Question 1 (Page 174) - Comparing Fractions - Chapter 7 Class 6 - Fractions (Ganita Prakash)

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Question 1 (Page 174) Compare the following fractions and justify your answers: (a) 8/3, 5/2 To compare, we need to make denominator same To do this, we multiply both denominators 3 × 2 = 6 So, our fractions become 𝟖/𝟑=𝟖/𝟑 ×𝟐/𝟐 =𝟏𝟔/𝟔 Since 16 > 15 We can write 16/6 > 16/6 Or 𝟖/𝟑 > 𝟓/𝟐 𝟓/𝟐=𝟓/𝟐 ×𝟑/𝟑 =𝟏𝟓/𝟔 Question 1 (Page 174) Compare the following fractions and justify your answers: (b) 4/9, 3/7To compare, we need to make denominator same To do this, we multiply both denominators 9 × 7 = 63 So, our fractions become 𝟒/𝟗=𝟒/𝟗 ×𝟕/𝟕 =𝟐𝟖/𝟔𝟑 𝟑/𝟕=𝟑/𝟕 ×𝟗/𝟗 =𝟐𝟕/𝟔𝟑 Since 28 > 27 We can write 28/63 > 27/63 Or 𝟒/𝟗 > 𝟑/𝟕 Question 1 (Page 174) Compare the following fractions and justify your answers: (c) 7/10, 9/14 To compare, we need to make denominator same To do this, we multiply both denominators 10 × 14 = 140 But this is too big We can also make denominator 70 So, our fractions become 𝟕/𝟏𝟎=𝟕/𝟏𝟎 ×𝟕/𝟕 =𝟒𝟗/𝟕𝟎 Since 49 > 45 We can write 49/70 > 45/70 Or 𝟕/𝟏𝟎 > 𝟗/𝟏𝟒 𝟗/𝟏𝟒=𝟗/𝟏𝟒 ×𝟓/𝟓 =𝟒𝟓/𝟕𝟎 Question 1 (Page 174) Compare the following fractions and justify your answers: (d) 12/5, 8/5 Here, the denominator is already same So, we just compare numerators Since 12 > 8 We can write 𝟏𝟐/𝟓 > 𝟖/𝟖 Question 1 (Page 174) Compare the following fractions and justify your answers: (e) 9/4, 5/2Basically, we need to make denominator same To do this, we multiply both denominators 4 × 2 = 8 But, this is too big We can just do 2 × 2 = 4 and only change 2nd fraction Let’s do that 𝟓/𝟐=𝟓/𝟐 ×𝟐/𝟐 =𝟏𝟎/𝟒 Thus, our fractions are 𝟗/𝟒 and 𝟏𝟎/𝟒 Since 9 < 10 We can write 9/4 < 10/4 Or 𝟗/𝟒 < 𝟓/𝟐