By using Ganita Prakash Book Class 6 Solutions and Chapter 7 Fractions Class 6 NCERT Solutions Question Answer, students can improve their problem-solving skills.
Class 6 Maths Chapter 7 Fractions Solutions
Fractions Class 6 Solutions Questions and Answers
7.1 Fractional Units and Equal Shares Figure it Out (Page No. 152 – 153)
Question 1.
Fill in the blanks with fractions.
(i) Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh _________ kg.
Solution:
\(\frac{1}{3}\)
(ii) A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is _________ kg.
Solution:
\(\frac{1}{4}\)
(iii) Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank _________ glass of sugarcane juice
Solution:
\(\frac{3}{4}\)
(iv) The big fish weighs \(\frac{1}{2}\) kg. The small one weighs \(\frac{1}{4}\)kg. Together they weigh _________ kg.
Solution:
\(\frac{3}{4}\)
(v) Arrange these fraction words in order of size from the smallest to the biggest in the empty box below.
One and a half, three quarters, one and a quarter, half, quarter, two and a half.
Solution:
quarter < half < three quarter < one and a quarter < one and a half < two and a half.
7.2 Fractional Units as Parts of a Whole Figure it Out (Page No. 155)
Question 1.
The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece?
Solution:
(a) \(\frac{1}{12}\)
(b) \(\frac{1}{4}\)
(c) \(\frac{1}{8}\)
(d) \(\frac{1}{6}\)
(e) \(\frac{1}{8}\)
(f) \(\frac{1}{6}\)
(g) \(\frac{1}{24}\)
(h) \(\frac{1}{24}\)
7.3 Measuring Using Fractional Units Figure it Out (Page No. 158)
Question 1.
Continue this table of \(\frac{1}{2}\) for 2 more steps.
Solution:
Question 2.
Can you create a similar table for \(\frac{1}{4}\) ?
Solution:
Question 3.
Make \(\frac{1}{3}\) using a paper strip. Can you use this to also make \(\frac{1}{6}\)?
Solution:
Do it yourself
Question 4.
Draw a picture and write an addition statement as above to show:
(a) 5 times \(\frac{1}{4}\) of a roti
Solution:
5 times \(\frac{1}{4}\) of a roti
= \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}\)
(b) 9 times \(\frac{1}{4}\) of a roti
Solution:
9 times \(\frac{1}{4}\) of a roti
= \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}\)
Question 5.
Match each fractional unit with the correct picture:
Solution:
7.4 Marking Fraction Lengths on the Number Line Figure it Out (Page No. 160)
Question 1.
On a number line, draw lines of lengths \(\frac{1}{10}, \frac{3}{10}\) and \(\frac{4}{5}\).
Solution:
Question 2.
Write five more fractions of your choice and mark them on the number line.
Solution:
Do it yourself.
Question 3.
How many fractions lie between 0 and 1 ? Think, discuss with your classmates, and write your answer.
Solution:
Infinitely many
Question 4.
What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is \(\frac{1}{2}\). So the blue line is \(\frac{1}{2}\) units long. Write the fraction that gives the length of the black line in the box.
Solution:
Fraction for the length of blue line = \(\frac{1}{2}\)
Fraction for the length of black line = \(\frac{3}{2}\)
Question 5.
Write the fraction that gives the lengths of the black lines in the respective boxes.
Solution:
\(\frac{6}{5}, \frac{7}{5}, \frac{8}{5}, \frac{9}{5}\)
7.5 Mixed Fractions Figure it Out (Page No. 162)
Question 1.
How many whole units are there in \(\frac{7}{2}\)?
Solution:
3
Question 2.
How many whole units are there in \(\frac{4}{3}\) and in \(\frac{7}{3}\)?
Solution:
1 and 2, respectively.
7.5 Mixed Fractions Figure it Out (Page No. 162)
Question 1.
Figure out the number of whole units in each of the following fractions:
(a) \(\frac{8}{3}\)
(b) \(\frac{11}{5}\)
(c) \(\frac{9}{4}\)
Solution:
(a) 2
(b) 2
(c) 2
Question 2.
Can all fractions greater than 1 be written as such mixed numbers?
Solution:
Yes.
Question 3.
Write the following fractions as mixed fractions (e.g. \(\frac{9}{2}\) = 4\(\frac{1}{2}\))
(a) \(\frac{9}{2}\)
Solution:
= 4\(\frac{1}{2}\)
(b) \(\frac{9}{5}\)
Solution:
= 1\(\frac{4}{5}\)
(c) \(\frac{21}{19}\)
Solution:
= 1\(\frac{2}{19}\)
(d) \(\frac{47}{9}\)
Solution:
= 5\(\frac{2}{9}\)
(e) \(\frac{12}{11}\)
Solution:
= 1\(\frac{1}{11}\)
(f) \(\frac{19}{6}\)
Solution:
= 3\(\frac{1}{6}\)
7.5 Mixed Fractions Figure it Out (Page No. 163)
Question 1.
Write the following mixed numbers as fractions:
(a) 3\(\frac{1}{4}\)
Solution:
\(\frac{13}{4}\)
(b) 7\(\frac{2}{3}\)
Solution:
\(\frac{23}{3}\)
(c) 9\(\frac{4}{9}\)
Solution:
\(\frac{85}{9}\)
(d) 3\(\frac{1}{6}\)
Solution:
\(\frac{19}{6}\)
(e) 2\(\frac{3}{11}\)
Solution:
\(\frac{25}{11}\)
(f) 3\(\frac{9}{10}\)
Solution:
\(\frac{39}{10}\)
7.5 Mixed Fractions Figure it Out (Page No. 164)
Answer the following questions after looking at the fraction wall:
Question 1.
Are the lengths \(\frac{1}{2}\) and \(\frac{3}{6}\) equal?
Solution:
Yes, \(\frac{1}{2}\) and \(\frac{3}{6}\) are equivalent fractions. Also, it is clear from given fraction wall that the length \(\frac{1}{2}\) and \(\frac{3}{6}\) are equal.
Question 2.
Are \(\frac{2}{3}\) and \(\frac{4}{6}\) equivalent fractions? Why?
Solution:
Yes, \(\frac{2}{3}\) and \(\frac{4}{6}\) are equivalent fractions because at the given fraction wall that the length \(\frac{2}{3}\) and length \(\frac{4}{6}\) are equal.
Question 3.
How many pieces of length \(\frac{1}{6}\) will make a length of \(\frac{1}{2}\) ?
Solution:
Three pieces of length \(\frac{1}{6}\) will make a length of \(\frac{1}{2}\).
Question 4.
How many pieces of length \(\frac{1}{6}\) will make a length of \(\frac{1}{3}\)?
Solution:
Two pieces of length \(\frac{1}{6}\) will make a length of \(\frac{1}{3}\).
7.6 Equivalent Fractions Figure it Out 7.7 Simplest form of a Fraction Figure it Out (Page No. 165)
Question 1.
Are \(\frac{3}{6}, \frac{4}{8}, \frac{5}{10}\) equivalent fractions? Why?
Solution:
Yes, because all of them have the same length.
Question 2.
Write two equivalent fractions for \(\frac{2}{6}\).
Solution:
\(\frac{1}{3}, \frac{3}{9}\)
Question 3.
(Write as many as you can)
Solution:
\(\frac{4}{6}=\frac{2}{3}=\frac{6}{9}=\frac{8}{12}=\frac{10}{15}\)
7.7 Simplest form of a Fraction Figure it Out (Page No. 166)
Question 1.
Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts.
Fraction of roti each child gets is ______
Division fact:
Addition fact:
Multiplication fact:
Compare your picture and answers with your classmates!
Solution:
Each child gets is \(\frac{3}{4}\) of a roti.
Division fact: 3 ÷ 4 = \(\frac{3}{4}\)
Addition fact: 3 = \(\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}\)
Multiplication fact: 3 = 4 × \(\frac{3}{4}\)
Question 2.
Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.
Solution:
Each roti is divided into 4 equal parts. Since, there are 4 children, each child will get 1 part from each of the 2 rotis. Thus, each child gets 2 parts which equals to \(\frac{2}{4}\) or \(\frac{1}{2}\) of a roti.
Division fact: 2 ÷ 4 or 1 ÷ 2
Addition fact: \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\) = 2
Multiplication fact: 4 × \(\frac{2}{4}\) = 2
Question 3.
Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?
Solution:
Anil would get \(\frac{2}{5}\) of a cake.
7.7 Simplest form of a Fraction Figure it Out (Page No. 168 – 169)
Question 1.
Find the missing numbers:
(a) 5 glasses of juice shared equally among 4 friends is the same as _____ glasses of juice shared equally among 8 friends.
So, \(\frac{5}{4}\) = _____
Solution:
10
(b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kg of potatoes divided equally in _____ bags.
So, \(\frac{4}{3}\) = _____
Solution:
9
(c) 7 rotis divided among 5 children is the same as rotis divided among _____ children.
So, \(\frac{7}{5}\) = _____
Solution:
14, 10 So, \(\frac{7}{5}=\frac{14}{10}\)
7.7 Simplest form of a Fraction Figure it Out (Page no. 172)
Question 2.
Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. (Page 172)
(a) \(\frac{7}{2}\) and \(\frac{3}{5}\)
Solution:
\(\frac{7 \times 2}{2 \times 2}\) and \(\frac{3 \times 2}{5 \times 2}=\frac{14}{4}\) and \(\frac{6}{10}\)
(b) \(\frac{8}{3}\) and \(\frac{5}{6}\)
Solution:
\(\frac{8 \times 2}{3 \times 2}\) and \(\frac{5 \times 2}{6 \times 2}=\frac{16}{6}\) and \(\frac{10}{12}\)
(c) \(\frac{3}{4}\) and \(\frac{3}{5}\)
Solution:
\(\frac{3 \times 2}{4 \times 2}\) and \(\frac{3 \times 2}{5 \times 2}=\frac{6}{8}\) and \(\frac{6}{10}\)
(d) \(\frac{6}{7}\) and \(\frac{8}{5}\)
Solution:
\(\frac{6 \times 2}{7 \times 2}\) and \(\frac{8 \times 2}{5 \times 2}=\frac{12}{14}\) and \(\frac{16}{10}\)
(e) \(\frac{9}{4}\) and \(\frac{5}{2}\)
Solution:
\(\frac{9 \times 2}{4 \times 2}\) and \(\frac{5 \times 2}{2 \times 2}=\frac{18}{8}\) and \(\frac{10}{4}\)
(f) \(\frac{1}{10}\) and \(\frac{2}{9}\)
Solution:
\(\frac{1 \times 2}{10 \times 2}\) and \(\frac{2 \times 2}{9 \times 2}=\frac{2}{20}\) and \(\frac{4}{18}\)
(g) \(\frac{8}{3}\) and \(\frac{11}{4}\)
Solution:
\(\frac{8 \times 2}{3 \times 2}\) and \(\frac{11 \times 2}{4 \times 2}=\frac{16}{6}\) and \(\frac{22}{8}\)
(h) \(\frac{13}{6}\) and \(\frac{1}{9}\)
Solution:
\(\frac{13 \times 2}{6 \times 2}\) and \(\frac{1 \times 2}{9 \times 2}=\frac{26}{12}\) and \(\frac{2}{18}\)
7.7 Simplest form of a Fraction Figure it Out (Page No. 173)
Question 1.
Express the following fractions in lowest terms:
(a) \(\frac{17}{51}\)
Solution:
\(\frac{1}{3}\)
(b) \(\frac{64}{144}\)
Solution:
\(\frac{4}{9}\)
(c) \(\frac{126}{147}\)
Solution:
\(\frac{6}{7}\)
(d) \(\frac{525}{112}\)
Solution:
\(\frac{75}{16}\)
7.8 Comparing Fractions Figure it Out (Page No. 174)
Question 1.
Compare the following fractions and justify your answers:
(a) \(\frac{8}{3}, \frac{5}{2}\)
Solution:
(b) \(\frac{4}{9}, \frac{3}{7}\)
Solution:
(c) \(\frac{7}{10}, \frac{9}{14}\)
Solution:
(d) \(\frac{12}{5}, \frac{8}{5}\)
Solution:
Clearly, \(\frac{12}{5}>\frac{8}{5}\)
(e) \(\frac{9}{4}, \frac{5}{2}\)
Solution:
\(\frac{9}{4}\)
Question 2.
Write the following fractions in ascending order.
(a) \(\frac{7}{10}, \frac{11}{15}, \frac{2}{5}\)
Solution:
(b) \(\frac{19}{24}, \frac{5}{6}, \frac{7}{12}\)
Solution:
Question 3.
Write the following fractions in descending order.
(a) \(\frac{25}{16}, \frac{7}{8}, \frac{13}{4}, \frac{17}{32}\)
Solution:
(b) \(\frac{3}{4}, \frac{12}{5}, \frac{7}{12}, \frac{5}{4}\)
Solution:
7.9 Relation to Number Sequences Figure it Out (Page No. 179)
Question 1.
Add the following fractions using Brahmagupta’s method:
(a) \(\frac{2}{7}+\frac{5}{7}+\frac{6}{7}\)
Solution:
\(\frac{2}{7}+\frac{5}{7}+\frac{6}{7}\)
= \(\frac{2+5+6}{7}=\frac{13}{7}\)
=1 \(\frac{6}{7}\)
(b) \(\frac{3}{4}+\frac{1}{3}\)
Solution:
\(\frac{3}{4}+\frac{1}{3}=\frac{3}{4} \times \frac{3}{3}+\frac{1}{3} \times \frac{4}{4}\)
= \(\frac{9}{12}+\frac{4}{12}=\frac{9+4}{12}\)
= \(\frac{13}{12}\)
= 1 \(\frac{1}{12}\)
(c) \(\frac{2}{3}+\frac{5}{6}\)
Solution:
\(\frac{2}{3}+\frac{5}{6}=\frac{2}{3} \times \frac{2}{2}+\frac{5}{6}\)
\(\frac{4}{6}+\frac{5}{6}=\frac{9}{6}=\frac{3}{2}\)
= 1 \(\frac{1}{2}\)
(d) \(\frac{2}{3}+\frac{2}{7}\)
Solution:
\(\frac{2}{3}+\frac{2}{7}=\frac{2}{3} \times \frac{7}{7}+\frac{2}{7} \times \frac{3}{3}\)
= \(\frac{14}{21}+\frac{6}{21}=\frac{20}{21}\)
(e) \(\frac{3}{4}+\frac{1}{3}+\frac{1}{5}\)
Solution:
\(\frac{45}{60}+\frac{20}{60}+\frac{12}{60}\)
= \(\frac{77}{60}\)
= 1\(\frac{17}{60}\)
(f) \(\frac{2}{3}+\frac{4}{5}\)
Solution:
\(\frac{10}{15}+\frac{12}{15}=\frac{22}{15}\)
= 1\(\frac{7}{15}\)
(g) \(\frac{4}{5}+\frac{2}{3}\)
Solution:
\(\frac{12}{15}+\frac{10}{15}=\frac{22}{15}\)
= 1\(\frac{7}{15}\)
(h) \(\frac{3}{5}+\frac{5}{8}\)
Solution:
\(\frac{24}{40}+\frac{25}{40}=\frac{49}{40}\)
= \(\frac{9}{40}\)
(i) \(\frac{9}{2}+\frac{5}{4}\)
Solution:
\(\frac{18}{4}+\frac{5}{4}=\frac{23}{4}\)
= 5\(\frac{3}{4}\)
(j) \(\frac{8}{3}+\frac{2}{7}\)
Solution:
\(\frac{56}{21}+\frac{6}{21}=\frac{62}{21}\)
= 2\(\frac{20}{21}\)
(k) \(\frac{3}{4}+\frac{1}{3}+\frac{1}{5}\)
Solution:
\(\frac{45}{60}+\frac{20}{60}+\frac{12}{60}=\frac{77}{60}\)
= 1\(\frac{17}{60}\)
(l) \(\frac{2}{3}+\frac{4}{5}+\frac{3}{7}\)
Solution:
\(\frac{70}{105}+\frac{84}{105}+\frac{45}{105}=\frac{199}{105}\)
= 1\(\frac{94}{105}\)
(m) \(\frac{9}{2}+\frac{5}{4}+\frac{7}{6}\)
Solution:
\(\frac{54}{12}+\frac{15}{12}+\frac{14}{12}=\frac{83}{12}\)
= \(\frac{11}{12}\)
Question 2.
Rahim mixes \(\frac{2}{3}\) litres of yellow paint with \(\frac{3}{4}\) litres of blue paint to make green paint. What is the volume of green paint he has made?
Solution:
Volume of yellow paint taken by Rahim = \(\frac{2}{3}\)L
Volume of blue paint taken by Rahim = \(\frac{3}{4}\) L
∴ Volume of green paint = \(\left(\frac{2}{3}+\frac{3}{4}\right)\) litres
Question 3.
Geeta bought \(\frac{2}{5}\) meter of lace and Shamim bought \(\frac{3}{4}\) meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border?
Solution:
Length of lace houht by Geeia = \(\frac{2}{5}\)metre
Length of lace bought by Shamim = \(\frac{3}{4}\) metre
Total length of lace bought = \(\left(\frac{2}{5}+\frac{3}{4}\right)\) metres
Yes, the lace will be sufficient to cover the whole border as it exceeds the parimeter
= 1 metre
7.9 Relation to Number Sequences Figure it Out (Page No. 181)
Question 1.
\(\frac{5}{8}-\frac{3}{8}\)
Solution:
We have, \(\frac{5}{8}-\frac{3}{8}\)
Here, \(\frac{5}{8}-\frac{3}{8}=\frac{2}{8}\)
Question 2.
\(\frac{7}{9}-\frac{5}{9}\)
Solution:
We have, \(\frac{7}{9}-\frac{5}{9}\)
Here, \(\frac{7}{9}-\frac{5}{9}=\frac{2}{9}\)
Question 3.
\(\frac{10}{27}-\frac{1}{27}\)
Solution:
\(\frac{10}{27}-\frac{1}{27}\)
Here, \(\frac{10}{27}-\frac{1}{27}\) = \(\frac{9}{27}=\frac{1}{3}\)
7.9 Relation to Number Sequences Figure it Out (Page No. 182)
Question 1.
Carry out the following subtractions using Brahmagupta’s method:
(a) \(\frac{8}{15}-\frac{3}{15}\)
Solution:
\(\frac{8}{15}-\frac{3}{15}\)
= \(\frac{5}{15}=\frac{1}{3}\)
(b) \(\frac{2}{5}-\frac{4}{15}\)
Solution:
\(\frac{2}{5}-\frac{4}{15}=\frac{2}{5} \times \frac{3}{3}-\frac{4}{15}\)
= \(\frac{6}{15}-\frac{4}{15}=\frac{2}{15}\)
(c) \(\frac{5}{6}-\frac{4}{9}\)
Solution:
\(\frac{5}{6}-\frac{4}{9}=\frac{5}{6} \times \frac{3}{3}-\frac{4}{9} \times \frac{2}{2}\)
= \(\frac{15}{18}-\frac{8}{18}=\frac{7}{18}\)
(d) \(\frac{2}{3}-\frac{1}{2}\)
Solution:
\(\frac{2}{3}-\frac{1}{2}=\frac{2}{3} \times \frac{2}{2}-\frac{1}{2} \times \frac{3}{3}\)
= \(\frac{4}{6}-\frac{3}{6}=\frac{1}{6}\)
Question 2.
Subtract as indicated:
(a) \(\frac{13}{4}\) from \(\frac{10}{3}\)
Solution:
(b) \(\frac{18}{5}\) from \(\frac{23}{3}\)
Solution:
(c) \(\frac{29}{7}\) from \(\frac{45}{7}\)
Solution:
\(\frac{45}{7}-\frac{29}{7}=\frac{16}{7}\)
Question 3.
Solve the following problems:
(a) Jaya’s school is \(\frac{7}{10}\) km from her home. She takes an auto for \(\frac{1}{2}\) km from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school?
Solution:
(a) Total distance between school and home = \(\frac{7}{10}\) km
Distance travelled in Auto = \(\frac{1}{2}\) km.
∴ Distance she walks daily to reach the school
(b) Jeevika takes \(\frac{10}{3}\) minutes to take a complete round of the park and her friend Namit takes \(\frac{13}{4}\) minutes to do the same. Who takes less time and by how much?
Solution:
Time taken by Jeevika = \(\frac{10}{3}\) minutes
and time taken by Narnit = \(\frac{13}{4}\) minutes
Now, \(\frac{10}{3} \times \frac{4}{4}=\frac{40}{12}\) and \(\frac{13}{4} \times \frac{3}{3}=\frac{39}{12}\)
Clearly, \(\frac{10}{3}\) > \(\frac{13}{4}\)
∴ Jeevika takes less ti me by \(\left(\frac{10}{3}-\frac{13}{4}\right)\) minutes
= \(\left(\frac{40}{12}-\frac{39}{12}\right)\) minutes
= \(\frac{1}{12}\) minutes.