Practicing with Maths Mela Class 5 Solutions Chapter 2 Fractions Question Answer NCERT Solutions improves a student’s confidence in the subject.
Class 5 Maths Chapter 2 Fractions Question Answer Solutions
Fractions Class 5 Maths Solutions
Class 5 Maths Chapter 2 Solutions
Playing with a Grid (NCERT Page 17-18)
Question 1.
(i) Shade \(\frac{1}{8}\) of Grid A in red.
(ii) Shade \(\frac{1}{6}\) of Grid B in blue.
(iii) Shade \(\frac{1}{12}\) of Grid C in yellow.
(iv) Do you see \(\frac{1}{3}\) in any of the grids? Mark it.
Answer:
i.
ii.
iii.
(iv) No, we do not see \(\frac{1}{3}\) in any of the grids.
Question 2.
(i) Is \(\frac{1}{3}\) equal to \(\frac{2}{6}\) ? Let us find out.
(ii) (a) Look at the picture and identify the fractions.
(b) Are there two different ways to write the fraction represented by the shaded part?
Answer:
(i) We have, \(\frac{1}{3}\) and \(\frac{2}{6}\)
On multiplying both the numerator and denominator of \(\frac{1}{3}\) by 2, we get
\(\frac{1 \times 2}{3 \times 2}\) = \(\frac{2}{6}\)
∴ \(\frac{1}{3}\) is equal to \(\frac{2}{6}\).
(ii) (a) The shaded part represents 2 out of 6 equal parts, so the fraction represented by the shaded part is \(\frac{2}{6}\) and the unshaded part represents 4 out of 6 equal parts, so the fraction represented by the unshaded part is \(\frac{4}{6}\).
(b) Yes, there are two different ways to write the fraction represented by the shaded part i.e. \(\frac{2}{6}\) and \(\frac{1}{3}\) because \(\frac{2}{6}\) can be simplified to \(\frac{1}{3}\). These are called equivalent fractions.
Fun with fraction kit (NCERT Pg 18)
Question 3.
When a \(\frac{1}{2}\) piece is broken into 2 equal parts, each part is a \(\frac{1}{4}\) piece. 2 pieces of \(\frac{1}{4}\) are equal to \(\frac{1}{2}\).
What else is equivalent to \(\frac{1}{2}\)?
\(\frac{1}{2}\) = \(\frac{2}{4}\) =…….. = ………. = ………
Answer:
When a \(\frac{1}{2}\) piece is broken into 3 equal parts, each part is a \(\frac{1}{6}\) piece, 3 pieces of \(\frac{1}{6}\) are equal to \(\frac{1}{2}\).
∴ \(\frac{1}{2}\) = \(\frac{3}{6}\)
Similarly, \(\frac{1}{2}\) = \(\frac{4}{8}\) and \(\frac{1}{2}\) = \(\frac{5}{10}\)
Hence, \(\frac{1}{2}\) = \(\frac{2}{4}\) = \(\frac{3}{6}\) = \(\frac{4}{8}\) =\(\frac{5}{10}\)
Let Us Do (NCERT Pg 19-20)
Question 4.
(i) In groups of 3 or 4, find different ways of making a whole with different fraction pieces from your kit.
(ii) Write the equivalent fractions for the following that you may find in the process.
(a) \(\frac{1}{3}\)
(b) \(\frac{1}{4}\)
(c) \(\frac{1}{5}\)
(d) \(\frac{1}{6}\)
(iii) Do you see how to generate equivalent fractions for any given fraction?
Discuss in class.
Answer:
(i) Some examples of making a whole with different fraction pieces from the kit in the groups of 3 or 4 are given below.
(a) Four \(\frac{1}{4}\) pieces make a whole
i.e. \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) = 1
(b) Three \(\frac{1}{3}\) pieces make a whole i.e. \(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) = 1
(c) One \(\frac{1}{2}\) piece and two \(\frac{1}{4}\) pieces make a whole
i.e. \(\frac{1}{2}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) = 1
(d) One \(\frac{1}{2}\) piece, one \(\frac{1}{3}\) piece and one \(\frac{1}{6}\) piece make a whole
i.e. \(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{6}\) = 1
and so on.
(ii) To write the equivalent fractions, multiply both the numerator and the denominator of a fraction by the same non-zero number.
Question 5.
Find the following using your kit. You can also shade and check by shading the following. The first one is partially done for you.
(i) How many \(\frac{1}{6}\) s make \(\frac{1}{3}\) ?
(ii) How many \(\frac{1}{8}\) s make
(a) \(\frac{1}{4}\) ?
(b) \(\frac{1}{2}\) ?
(iii) How many \(\frac{1}{12}\) s make
(a) \(\frac{1}{2}\)
(b) \(\frac{1}{3}\)
(c) \(\frac{1}{4}\)
(d) \(\frac{1}{6}\) ?
Answer:
(i) Here, we have
Clearly, 2 pieces of \(\frac{1}{6}\) make \(\frac{1}{3}\).
(ii) (a) Here, we have
\(\frac{1}{4}\) \(\frac{1}{4}\) \(\frac{1}{4}\) \(\frac{1}{4}\)
Clearly, 2 pieces of \(\frac{1}{8}\) make \(\frac{1}{4}\).
(b) Here, we have
Clearly, 4 pieces of \(\frac{1}{8}\) make \(\frac{1}{2}\).
(iii) (a) Here, we have
Clearly, 6 pieces of \(\frac{1}{12}\) make \(\frac{1}{2}\).
(b) Here, we have
Clearly, 4 pieces of \(\frac{1}{12}\) make \(\frac{1}{3}\).
(c) Here, we have
Clearly, 3 pieces of \(\frac{1}{12}\) make \(\frac{1}{4}\).
(d) Here, we have
Clearly, 2 pieces of \(\frac{1}{12}\) make \(\frac{1}{6}\).
Question 6.
(i) Do as instructed using your fraction kit.
(a) Make a whole using only \(\frac{1}{6}\) and \(\frac{1}{12}\) pieces.
(b) Make a whole using \(\frac{1}{12}\), \(\frac{1}{4}\), and \(\frac{1}{2}\) pieces.
(c) Make a whole using any five pieces of the same size.
(d) Make a whole using any seven pieces.
(ii) Play in a group with this kit and find other interesting combinations to make a whole. Write or draw your findings.
Answer:
(i) (a) Here, we have
Clearly, 4 pieces of \(\frac{1}{6}\) and 4 pieces of \(\frac{1}{12}\) make a whole.
(b) Here, we have
Clearly, 3 preces of \(\frac{1}{12}\), 1 piece of \(\frac{1}{4}\) and 1 piece of \(\frac{1}{2}\) make a whole.
(c) Here, we have
Clearly, 5 equal pieces of \(\frac{1}{5}\) make a whole.
(d) Here, we have
Clearly, 7 pieces of \(\frac{1}{7}\) make a whole.
(ii) We can take the following fractions:
Clearly, 9 pieces of \(\frac{1}{9}\) make a whole.
Clearly, 8 pieces of \(\frac{1}{8}\) make a whole.
Making Equivalent Fractions (NCERT Pg 20-21)
Question 7.
(i) Divide the wholes given below into more equal parts and find fractions equivalent to \(\frac{1}{3}\). Write them in the boxes below the images.
(ii) Do you see any pattern in all the equivalent fractions that you found?
Answer:
(i)
From figure 1 The shaded area consists of 5 parts out of 15. So, the fraction is \(\frac{5}{15}\), which is equivalent to \(\frac{1}{3}\).
From figure 2 The shaded area consists of 6 parts out of 18. So, the fraction is \(\frac{6}{18}\), which is equivalent to \(\frac{1}{3}\).
From figure 3 The shaded area consists of 7 parts out of 21. So, the fraction is \(\frac{7}{21}\), which is equivalent to \(\frac{1}{3}\).
(ii) Yes, we observe that the numerator is getting added by 1 and the denominator is getting added by 3 with corresponding numerator and denominator respectively.
∴ \(\frac{1}{3}\) = \(\frac{2}{6}\) = \(\frac{3}{9}\) = \(\frac{4}{12}\) =\(\frac{5}{15}\) = \(\frac{6}{18}\) = \(\frac{7}{21}\) = \(\frac{8}{24}\) =\(\frac{12}{36}\)
Question 8.
How do you know when a fraction is equivalent to another? Discuss in class.
Answer:
We can get one from the other by multiplying or dividing both the numerator and denominator by the same number. e.g. \(\frac{2}{4}\) and \(\frac{3}{6}\) are both equivalent to \(\frac{1}{2}\). i.e. \(\frac{1}{2}\)=\(\frac{1 \times 2}{2 \times 2}\)=\(\frac{2}{4}\) and \(\frac{1}{2}\)=\(\frac{1 \times 3}{2 \times 3}\)=\(\frac{3}{6}\)
Question 9.
The below pictures show \(\frac{2}{5}\) of a whole. Find the different fractions that are equivalent to \(\frac{2}{5}\) and write your fractions below each image.
Answer:
(c)
From the figure, the whole is divided into 15 equal parts with 6 shaded parts. This represents the fraction \(\frac{6}{15}\).
Since, \(\frac{2 \times 3}{5 \times 3}\) = \(\frac{6}{15}\).
So, this is an equivalent fraction to \(\frac{2}{5}\).
(d)
From the figure, the whole is divided into 20 equal parts with 8 shaded parts.
This represents the fraction \(\frac{8}{20}\).
Since, \(\frac{2 \times 4}{5 \times 4}\) = \(\frac{8}{20}\).
So, this is an equivalent fraction to \(\frac{2}{5}\).
Let Us Do [NCERT Pg 22]
Question 10.
Fill in the blanks with equivalent fractions. There may be more than one answer.
(i) \(\frac{1}{7}\) = ………….
(ii) \(\frac{2}{3}\) = …………
(iii) \(\frac{3}{4}\) = ………..
(iv) \(\frac{3}{5}\) = ……….
Answer:
(i) On multiplying both the numerator and denominator by 2,3,4, ……., we get
So, the equivalent fraction are
\(\frac{2}{14}\), \(\frac{3}{21}\), \(\frac{4}{28}\) ……..
(ii) On multiplying both the numerator and denominator by 2,3,4 ……….., we get
So, the equivalent fractions are \(\frac{4}{6}\), \(\frac{6}{9}\), \(\frac{8}{12}\) …….
(iii) On multiplying both the numerator and denominator by 2,3,4 ………., we get
So, the equivalent fractions are \(\frac{6}{8}\), \(\frac{9}{12}\), \(\frac{12}{16}\) …….
(iv) On multiplying both the numerator and denominator by 2,3,4 ……., we get
So, the equivalent fractions are \(\frac{6}{10}\), \(\frac{9}{15}\), \(\frac{12}{20}\) …….
Question 11.
Put a tick (✓) against the fractions that are equivalent.
(i) \(\frac{2}{3}\) and \(\frac{3}{4}\)
(ii) \(\frac{3}{5}\) and \(\frac{6}{10}\)
(iii) \(\frac{4}{12}\) and \(\frac{2}{6}\)
(iv) \(\frac{6}{9}\) and \(\frac{1}{3}\)
Answer:
(i) We have, \(\frac{2}{3}\) and \(\frac{3}{4}\)
These fractions are already in their simplest form.
Since, their numerators and denominators are different, so they are not equivalent.
(ii) We have, \(\frac{3}{5}\) and \(\frac{6}{10}\)
On multiplying both the numerator and denominator of \(\frac{3}{5}\) by 2, we get
\(\frac{3}{5}\) = \(\frac{3 \times 2}{5 \times 2}\) = \(\frac{6}{10}\)
So, fractions \(\frac{3}{5}\) and \(\frac{6}{10}\) are equivalent.
(iii) We have, \(\frac{4}{12}\) and \(\frac{2}{6}\)
On multiplying both the numerator and denominator of \(\frac{2}{6}\) by 2, we get
\(\frac{2}{6}\) = \(\frac{2 \times 2}{6 \times 2}\) = \(\frac{4}{12}\)
So, fractions \(\frac{4}{12}\) and \(\frac{2}{6}\) are equivalent.
(iv) We have, \(\frac{6}{9}\) and \(\frac{1}{3}\)
On multiplying both the numerator and denominator of \(\frac{1}{3}\) by 6 (to make numerator same), we get
\(\frac{1}{3}\) = \(\frac{1}{3}\) × \(\frac{6}{6}\)
= \(\frac{6}{18}\) ≠ \(\frac{6}{9}\)
Also, on multiplying both the numerator and denominator of \(\frac{1}{3}\) by 3 (to make denominator same), we get
\(\frac{1}{3}\) = \(\frac{1}{3}\) × \(\frac{3}{3}\) = \(\frac{3}{9}\) ≠ \(\frac{6}{9}\)
So, fractions \(\frac{6}{9}\) and \(\frac{1}{3}\) are not equivalent.
Question 12.
Fill in the boxes such that the fractions become equivalent.
Answer:
(i) 
On multiplying both the numerator and denominator of \(\frac{2}{5}\) by 2 , we get
\(\frac{2 \times 2}{5 \times 2}\) = \(\frac{4}{10}\)
∴ \(\frac{2}{5}\) = \(\frac{4}{10}\)
(ii) 
On multiplying both the numerator and denominator of \(\frac{3}{4}\) by 4, we get
\(\frac{3 \times 4}{4 \times 4}\) = \(\frac{12}{16}\)
∴ \(\frac{3}{4}\) = \(\frac{12}{16}\)
(iii) 
On multiplying both the numerator and denominator of \(\frac{4}{7}\) by 2, we get
\(\frac{4 \times 2}{7 \times 2}\) = \(\frac{8}{14}\)
∴ \(\frac{4}{7}\) = \(\frac{8}{14}\)
(iv) 
On multiplying both the numerator and denominator of \(\frac{5}{9}\) by 5, we get
\(\frac{5 \times 5}{9 \times 5}\) = \(\frac{25}{45}\)
∴ \(\frac{5}{9}\) = \(\frac{25}{45}\)
Let Us Do (NCERT Pg 23)
Question 13.
Compare the fractions given below using < and > signs.
(i) \(\frac{1}{4}\) ………….. \(\frac{3}{4}\)
(ii) \(\frac{3}{5}\) …………. \(\frac{4}{5}\)
(iii) \(\frac{5}{7}\) ………….. \(\frac{2}{7}\)
(iv) \(\frac{7}{8}\) …………. \(\frac{3}{8}\)
(v) \(\frac{5}{10}\) …………. \(\frac{6}{10}\)
(vi) \(\frac{2}{6}\) …………… \(\frac{1}{6}\)
Answer:
(i) We have, \(\frac{1}{4}\) ………….. \(\frac{3}{4}\)
Since, the denominators are same.
Now, on comparing the numerators, we get 1 < 3
We know that for same denominator, the fraction with larger numerator is greater.
So, \(\frac{1}{4}\) < \(\frac{3}{4}\)
(ii) We have, \(\frac{3}{5}\) ……. . . \(\frac{4}{5}\)
Since, the denominators are same.
Now, on comparing the numerators, we get 3 < 4
We know that for same denominator, the fraction with larger numerator is greater.
So, \(\frac{3}{5}\)<\(\frac{4}{5}\)
(iii) We have, \(\frac{5}{7}\) ……. ……. \(\frac{2}{7}\) Since, the denominators are same. Now, on comparing the numerators, we get 5 >2
We know that for same denominator, the fraction with larger numerator is greater.
So, \(\frac{5}{7}\) > \(\frac{2}{7}\)
(iv) We have, \(\frac{7}{8}\) ……. ……. \(\frac{3}{8}\)
Since, the denominators are same.
Now, on comparing the numerators, we get 7 > 3
We know that for same denominator, the fraction with larger numerator is greater.
So, \(\frac{7}{8}\) > \(\frac{3}{8}\)
(v) We have, \(\frac{-5}{10}\) …….. \(\frac{6}{10}\)
Since, the denominators are same.
Now, on comparing the numerators, we get 5 < 6
Since, we know that for same denominator, the fraction with larger numerator is greater.
So, \(\frac{5}{10}\) < \(\frac{6}{10}\)
(vi) We have, \(\frac{2}{6}\) ……. ……. \(\frac{1}{6}\)
Since, the denominators are same. Now, on comparing the numerators, we get 2 > 1
Since, we know that for same denominator, the fraction with larger numerator is greater.
So, \(\frac{2}{6}\) > \(\frac{1}{6}\)
Question 14.
Compare the following fractions using < and > signs.
(i) \(\frac{3}{8}\) ……. ……. \(\frac{3}{7}\)
(ii) \(\frac{4}{9}\) ……. ……. \(\frac{4}{10}\)
(iii) \(\frac{2}{7}\) ……. ……. \(\frac{2}{5}\)
(iv) \(\frac{5}{7}\) ……. ……. \(\frac{5}{6}\)
(v) \(\frac{6}{9}\) ……. ……. \(\frac{6}{10}\)
(vi) \(\frac{7}{9}\) ……. ……. \(\frac{7}{11}\)
Answer:
(i) We have, \(\frac{3}{8}\) and \(\frac{3}{7}\)
Since, the numerators are same.
Now, on comparing the denominators, we get 8 > 7
We know that for same numerator, the fraction with smaller denominator is greater.
∴ \(\frac{3}{8}\) < \(\frac{3}{7}\)
(ii) We have, \(\frac{4}{9}\) and \(\frac{4}{10}\)
Since, the numerators are same.
Now, on comparing the denominators, we get 9 < 10 We know that for same numerator, the fraction with smaller denominator is greater.
∴ \(\frac{4}{9}\) > \(\frac{4}{10}\)
(iii) Do same as part (i)
Here, \(\frac{2}{7}\) < \(\frac{2}{5}\)
(iv) Do same as part (i)
Here, \(\frac{5}{7}\) < \(\frac{5}{6}\) (v) Do same as part (i) Here, \(\frac{6}{9}\) > \(\frac{6}{10}\)
(vi) So same as part (i)
Here, \(\frac{7}{9}\) > \(\frac{7}{11}\)
Fraction Greater Than 1 (NCERT Pg 24-28)
Question 15.
Dadiji had 7 pieces of \(\frac{1}{2}\) paratha. How many parathas did she eat? Find out.
Answer:
Given, the number of pieces of \(\frac{1}{2}\) paratha eaten by Dadiji = 7
So, the number of parathas eaten by Dadiji
= \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\)
= 1 + 1 + 1 + \(\frac{1}{2}\) = 3 \(\frac{1}{2}\)
Thus, Dadiji ate 3 whole parathas and 1 piece of \(\frac{1}{2}\) paratha.
Question 16.
(i) 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 the to find the answer.
(ii) How many parathas were made on this day? Find out.
Answer:
(i) Given, the number of pieces of \(\frac{1}{2}\) paratha eaten by Raman = 6
So, the number of parathas eaten by Raman = \(\frac{1}{2}\) + \(\frac{1}{2}\) +\(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) = \(\frac{6}{2}\) = 3
The number of pieces of \(\frac{1}{2}\) paratha eaten by Dadiji = 7
So, the number of parathas eaten by Dadaji
= \(\frac{1}{2}\)+\(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\)
= 1 + 1 + 1 + \(\frac{1}{2}\)
= 3 + \(\frac{1}{2}\) = 3 \(\frac{1}{2}\)
and the number of pieces of \(\frac{1}{2}\) paratha eaten by Baba =5
So, the number of parathas eaten by Baba
= \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\)
= 1 + 1 + \(\frac{1}{2}\) = 2 + \(\frac{1}{2}\) = 2 \(\frac{1}{2}\)
(ii) Total number of parathas were made on this day = Number of parathas eaten by Raman + Number of parathas eaten by Dadaiji + Number of parathas eaten by Baba = 3 + \(\frac{7}{2}\) + \(\frac{5}{2}\) = 3 × \(\frac{2}{2}\) + \(\frac{7}{2}\) + \(\frac{5}{2}\) = \(\frac{6}{2}\) +\(\frac{7}{2}\) + \(\frac{5}{2}\) = \(\frac{18}{2}\) = 9
Question 16.
(i) 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.
(ii) How many parathas were made on this day? Find out.
Answer:
(i) Given, the number of pieces of \(\frac{1}{4}\) paratha eaten by Raman =7
So, the number of parathas eaten by Raman
The number of pieces of \(\frac{1}{4}\) paratha eaten by Radhika = 6
So, the number of parathas eaten by Radhika
The number of pieces of \(\frac{1}{4}\) paratha eaten by Maa = 8
So, the number of parathas eaten by Maa
The number of pieces of \(\frac{1}{4}\) paratha eaten by Dadiji = 10
So, the number of parathas eaten by Dadiji
And the number of pieces of \(\frac{1}{4}\) paratha eaten by Baba = 12
So, the number of parathas eaten by Baba
(ii) Total number of parathas were made on this day = Quantity of Raman’s paratha
+ Quantity of Radhika’s paratha
+ Quantity of Maa’s paratha
+ Quantity of Dadiji’s paratha
+ Quantity of Baba’s paratha
= \(\frac{7}{4}\) +\(\frac{6}{4}\) + \(\frac{8}{4}\)+\(\frac{10}{4}\) + \(\frac{12}{4}\)
= \(\frac{43}{4}\) = 10 \(\frac{3}{4}\)
So, 10 whole parathas and \(\frac{3}{4}\) of a whole paratha were made on this day.
Let Us Do (NCERT Page 28)
Question 18.
Use parathas and number lines to show the following fractions in your notebook.
(i) \(\frac{2}{3}\) and \(\frac{5}{3}\)
(ii) \(\frac{3}{4}\) and \(\frac{5}{4}\)
(iii) \(\frac{4}{8}\) and \(\frac{9}{8}\)
Answer:
(i) We have, \(\frac{2}{3}\) and \(\frac{5}{3}\)
The number line representation is shown below
(ii) We have, \(\frac{3}{4}\) and \(\frac{5}{4}\)
The number line representation is shown below
(iii) We have, \(\frac{4}{8}\) and \(\frac{9}{8}\)
The number line representation is shown below
Question 19.
Circle the fractions that are greater than one (whole). How do you know? Discuss your reasoning in the class.
Answer:
We know that if the fraction is greater than one, then the numerator is greater than the denominator.
So, the fractions greater that one are \(\frac{5}{4}\), \(\frac{9}{4}\), \(\frac{7}{3}\), \(\frac{13}{11}\), \(\frac{12}{8}\) and \(\frac{12}{5}\).
Let Us Do (NCERT Pg 29)
Question 20.
Compare the following fractions using 1 as a reference. Share your reasoning in the class.
(i) \(\frac{8}{7}\) ……. ……. \(\frac{9}{15}\)
(ii) \(\frac{13}{20}\) ……. ……. \(\frac{17}{15}\)
(iii) \(\frac{7}{6}\) ……. ……. \(\frac{8}{8}\)
(iv) \(\frac{6}{6}\) ……. ……. \(\frac{19}{12}\)
(v) \(\frac{12}{9}\) ……. ……. \(\frac{4}{5}\)
(vi) \(\frac{15}{5}\) ……. ……. \(\frac{16}{4}\)
Answer:
(i) We have, \(\frac{8}{7}\) and \(\frac{9}{15}\)
On comparing the numerator and denominator of both the fractions, we get
8 > 7 and 9 < 15
∴ \(\frac{8}{7}\) > 1 and \(\frac{9}{15}\)<1
Therefore, \(\frac{8}{7}\) > \(\frac{9}{15}\)
(ii) We have, \(\frac{13}{20}\) and \(\frac{17}{15}\)
On comparing the numerator and denominator of both the fractions, we get
13 < 20 and 17 > 15
∴ \(\frac{13}{20}\) < 1 and \(\frac{17}{15}\) > 1
Therefore, \(\frac{13}{20}\) < \(\frac{17}{15}\).
(iii) We have, \(\frac{7}{6}\) and \(\frac{8}{8}\)
On comparing the numerator and denominator of both the fractions, we get
7 > 6 and 8 = 8
∴ \(\frac{7}{6}\) > 1 and \(\frac{8}{8}\) = 1
Therefore, \(\frac{7}{6}\) > \(\frac{8}{8}\)
(iv) We have, \(\frac{6}{6}\) and \(\frac{19}{12}\)
On comparing the numerator and denominator of both the fractions, we get
6 = 6 and 19 > 12
∴ \(\frac{6}{6}\) = 1 and \(\frac{19}{12}\) > 1
Therefore, \(\frac{6}{6}\) < \(\frac{19}{12}\)
(v) We have, \(\frac{12}{9}\) and \(\frac{4}{5}\)
On comparing the numerator and denominator of both the fractions, we get
12 > 9 and 4 < 5 ∴ \(\frac{12}{9}\) > 1 and \(\frac{4}{5}\) < 1
Therefore, \(\frac{12}{9}\) > \(\frac{4}{5}\)
(vi) We have, \(\frac{15}{5}\) and \(\frac{16}{4}\)
On simplifying both the fractions, we get
\(\frac{15}{5}\) = 3 and \(\frac{16}{4}\) = 4
∵ 3 < 4
Therefore, \(\frac{15}{5}<[latex]\frac{16}{4}\)
Let Us Do (NCERT Pg 30)
Question 21.
Circle the fractions below that are equal to \(\frac{1}{2}\).
Answer:
On simplifying the given fractions, we get
Question 22.
Some fractions are written in the box below. Circle the fractions that are less than half. How do you know? Discuss your reasoning in the class.
Answer:
On comparing the given fractions in the box with fraction \(\frac{1}{2}\), we get
(i)
Here, 2 < 3
We know that for same denominator, the fraction with larger numerator is greater.
∴ \(\frac{2}{6}\) < \(\frac{3}{6}\)
Therefore, \(\frac{3}{9}\) < \(\frac{1}{2}\)
Here, 8 > 5
We know that for same denominator, the fraction with larger numerator is greater.
∴ \(\frac{8}{10}\) > \(\frac{5}{10}\)
Therefore, \(\frac{12}{15}\) > \(\frac{1}{2}\)
Let Us Do (NCERT Pg 31)
Question 23.
Compare the following fractions. Where possible, compare the fractions with \(\frac{1}{2}\).
Answer:
(i) To compare \(\frac{2}{9}\) and \(\frac{1}{2}\),
we first make the denominator same.
In order to make the denominator of both the fractions same, we multiply both the numerator and denominator of \(\frac{2}{9}\) by 7 and that of \(\frac{4}{7}\) by 9.
Now, on comparing numerators 14 and 36, we get 14 < 36
We know that for same denominator, the fraction with larger number is greater.
∴ \(\frac{14}{63}\) < \(\frac{36}{63}\)
Therefore, \(\frac{2}{9}\)<\(\frac{4}{7}\)
(ii) Do same as part (i).
Try This (NCERT Pg 31)
Question 24.
If the length of an ant is \(\frac{1}{4}\) cm then what is the total length of 16 such ants walking in a line? Use the number line given below.
Answer:
Given, the length of an ant = \(\frac{1}{4}\) cm
So, the length of 16 such ants
