\(\frac{3}{8}\) ____ \(\frac{3}{7}\)
Here, \(\frac{1}{8}\) is smaller than \(\frac{1}{7}\). So, \(\frac{3}{8}<\frac{3}{7}\)
(b) \(\frac{4}{9}\) ____ \(\frac{4}{10}\)
Solution:
\(\frac{4}{9}\) ____ \(\frac{4}{10}\)
Here, \(\frac{1}{9}\) is bigger than \(\frac{1}{10}\). So, \(\frac{4}{9}>\frac{4}{10}\).
(c) \(\frac{2}{7}\) ____ \(\frac{2}{5}\)
Solution:
\(\frac{2}{7}\) ____ \(\frac{2}{5}\)
Here, \(\frac{1}{7}\) is smaller than \(\frac{1}{5}\). So, \(\frac{2}{7}<\frac{2}{5}\)
(d) \(\frac{5}{7}\) ____ \(\frac{5}{6}\)
Solution:
\(\frac{5}{7}\) ____ \(\frac{5}{6}\)
Here, \(\frac{1}{7}\) is smaller than \(\frac{1}{6}\). So, \(\frac{5}{7}<\frac{5}{6}\)
(e) \(\frac{6}{9}\) ____ \(\frac{6}{10}\)
Solution:
\(\frac{6}{9}\) ____ \(\frac{6}{10}\)
Here, \(\frac{1}{9}\) is bigger than \(\frac{1}{10}\). So, \(\frac{6}{9}>\frac{6}{10}\)
(f) \(\frac{7}{9}\) ____ \(\frac{7}{11}\)
Solution:
\(\frac{7}{9}\) ____ \(\frac{7}{11}\)
Here, \(\frac{1}{9}\) is bigger than \(\frac{1}{11}\). So, \(\frac{7}{9}>\frac{7}{11}\)
NCERT Textbook Pages 24-28
Fractions Greater Than 1
Raman’s father makes nice soft parathas. He cuts the parathas either into halves (2 equal parts) or fourths (4 equal parts) before serving them. He asks his children (Raman and Radhika) each day to find out the number of parathas he made.
Maa took 5 pieces of \(\frac{1}{2}\) paratha. How many parathas did she eat?
Dadiji had 7 pieces of \(\frac{1}{2}\) paratha. How many parathas did she eat?
Solution:
= 7 pieces of \(\frac{1}{2}\) paratha
= \(\frac{7}{2}\) parathas
= 3 + \(\frac{1}{2}\) parathas
= 3\(\frac{1}{2}\) parathas.
So, dadiji ate 3\(\frac{1}{2}\) parathas.
Raman ate 6 pieces of \(\frac{1}{2}\) paratha, Dadaji ate 7 pieces of \(\frac{1}{2}\) paratha and Baba ate 5 pieces of \(\frac{1}{2}\) paratha. How many parathas did each of them eat?
Use the number line to find the answer.
Solution:
In the given number lines each part represents \(\frac{1}{2}\). Since Raman ate 6 pieces of \(\frac{1}{2}\) parathas, mark 6 points on number line.
\(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{6}{2}\)
Therefore, Raman ate 3 parathas.
Dadaji ate 7 pieces of \(\frac{1}{2}\) paratha. So, mark 7 points on number line.
\(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{7}{2}=3 \frac{1}{2}\)
Therefore, dadaji ate 3\(\frac{1}{2}\) parathas.
Baba ate 5 pieces of \(\frac{1}{2}\) paratha. So, mark 5 points on number line.
\(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{5}{2}=2 \frac{1}{2}\)
Therefore, Baba are 2\(\frac{1}{2}\) parathas.
How many parathas were made on this day? Find out.
Solution:
Number of parathas eaten by Maa = 2 \(\frac{1}{2}\) = \(\frac{5}{2}\)
Number of parathas eaten by Radhika = 3 = \(\frac{6}{2}\)
Number of parathas eaten by Dadiji = 3\(\frac{1}{2}\) = \(\frac{7}{2}\)
Number of parathas eaten by Raman = 3\(\frac{1}{2}\) = \(\frac{6}{2}\)
Number of parathas eaten by Dadaji = 3\(\frac{1}{2}\) = \(\frac{7}{2}\) and
Number of parathas eaten by Baba = \(\frac{5}{2}\) = 2\(\frac{1}{2}\)
The total number of parathas made on this day was \(\frac{5}{2}+\frac{6}{2}+\frac{7}{2}+\frac{6}{2}+\frac{7}{2}+\frac{5}{2}=\frac{36}{2}\) = 18 parathas.
Raman ate 7 pieces of \(\frac{1}{4}\), Radhika ate 6 pieces of \(\frac{1}{4}\), Maa ate 8 pieces of \(\frac{1}{4}\), Dadiji ate 10 pieces of \(\frac{1}{4}\), and Baba ate 12 pieces of \(\frac{1}{4}\) paratha. Use a number line to find out how many parathas were eaten by each of them.
Solution:
In the given number lines. Divide the distance between 0 and 1 into 4 equal parts. Each part represents \(\frac{1}{4}\).
Since, Raman ate 7 pieces of \(\frac{1}{4}\) paratha, mark 7 points on number line.
Therefore, Raman ate \(\frac{7}{4}\) parathas or 1 \(\frac{3}{4}\) parathas.
Radhika ate 6 pieces of \(\frac{1}{4}\) paratha. So, mark 6 points on number line.
Therefore, Radhika ate \(\frac{6}{4}\) = 1\(\frac{1}{2}\) parathas.
Maa ate 8 pieces of \(\frac{1}{4}\) paratha. So, mark 8 points on number line.
Therefore, Maa ate \(\frac{8}{4}\) or 2 parathas.
Dadiji ate 10 pieces of \(\frac{1}{4}\) paratha. So, mark 10 points on number line.
= \(\frac{10}{4}\) = 2 + \(\frac{2}{4}\) = 2\(\frac{2}{4}\) = 2\(\frac{1}{2}\)
Therefor, Dadaji ate \(\frac{10}{2}\). or 2\(\frac{1}{2}\) parathas 12 point on number line.
= 1 + 1 + 1 = 3
Therefore, Baba ate 3 parathas.
How many parathas were made on this day? Find out.
Solution:
Number of parathas eaten by Dadaji = \(\frac{9}{4}\)
Number of parathas eaten by Raman = \(\frac{7}{4}\)
Number of parathas eaten by Radhika = \(\frac{6}{4}\)
Number of parathas eaten by Maa = \(\frac{8}{4}\)
Number of parathas eaten by Dadiji = \(\frac{10}{4}\)
Number of parathas eaten by Baba = \(\frac{12}{4}\)
∴ The total number of parathas made on this day
= \(\frac{9}{4}+\frac{7}{4}+\frac{6}{4}+\frac{8}{4}+\frac{10}{4}+\frac{12}{4}\)
= \(\frac{9+7+6+8+10+12}{4}=\frac{52}{4}\)
= 13 parathas
NCERT Textbook Page 28
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