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.
Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ____________ kg.
Solution:
\(\frac{1}{3}\)
As weight is to be divided into three equal parts. So, each equal part will be \(\frac{1}{3}\).
Question 2.
A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is __kg.
Solution:
Here, 1 kg of rise is packed in 4 packets of equal weight, then weight of each packet
= \(\frac{\text { Total weight }}{\text { No. of packets }}=\frac{1}{4}\)
Question 3.
Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank _________ glass of sugarcane juice
Solution:
If 3 glasses of juice is shared among 4 friends, then each one will get \(\frac{3}{4}\) glasses of juice.
Question 4.
The big fish weighs \(\frac{1}{2}\) kg. The small one weighs \(\frac{1}{4}\)kg. Together they weigh _________ kg.
Solution:
\(\frac{3}{4}\)
Question 5.
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-quarters, one and a quarter, one 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:
We get this piece by breaking the chikki into 12 equal pieces. So this is \(\frac{1}{12}\) chikki.
Solution:
We get this piece by breaking the chikki into 4 equal pieces. So this is \(\frac{1}{4}\) chikki.
Solution:
We get this piece by breaking the chikki into 8 equal pieces. So this is \(\frac{1}{8}\) chikki.
Solution:
We get this piece by breaking the chikki into 6 equal pieces. So this is \(\frac{1}{6}\) chikki.
Solution:
We get this piece by breaking the chikki into 8 equal pieces. So this is \(\frac{1}{8}\) chikki.
Solution:
We get this piece by breaking the chikki into 12 equal pieces. So this is \(\frac{2}{12}=\frac{1}{6}\) chikki.
Solution:
We get this piece by breaking the chikki into 24 equal pieces. So this is \(\frac{1}{24}\) chikki.
Solution:
We get this piece by breaking the chikki into 24 equal pieces. So this is \(\frac{1}{24}\) chikki.
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:
Here
represents a full roti (whole)
Step 1.
= \(\frac{1}{2}\) = 1 times half
Step 2.
= \(\frac{1}{2}\) + \(\frac{1}{2}\) = 2 times half
Step 3.
= \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\) = 3 times half
Step 4.
= \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\) = 4 times half
Step 5.
= \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\) = 5 times half
Step 6.
= \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\) = 6 times half
= 6 × \(\frac{1}{2}=\frac{6}{2}\) = 3
Step 7.
= \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\) = 7 times half
= 7 × \(\frac{1}{2}=\frac{7}{2}\)
Question 2.
Can you create a similar table for \(\frac{1}{4}\)?
Solution:
Yes
Question 3.
Make \(\frac{1}{3}\) using a paper strip. Can you use this to also make \(\frac{1}{6}\)?
Solution:
Question 4.
Draw a picture and write an addition statement as above to show:
(a) 5 times of a roti
(b) 9 times of a roti
Solution:
Represents a full roti (whole)
(a)
5 times \(\frac{1}{4}\) of a roti
= \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{5}{4}\)
1 full and \(\frac{1}{4}\) roti
(b)
9 times \(\frac{1}{4}\) of a roti
= \(\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{9}{4}\)
2 full and \(\frac{1}{4}\) of roti
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:
We divide the length between 0 and 1 on a number line into 10 equal parts. The point A represents \(\frac{1}{10}\).
The point B represents \(\frac{3}{10}\)
We divide the length between 0 and 1 on a number line into 5 equal parts. The point C represents \(\frac{4}{5}\).
Question 2.
Write five more fractions of your choice and mark them on the number line.
Solution:
Let \(\frac{1}{5}, \frac{3}{4}, \frac{7}{8}, \frac{4}{7}\) and \(\frac{2}{9}\) be the five fractions.
These fractions are marked on a number line as shown below.
(Answers may vary)
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:
We can write it as:
\(\frac{7}{2}=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\) = 3 + \(\frac{1}{2}\)
So, there are 3 whole units in \(\frac{7}{2}\).
Question 2.
How many whole units are there in \(\frac{4}{3}\) and in \(\frac{7}{3}\)?
Solution:
We can write the given fractions as:
\(\frac{4}{3}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1+\frac{1}{3}\)
So, there is 1 whole unit in \(\frac{4}{3}\)
\(\frac{7}{3}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=2+\frac{1}{3}\)
So, there are 2 whole units in fraction \(\frac{7}{3}\).
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) \(\frac{9}{4}\)
We saw that
Fraction ← \(\frac{7}{3}\) = 2 + \(\frac{1}{3}\) → Mixed number
[This number is thus also called ‘two and one third’. We also write it as 2\(\frac{1}{3}\).]
Solution:
(a) \(\frac{8}{3}\)
Numerator 8 is split/divided into as many 3’s i.e. denominator no.: 8 = 3 + 3 + 2
= 1 + 1 + \(\frac{2}{3}\) = 2 \(\frac{2}{3}\)
∴ No. of whole units in \(\frac{8}{3}\) = 2 whole units.
(b) \(\frac{11}{5}=\frac{5}{5}+\frac{5}{5}+\frac{1}{5}\) [Numerator 11 = 5 + 5 + 1]
= 1 + 1 + \(\frac{1}{5}\)
= 2\(\frac{1}{5}\)
(c) \(\frac{9}{4}=\frac{4}{4}+\frac{4}{4}+\frac{1}{4}\)
= 1 + \(\frac{1}{4}\) [Numerator 9 = 4 + 4 + 1]
= 2\(\frac{1}{4}\)
∴ No. of whole units in \(\frac{9}{4}\) = 2 whole units.
Question 2.
Can all fractions greater than 1 be written as such mixed numbers?
A mixed number /mixedfraction contains a whole number (called the whole part) and a fraction that is less than 1 (called the fractional part).
Solution:
Yes, all fractions greater than 1 can be written as mixed fractions/numbers.
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:
3\(\frac{1}{4}\) = 1 + 1 + 1 + \(\frac{1}{4}\)
(b) 7\(\frac{2}{3}\)
Solution:
7\(\frac{2}{3}\) = 1 + 1 + 1 + 1 + 1 + 1 + 1 + \(\frac{2}{3}\)
= \(\frac{3}{3}+\frac{3}{3}+\frac{3}{3}+\frac{3}{3}+\frac{3}{3}+\frac{3}{3}+\frac{3}{3}+\frac{2}{3}=\frac{23}{3}\)
(c) 9\(\frac{4}{9}\)
Solution:
9\(\frac{4}{9}\) = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + \(\frac{4}{9}\)
= \(\frac{9}{9}+\frac{9}{9}+\frac{9}{9}+\frac{9}{9}+\frac{9}{9}+\frac{9}{9}+\frac{9}{9}+\frac{9}{9}+\frac{9}{9}+\frac{4}{9}=\frac{85}{9}\)
(d) 3\(\frac{1}{6}\)
Solution:
3\(\frac{1}{6}\) = 1 + 1 + 1 + \(\frac{1}{6}\)
= \(\frac{6}{6}+\frac{6}{6}+\frac{6}{6}+\frac{1}{6}=\frac{19}{6}\)
(e) 2\(\frac{3}{11}\)
Solution:
2\(\frac{3}{11}\) = 1 + 1 + \(\frac{3}{11}\)
= \(\frac{11}{11}+\frac{11}{11}+\frac{3}{11}=\frac{25}{11}\)
(f) 3\(\frac{9}{10}\)
Solution:
3\(\frac{9}{10}\) = 1 + 1 + 1 + \(\frac{9}{10}\)
= \(\frac{10}{10}+\frac{10}{10}+\frac{10}{10}+\frac{9}{10}=\frac{39}{10}\)
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:
\(\frac{2}{6}=\frac{2}{6} \times \frac{2}{2}=\frac{4}{12}\)
\(\frac{2}{6}=\frac{2}{6} \times \frac{3}{3}=\frac{6}{18}\)
\(\frac{2}{6}=\frac{2}{6} \times \frac{4}{4}=\frac{8}{24}\)
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:
Fraction of roti each child gets is \(\frac{3}{4}\).
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 child will get \(\frac{1}{2}\) rotis
Division fact: 2 ÷ 4 or 1 ÷ 2
Addition fact: 2 = \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}\)
Multiplication fact: 2 = 4 × \(\frac{2}{4}\) or 4 × \(\frac{1}{2}\)
Question 3.
Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?
Solution:
From each cake, 5 divisions are to be made
So, from each cake Anil will get \(\frac{1}{5}\) of the part.
So, cake received by Anil = \(\frac{1}{5}+\frac{1}{5}=\frac{2}{5}\)
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:
Here 51 is divisible by 17 then \(\frac{51}{17}\) = 3
∴ \(\frac{17}{51}=\frac{17}{17 \times 3}=\frac{1}{3}\)
which is the lowest term.
(b) \(\frac{64}{144}\)
Solution:
Here 64 and 144 are both multiples of 16. So we divide both by 16.
\(\frac{64}{144}=\frac{64 \div 16}{144 \div 16}\)
= \(\frac{4}{9}\)
(c) \(\frac{126}{147}\)
Solution:
Here, \(\frac{126}{147}\)
= \(\frac{126 \div 7}{147 \div 7}\)
[∵ HCF of 126 and 147 is 7 × 3 = 21]
= \(\frac{18 \div 3}{21 \div 3}\)
= \(\frac{6}{7}\)
(d) \(\frac{525}{112}\)
Solution:
Here 525 and 112 are both multiples of 7, we divide both by 7.
= \(\frac{525 \div 7}{112 \div 7}\)
= \(\frac{75}{16}\)
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:
\(\frac{12}{5}>\frac{8}{5}\)
(e) \(\frac{9}{4}, \frac{5}{2}\)
Solution:
\(\frac{5}{2}=\frac{5 \times 2}{2 \times 2}=\frac{10}{4}\)
As \(\frac{10}{4}>\frac{9}{4}\). So, \(\frac{5}{2}>\frac{9}{4}\)
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) \(\frac{25}{16}, \frac{7}{8}, \frac{13}{4}, \frac{17}{32}\)
(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:
Here \(\frac{2}{7}+\frac{5}{7}+\frac{6}{7}\)
(b) \(\frac{3}{4}+\frac{1}{3}\)
Solution:
Here \(\frac{3}{4}+\frac{1}{3}\)
Here LCM of denominators 4 and 3 is 12
∴ Equivalent fraction of \(\frac{3}{4}\) with denominators 12 is \(\frac{9}{12}\) and equivalent fraction of \(\frac{1}{3}\) with denominators 12 is \(\frac{4}{12}\)
(c) \(\frac{2}{3}+\frac{5}{6}\)
Solution:
Given \(\frac{2}{3}+\frac{5}{6}\)
Now LCM of 3 and 6 is 6.
Expressing as equivalent fractions with denominators 6, we get
(d) \(\frac{2}{3}+\frac{2}{7}\)
Solution:
Here \(\frac{2}{3}+\frac{2}{7}\)
Now LCM of 3 and 7 is 21
Expressing as equivalent fractions with denominators 21, we get
(e) \(\frac{3}{4}+\frac{1}{3}+\frac{1}{5}\)
Solution:
Here \(\frac{3}{4}+\frac{1}{3}+\frac{1}{5}\)
Now LCM of 4, 3, 5 is 60.
Expressing as equivalent fractions with denominators 60, we get
(f) \(\frac{2}{3}+\frac{4}{5}\)
Solution:
Here \(\frac{2}{3}+\frac{4}{5}\)
Now LCM of 3 and 5 is 15
Expressing as equivalent fractions with denominators 15, we get
(g) \(\frac{4}{5}+\frac{2}{3}\)
Solution:
Here \(\frac{4}{5}+\frac{2}{3}\)
Now LCM of 5 and 3 is 15
Thus expressing as equivalent fractions with denominators 15, we get
(h) \(\frac{3}{3}+\frac{5}{8}\)
Solution:
Given \(\frac{3}{3}+\frac{5}{8}\)
Here LCM of 5 and 8 is 40
Expressing as equivalent fractions with denominators 40, we get
(i) \(\frac{9}{2}+\frac{5}{4}\)
Solution:
Here \(\frac{9}{2}+\frac{5}{4}\)
Now LCM of 2 and 4 is 4.
Expressing as equivalent fractions with denominators 4, we get
(j) \(\frac{8}{3}+\frac{2}{7}\)
Solution:
Given \(\frac{8}{3}+\frac{2}{7}\)
Here LCM of 3 and 7 is 21
Expressing as equivalent fractions with denominators 21, we get
(k) \(\frac{3}{4}+\frac{1}{3}+\frac{1}{5}\)
Solution:
Here \(\frac{3}{4}+\frac{1}{3}+\frac{1}{5}\)
Now LCM of 4, 3, 5 is 60
Expressing as equivalent fractions with denominators 60, we get
(l) \(\frac{2}{3}+\frac{4}{5}+\frac{3}{7}\)
Solution:
Here \(\frac{2}{3}+\frac{4}{5}+\frac{3}{7}\)
Now LCM of 3, 5 and 7 is 105.
Expressing as equivalent fractions with denominators 105, we get
(m) \(\frac{9}{2}+\frac{5}{4}+\frac{7}{6}\)
Solution:
Given \(\frac{9}{2}+\frac{5}{4}+\frac{7}{6}\)
Here LCM of 2, 4, 6 is 12.
Now expressing as equivalent fractions with denominators 12, we get
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
Thus, volume of green paint = Volume of yellow paint + Volume of blue paint
= \(\frac{2}{3}\)L + \(\frac{3}{4}\)L
The denominators of the given fractions are 3 and 4. The LCM of 3 and 4 is 12.
Then, \(\frac{2}{3}=\frac{2 \times 4}{3 \times 4}=\frac{8}{12}, \frac{3}{4}=\frac{3 \times 3}{4 \times 3}=\frac{9}{12}\)
Therefore \(\frac{2}{3}+\frac{3}{4}=\frac{8}{12}+\frac{9}{12}=\frac{17}{12}=1 \frac{5}{12}\)
Thus, Volume of green paint Rahim made = 1\(\frac{5}{12}\) L.
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:
Geeta bought \(\frac{2}{5}\) m of lace and Shamin bought \(\frac{3}{4}\) m of lace.
Total length of the lace = \(\left(\frac{2}{5}+\frac{3}{4}\right)\) m
The denominators of the given fractions are 5 and 4. The LCM of 5 and 4 is 20.
Then \(\frac{2}{5}=\frac{2 \times 4}{5 \times 4}=\frac{8}{20}, \frac{3}{4}=\frac{3 \times 5}{4 \times 5}=\frac{15}{20}\)
Therefore, \(\frac{2}{5}+\frac{3}{4}=\frac{8}{20}+\frac{15}{20}=\frac{23}{20}=1 \frac{3}{20}\)
Thus, the total length of the lace is 1\(\frac{3}{20}\) m.
Yes, the lace will be sufficient to cover the whole border.
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 \(\frac{10}{3}\)
(b) \(\frac{18}{5}\) from \(\frac{23}{3}\)
(c) \(\frac{29}{7}\) from \(\frac{45}{7}\)
Solution:
Question 3.
Solve the following problems:
(a) Java’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:
Given distance between Jaya’s school and home is \(\frac{7}{10}\) km and distance covered by Jaya in auto is \(\frac{1}{2}\) km.
∴ Distance Jaya covered by walking = \(\frac{7}{10}\)km – \(\frac{1}{2}\)km
LCM of 10 and 2 is 10.
Hence Jaya walks \(\frac{1}{5}\) km or 200 meters to reach her school.
(b) Jeevika takes \(\frac{10}{3}\) minutes to take a complete round of the park and her 13 friend Namit takes \(\frac{13}{4}\) minutes to do the same. Who takes less time and by how much?
Solution:
Time taken by Jeevika to cover 1 round of park = \(\frac{10}{3}\)mm
Time taken by Namit to cover 1 round of 13 park= \(\frac{13}{4}\) min
To find who takes less time we need to compare \(\frac{10}{3}\) and \(\frac{13}{4}\)
Here, LCM of 3 and 4 is 12
\(\frac{10 \times 4}{3 \times 4}\) and \(\frac{13 \times 3}{4 \times 3}\)
[Expressing fractions in fractional unit \(\frac{1}{12}\)]
= \(\frac{40}{12}\) and \(\frac{39}{12}\)
\(\frac{40}{12}>\frac{39}{12}\)
Hence Namit takes less time
\(\frac{40}{12}-\frac{39}{12}\)
= \(\frac{40-39}{12}=\frac{1}{12}\)
Namit takes \(\frac{1}{2}\) of minutes less than Jeevika.