractions are 5 and 20 35 = (35 ÷ 7 ) = 5 21 3
8 32 Hence, the simplest form of . is

By cross multiplication, we have: a c 35 5
b d LIKE AND UNLIKE FRACTIONS
Now, 5 × 32 = 160 and 8 × 20 = 160. LIKE FRACTIONS Fractions having the same denominator are called like fractions.
(5 × 32)= (8 × 20) Thus, 2 , 4 , 5 , 8 are like fractions.

Hence, 5 and 20 are euqivalent fraction. 9 9 9 9
8 32 UNLIKE FRACTIONS Fractions having dljferent denominators are called unlike fractions.

EXAMPLE 6: Show that 7 and 36 are equivalent fractions. Thus, 1 , 3 , 5 , 7 are all unlike fractions.
12 60 2 4 6 9

SOLUTION: The given fraction are 7 and 36 CONVERTING UNLIKE FRACTIONS INTO LIKE FRACTIONS
12 60
By cross multiplication, we have: 7 36 Rule Suppose some unlike fractions are given. Convert each one of them into an equivalent
12 60 fraction having a denominator equal to the LCM of all the denominators of the given fractions.
Now, 7 × 60 = 420 and 12 × 36 = 432. 1 2 5 4
(7 × 60) ≠ (12 × 36). EXAMPLE 10: Convert the fractions , , and into like fractions.
7 36 2 3 6 9
Hence, and are not equivalent fractions.
12 60
SOLUTION: The given fractions are 1 , 2 , 5 and 4
2 3 6 9