Find the simplest form of (i) \(\frac{69}{92}\)(ii) \(\frac{473}{64

1.	Find the simplest form of (i) \(\frac{69}{92}\)(ii) \(\frac{473}{645}\)(iii) \(\frac{1095}{1168}\)(iv) \(\frac{368}{496}\)
Answer» (i) Prime factorization of 69 and 92 is: 69 = 3 × 23 92 = 2² × 23 Therefore, \(\frac{69}{92}\) = \(\frac{3\times23}{2^2\times23}\) = \(\frac{3}{2^2}\) = \(\frac{3}{4}\) Thus, simplest form of \(\frac{69}{92}\) is \(\frac{3}{4}\) (ii) Prime factorization of 473 and 645 is: 473 = 11 × 43 645 = 3 × 5 × 43 Therefore, \(\frac{473}{645}\) = \(\frac{11\times43}{3\times5\times43}\) = \(\frac{11}{15}\) Thus, simplest form of \(\frac{473}{645}\) is \(\frac{11}{15}\) (iii) Prime factorization of 1095 and 1168 is: 1095 = 3 × 5 × 73 1168 = 2⁴ × 73 Therefore, \(\frac{1095}{1168}\) = \(\frac{3\times5\times73}{2^4\times73}\) = \(\frac{15}{16}\) Thus, simplest form of \(\frac{1095}{1168}\) is \(\frac{15}{16}\) (iv) Prime factorization of 368 and 496 is: 368 = 2⁴ × 23 496 = 2⁴ × 31 Therefore, \(\frac{368}{496}\) = \(\frac{2^4\times23}{2^4\times31}\) = \(\frac{23}{31}\) Thus, simplest form of \(\frac{368}{496}\) is \(\frac{23}{31}\)

Find the simplest form of (i) \(\frac{69}{92}\)(ii) \(\frac{473}{645}\)(iii) \(\frac{1095}{1168}\)(iv) \(\frac{368}{496}\)

Answer»

(i) Prime factorization of 69 and 92 is:

69 = 3 × 23

92 = 2² × 23

Therefore, \(\frac{69}{92}\) = \(\frac{3\times23}{2^2\times23}\) = \(\frac{3}{2^2}\) = \(\frac{3}{4}\)

Thus, simplest form of \(\frac{69}{92}\) is \(\frac{3}{4}\)

(ii) Prime factorization of 473 and 645 is:

473 = 11 × 43

645 = 3 × 5 × 43

Therefore, \(\frac{473}{645}\) = \(\frac{11\times43}{3\times5\times43}\) = \(\frac{11}{15}\)

Thus, simplest form of \(\frac{473}{645}\) is \(\frac{11}{15}\)

(iii) Prime factorization of 1095 and 1168 is:

1095 = 3 × 5 × 73

1168 = 2⁴ × 73

Therefore, \(\frac{1095}{1168}\) = \(\frac{3\times5\times73}{2^4\times73}\) = \(\frac{15}{16}\)

Thus, simplest form of \(\frac{1095}{1168}\) is \(\frac{15}{16}\)

(iv) Prime factorization of 368 and 496 is:

368 = 2⁴ × 23

496 = 2⁴ × 31

Therefore, \(\frac{368}{496}\) = \(\frac{2^4\times23}{2^4\times31}\) = \(\frac{23}{31}\)

Thus, simplest form of \(\frac{368}{496}\) is \(\frac{23}{31}\)