Ex 3.3, 1

Transcript

Ex 3.3, 1 (i) Prove that the following rational numbers are equal: (i) 2/3 and 4/6 To check if they are equal, we make them equal and cross-multiply Now, assuming 𝟐/𝟑 = 𝟒/𝟔 Cross-multiplying 𝟐/𝟑 = 𝟒/𝟔 2 × 6 = 3 × 4 12 = 12 Ex 3.3, 1 (ii) Prove that the following rational numbers are equal: (ii) 5/4 and 10/8 To check if they are equal, we make them equal and cross-multiply Now, assuming 𝟓/𝟒 = 𝟏𝟎/𝟖 Cross-multiplying 𝟓/𝟒 = 𝟏𝟎/𝟖 5 × 8 = 4 × 10 40 = 40 Since this true Hence, the rational numbers are equal Ex 3.3, 1 (iii) Prove that the following rational numbers are equal: (iii) −3/5 and −6/10 To check if they are equal, we make them equal and cross-multiply Now, assuming (−𝟑)/𝟓 = (−𝟔)/𝟏𝟎 Cross-multiplying (−𝟑)/𝟓 = (−𝟔)/𝟏𝟎 –3 × 10 = –6 × 5 –30 = –30 Since this true Hence, the rational numbers are equal Ex 3.3, 1 (iv) Prove that the following rational numbers are equal: (iv) 9/3 and 3 To check if they are equal, we make them equal and cross-multiply Now, assuming 9/3 = 3 𝟗/𝟑 = 𝟑/𝟏 Cross-multiplying 𝟗/𝟑 = 𝟑/𝟏 9 × 1 = 3 × 3 9 = 9 Since this true Hence, the rational numbers are equal