AP Board 5th Class Maths Solutions 8th Lesson Fractions

Andhra Pradesh AP Board 5th Class Maths Solutions 8th Lesson Fractions Textbook Exercise Questions and Answers.

AP State Syllabus 5th Class Maths Solutions Chapter 8 Fractions

I. Observe the following table.

What do you observe from the above table?
Here, in all fractions the numerator is less than the denominator.

II. If Hema and Gopi got 7 and 9 biscuits then complete this table.

III. Observe the fractions : $$\frac{3}{4}, \frac{4}{5}, \frac{6}{7}, \frac{12}{13}, \frac{25}{28}$$

What do you say?
Here is all fractions have numerator is greater than or equal to denominator. These types of fractions are called improper fractions.

Do this: (TextBook Page No.129)

Question 1.
Write any 5 proper fractions.
Proper fractions: $$\frac{3}{4}, \frac{4}{5}, \frac{6}{7}, \frac{12}{13}, \frac{25}{28}$$

Question 2.
Write any 5 1m proper fractions.
Improper fractions: $$\frac{7}{6}, \frac{26}{22}, \frac{21}{20}, \frac{28}{25}, \frac{13}{12}$$

Question 3.
Write any 5 mixed fractions.
Mixed fractions: $$3 \frac{2}{3}, 7 \frac{1}{2}, 9 \frac{3}{5}, 8 \frac{2}{3}, 6 \frac{5}{7}$$

Question 4.
Convert these fraction into mixed fraction $$\frac{5}{2}, \frac{7}{3}, \frac{9}{4}, \frac{11}{2}$$
Conversion of fraction into mixed fraction.

Question 5.
Convert these fractions into improper fraction $$4 \frac{2}{3}, 5 \frac{3}{4}, 6 \frac{2}{5}, 3 \frac{1}{2}$$.
Conversion of Mixed fractions into improper fractions

$$4 \frac{2}{3}=\frac{3 \times 4+2}{3}=\frac{14}{3}$$ $$5 \frac{3}{4}=\frac{4 \times 5+3}{4}=\frac{23}{4}$$ $$6 \frac{2}{5}=\frac{5 \times 6+2}{5}=\frac{32}{5}$$

$$3 \frac{1}{2}=\frac{2 \times 3+1}{2}=\frac{7}{2}$$.

Do this: (TextBook Page No. 132)

Question 1.
Write any three equivalent fractions to the given fractions.
a) $$\frac{4}{8}$$
b) $$\frac{1}{3}$$
c) $$\frac{3}{7}$$
d) $$\frac{20}{24}$$
a) Equivalent fractions to $$\frac{4}{8}=\frac{8}{16}=\frac{12}{24}=\frac{16}{32}$$
b) Equivalent fractions to $$\frac{1}{3}=\frac{3}{9}=\frac{2}{6}=\frac{4}{12}$$
c) Equivalent fractions to $$\frac{3}{7}=\frac{9}{21}=\frac{6}{14}=\frac{12}{28}$$
d) Equivalent fractions to $$\frac{20}{24}=\frac{40}{48}=\frac{60}{72}=\frac{80}{96}$$

Exercise 1:

Question 1.
Simplify the following fractions. (by cancellation method).
(i) $$\frac{105}{15}$$
(ii) $$\frac{200}{20}$$
(iii) $$\frac{7}{10}$$
(iv) $$\frac{666}{66}$$
(v) $$\frac{125}{1000}$$
(vi) $$\frac{120}{200}$$

Question 2.
Simplify the following fractions. (by H.C.F. method)
(i) $$\frac{12}{18}$$
(ii) $$\frac{14}{35}$$
(iii) $$\frac{22}{55}$$
(iv) $$\frac{27}{36}$$
(v) $$\frac{128}{164}$$
(vi) $$\frac{210}{427}$$
(i) HCF of 12 and 18 is 6.
$$\frac{12 \div 6}{18 \div 6}=\frac{2}{3}$$
So, $$\frac{2}{3}$$ is the simplest form of $$\frac{12}{18}$$.

(ii) HCF of 14 and 35 is 7.
$$\frac{14 \div 7}{35 \div 7}=\frac{2}{5}$$
So, $$\frac{2}{5}$$ is the simplest form of $$\frac{14}{35}$$.

(iii) HCF of 22 and 55 is 11.
$$\frac{22 \div 11}{55 \div 11}=\frac{2}{5}$$
So, $$\frac{2}{5}$$ is the simplest form of $$\frac{22}{55}$$.

(iv) HCF of 27 and 36 is 9.
$$\frac{27 \div 9}{36 \div 9}=\frac{3}{4}$$
So, $$\frac{3}{4}$$ is the simplest form of $$\frac{27}{36}$$.

(v) HCF of 128 and 164 is 4.
$$\frac{128 \div 4}{164 \div 4}=\frac{32}{41}$$
So, $$\frac{32}{41}$$ is the simplest form of $$\frac{128}{164}$$.

(vi) HCF of 210 and 427 is 7.
$$\frac{210 \div 7}{427 \div 7}=\frac{30}{61}$$
So, $$\frac{30}{61}$$ is the simplest form of $$\frac{210}{427}$$.

Question 3.
Convert the following fractions into the simplest form by both the methods.
(i) $$\frac{16}{64}$$
(ii) $$\frac{12}{18}$$
(iii) $$\frac{30}{50}$$
(iv) $$\frac{40}{25}$$
(v) $$\frac{16}{32}$$
(vi) $$\frac{8}{40}$$
(i) 1s tMethod: HCF of 16 and 64 is 4.
$$\frac{16 \div 4}{64 \div 4}=\frac{4}{16}=\frac{1}{4}$$
So, $$\frac{1}{4}$$ is the simplest form of $$\frac{16}{64}$$.

2nd Method =

(ii) 1st Method HCF of 12 and 28 is 4.
$$\frac{12 \div 4}{28 \div 4}=\frac{3}{7}$$,
So $$\frac{3}{5}$$ is simplest form of $$\frac{12}{28}$$ .
2nd Method: =

iii) 1st Method : HCF of 30 and 50 is 10.
$$\frac{30 \div 10}{50 \div 10}=\frac{3}{5}$$
So, $$\frac{3}{5}$$ is simplest form of $$\frac{30}{50}$$
2nd method $$\frac{30}{50}=\frac{3}{5}$$.

(iv) 1st method: HCF of 40 and 25 is 5
$$\frac{40 \div 5}{25 \div 5}=\frac{8}{5}$$
So $$\frac{8}{5}$$ is simplest form of $$\frac{40}{25}$$
2nd method:

(v) 1st method: HCF of 16 and 32 is 16.
$$\frac{16+16}{32+16}=\frac{1}{2}$$,
So $$\frac{1}{2}$$ is the simplest form of $$\frac{16}{32}$$.
2nd method:

vi) 1st method: HCF of 8 and 40 is 8.
$$\frac{8 \div 8}{40 \div 8}=\frac{1}{5}$$,
So $$\frac{1}{5}$$ is simplest form of $$\frac{8}{48}$$.
2nd method:

Question 4.
To get equivalent fractions what should we do a given fraction ?
To get equivalent fractions, we multiply / divide both numerator and denominator by the same number.

Question 5.
Write any three equivalent fractions to the given fractions.
(i) $$\frac{5}{8}$$
(ii) $$\frac{32}{64}$$
(iii) $$\frac{3}{7}$$
(iv) $$\frac{125}{255}$$
(v) $$\frac{7}{10}$$
(i) Equivalent fractions to $$\frac{5}{8}$$ is $$\frac{10}{16}, \frac{15}{24} \text { and } \frac{20}{32}$$
(ii) Equivalent fractions to $$\frac{1}{2}, \frac{2}{4}, \frac{4}{8}, \frac{8}{16}$$
(iii) Equivalent fractions to $$\frac{3}{7}$$ is $$\frac{6}{14}, \frac{9}{21}, \frac{12}{28$$
(iv) Equivalent fractions to $$\frac{125}{255}$$ is $$\frac{5}{9}, \frac{25}{45} \text { and }$$
(v) Equivalent fractions to $$\frac{7}{10}$$ is $$\frac{14}{20}, \frac{21}{30}$$ and $$\frac{35}{50}$$

Question 6.
Govindamma distributed her 4 acrse of land to her 3 sons, then write the part of land each got in the form of a fraction.
Total land = 4 acres
No. of sons = 3
Part of land each got in the form of fraction = $$\frac{4}{3}$$ = 1$$\frac{1}{3}$$.

Do these : (TextBook Page No.137)

Question 1.
Observe the example and write the correct fractions in the other circles.

Question 2.
Find the sum.
(i) $$\frac{2}{10}+\frac{4}{10}$$
(ii) $$\frac{2}{6}+\frac{3}{6}$$
(iii) $$1 \frac{1}{4}+3 \frac{1}{4}$$
(iv) $$2 \frac{1}{5}+3 \frac{1}{5}$$
(i) $$\frac{2}{10}+\frac{4}{10}=\frac{2+4}{10}=\frac{6}{10}$$
(ii) $$\frac{2}{6}+\frac{3}{6}=\frac{2+3}{6}=\frac{5}{6}$$
(iii) $$1 \frac{1}{4}+3 \frac{1}{4}=\frac{5}{4}+\frac{13}{4}=\frac{18}{4}$$
(iv) $$2 \frac{1}{5}+3 \frac{1}{5}=\frac{11}{5}+\frac{16}{5}+\frac{27}{5}$$

Question 3.
$$\frac{1}{2}$$ kg of a sugar packet, $$\frac{3}{6}$$ kg of jaggery are in a bag. Then what is the
total weight of two items in the bag?
Weight of sugar packet = $$\frac{1}{2}$$ kg
Weight ofjaggery packet = $$\frac{3}{6}$$ kg = $$\frac{1}{2}$$ kg
Total weight of two items = $$\frac{1}{2}$$ + $$\frac{3}{6}$$
$$\frac{3}{6}+\frac{3}{6}=\frac{3+3}{6}=\frac{6}{6}$$ = 1.

Question 4.
Sakru paints $$\frac{1}{5}$$ th part of a wall on first day. $$\frac{2}{5}$$ th part of the wall on second day Then how much part lie painted in both the days?
Painting part of wall on first day = $$\frac{1}{5}$$
Painting part of wall on second day = $$\frac{2}{5}$$
Painting part of wall on both the days = $$\frac{1}{5}+\frac{2}{5}=\frac{1+2}{5}=\frac{3}{5}$$

Question 5.
Polamma had some money. She spent $$\frac{3}{6}$$th part of money on books. $$\frac{1}{6}$$ th part of money on pens, pencils and erasers. Then how much part money did she spend ¡n total?
Money spent on books = $$\frac{3}{6}$$th part
Money spent on pens = $$\frac{1}{6}$$th part
pencils and erasers.
Money spent in total = $$\frac{3}{6}+\frac{1}{6}=\frac{3+1}{6}$$ = $$\frac{4}{6}$$th part

Do these: (TextBook Part No. 139)

Question 1.
Complete this.

Question 2.
Find the sum.
(i) $$\frac{1}{5}+\frac{3}{4}$$
(ii) $$\frac{3}{4}+\frac{5}{6}$$
(iii) $$1 \frac{2}{3}+2 \frac{5}{6}$$
(iv) $$3 \frac{1}{8}+2 \frac{5}{6}$$

Question 3.
Seetamma read $$\frac{1}{5}$$ th part of a book on Monday, $$\frac{4}{10}$$ part of the book on Tuesday. Then how much part did she complete on two days ?
Book read on Monday = $$\frac{1}{5}$$ th part
Book read on Tuesday = $$\frac{4}{10}$$ th part
Book read on two days = $$\frac{1}{5}$$ + $$\frac{4}{10}$$
LCM of 5 and 10 is 10.
= $$\frac{1}{5} \times \frac{2}{2}+\frac{4}{10} \times \frac{1}{1}$$
= $$\frac{2}{10}+\frac{4}{10}=\frac{2+4}{10}=\frac{6}{10}$$

Question 4.
Polayya painted a wall of $$\frac{3}{4}$$ th part on 1st day and $$\frac{3}{6}$$ th part of the wall on 2nd day. Then how much part he painted the wall in two days ?
Painted part of wal on 1 st day = $$\frac{1}{5}$$
Painted part of wall on 2nd day = $$\frac{3}{6}$$
Painted part in two days = $$\frac{1}{5}$$ + $$\frac{3}{6}$$
LCM of 5 and 6 is = 30
= $$\frac{1}{5} \times \frac{6}{6}+\frac{3}{6} \times \frac{5}{5}=\frac{21}{30}=\frac{7^{t h}}{10} \text { Part }$$

Try this: (TextBook Part No.139)

Question 1.
Add $$5 \frac{6}{8}+4 \frac{1}{7}$$

Do this: (TextBook Page No.141)

Question 1.
Complete this:

Question 2.
Do the following.
(i) $$\frac{6}{10}-\frac{1}{10}$$
(ii) $$\frac{3}{15}-\frac{1}{15}$$
(iii) $$1 \frac{3}{15}-1 \frac{1}{15}$$
(iv) $$2 \frac{4}{7}-1 \frac{2}{7}$$
(i) $$\frac{6}{10}-\frac{1}{10}$$
= $$\frac{6-1}{10}=\frac{5}{10}$$

(ii) $$\frac{3}{15}-\frac{1}{15}$$
= $$\frac{3-1}{15}-\frac{2}{15}$$

Question 3.
Eswar painted $$\frac{1}{6}$$ th part of a wall on first day. Then how much part will remain to complete?
Painted part ofwal on Sunday = $$\frac{1}{6}$$th part
Total part = 1
Remaining part to complete = $$\frac{1}{1}-\frac{1}{6}$$
LCM of 1 and 6 is 6.
= $$\frac{1}{1} \times \frac{6}{6}-\frac{1}{6} \times \frac{1}{1}=\frac{6}{6}-\frac{1}{6}$$
= $$\frac{6-1}{6}-\frac{5}{6}$$.

Question 4.
Gown completed $$\frac{1}{4}$$ part of her homework on Sunday. $$\frac{5}{12}$$ part on Sunday morning. How much part did she complete? How much part of home work is left?
Work complete on Saturday = $$\frac{1}{4}$$
Work completed on Sunday = $$\frac{5}{12}$$
Work completed both days = $$\frac{1}{4}$$ + $$\frac{5}{12}$$
LCM of 4 and 12 is 12.
= $$\frac{1}{4} \times \frac{3}{3}+\frac{5}{12} \times \frac{1}{1}$$
= $$\frac{3}{12}+\frac{5}{12}=\frac{3+5}{12}=\frac{8}{12}$$
Remainig part left = $$\frac{1}{1}-\frac{8}{12}$$
LCM of 1 and 12 is 12
= $$\frac{1}{1} \times \frac{12}{12}-\frac{8}{12} \times \frac{1}{1}$$
= $$\frac{12}{12}-\frac{8}{12}=\frac{12-8}{12}=\frac{4}{12}=\frac{1}{3} \text { th part }$$

Try these: (TextBook Part No.142)

Question 1.
Complete this:

Exercise 2:

Question 1.
Do the following:
a) $$\frac{3}{4}+\frac{7}{4}$$
b) $$1 \frac{1}{2}$$
c) $$\frac{8}{3}+\frac{2}{5}$$
d) $$\frac{6}{3}+\frac{7}{4}$$
e) $$\frac{3}{5}+\frac{9}{11}$$
f) $$\frac{10}{10}+\frac{5}{20}$$
g) $$\frac{9}{10}+\frac{4}{15}$$
h) $$\frac{5}{20}+\frac{13}{30}$$

Question 2.
Do the following.
a) $$\frac{3}{7}-\frac{1}{7}$$
b) 6 – $$\frac{1}{3}$$
c) $$\frac{3}{8}-\frac{3}{16}$$
d) $$\frac{8}{7}-\frac{5}{8}$$
e) $$\frac{8}{7}-\frac{5}{8}$$
f) $$\frac{13}{15}-\frac{7}{20}$$
g) $$\frac{63}{40}-\frac{9}{10}$$
h) $$\frac{7}{15}-\frac{3}{10}$$
a) $$\frac{3}{7}-\frac{1}{7}$$
= $$\frac{3-1}{7}-\frac{2}{7}$$

Question 3.
Find the difference between 5$$\frac{1}{3}$$ and 2$$\frac{4}{7}$$
$$\frac{15+1}{3}-\frac{14+4}{7}=\frac{16}{3}-\frac{18}{7}$$
LCM of 3 and 7 = 21
$$\frac{16}{3} \times \frac{7}{7}-\frac{18}{7} \times \frac{3}{3}$$
= $$\frac{112}{21}-\frac{54}{21}=\frac{58}{21}$$

Question 4.
Seetha purchased 1$$\frac{1}{2}$$ litre of sunflower oil, $$\frac{3}{4}$$ litre of groundnut oil. How much of oil she purchased in total?
Purchased quantity of sunflower oil = 1$$\frac{1}{2}$$ litr.
Purchased quantity of ground nut oil = $$\frac{3}{4}$$ litr.
Purchased quantity of total oil = 1 $$\frac{1}{2}$$ + $$\frac{3}{4}$$
= $$\frac{3}{2}$$ + $$\frac{3}{4}$$
LCM of 2, 4 is 4
= $$\frac{3}{2} \times \frac{2}{2}+\frac{3}{4} \times \frac{1}{1}$$
= $$\frac{6}{4}+\frac{3}{4}=\frac{6+3}{4}=\frac{9}{4}$$

Question 5.
Vimala purchased 1 $$\frac{3}{4}$$ m of cotton cloth for skirt, $$\frac{3}{4}$$ m of cloth for blouse. How much cloth is purchased by her?
Purchased cloth for skirt = 1 $$\frac{3}{4}$$ m
Purchased cloth for blouse = $$\frac{3}{4}$$ m
Purchased cloth Total = 1$$\frac{3}{4}$$ + $$\frac{3}{4}$$
= $$\frac{7}{4}$$ + $$\frac{3}{4}$$ = $$\frac{10}{4}$$ m.

Question 6.
A water tank is filled with $$\frac{9}{10}$$th part of water, but $$\frac{3}{5}$$ th part of water is consumed in a day. Then find the remaining part of water in the tank?
Total quantity of water infilled in tank = $$\frac{9}{10}$$ th part
Consumed quantity of water is = $$\frac{3}{5}$$ th part
Remaining part of water in the tank = $$\frac{9}{10}-\frac{3}{5}=\frac{9-6}{10}=\frac{3}{10} \text { th part }$$

Do these: (TextBook Page No.145)

Question 1.
Four hundred and eighty five (point) two six seven.

Question 2.
Write the place value of all digits in 293.819
Given numbers = 293.819
place valu e of 2 = 200
place value of 9 = 90
place value of 5 = 5
place value of 8 = $$\frac{1}{80}$$
place value of 1 = $$\frac{1}{900}$$
place value of 9 = $$\frac{9}{1000}$$

Question 3.
Write any 5 examples for decimal fractions.
(i) $$\frac{4756}{100}$$ = 47.56
(ii) $$\frac{87685}{1000}$$ = 87.685
(iii) $$\frac{763407}{1000}$$ = 763.407
(iv) $$\frac{86734}{10000}$$ = 8.6734
(v) $$\frac{96302}{10}$$= 9630.2

Exercise 3:

Question 1.
Fill in the blanks:

a) In improper fraction, numerator is ………………… than the denominator.
greater

b) $$\frac{6}{6}$$ is ………………… fraction (which type?)
improper

c) 3$$\frac{1}{2}$$ is ………………… fraction (which type?)
mixed

d) $$\frac{9}{6}$$ ………………… is fraction (which type?)
improper

e) $$\frac{2}{5}$$ is ………………… fraction (which type?)
proper

f) A function having whole number and proper fraction is called ………………… fraction.
(mixed)

Question 2.
Convert $$\frac{9}{6}$$ into mixed fraction.
Mixed fraction of $$\frac{9}{6}=1 \frac{3}{6}$$.

Question 3.
Convert 2$$\frac{1}{5}$$ into an improper fraction.
Improper fraction of $$2 \frac{1}{5}=\frac{2 \times 5+1}{5}=\frac{11}{5}$$.

Question 4.
Write any 5 equivalent fractions to $$\frac{2}{3}$$.
Equivalent fractions of $$\frac{2}{3}$$ is $$\frac{4}{6}, \frac{6}{9}, \frac{8}{12}, \frac{10}{15}$$ and $$\frac{16}{18}$$.

Question 5.
Write simplest form of fraction for $$\frac{25}{75}$$.
Cancilation method: =
∴ Simplest form of $$\frac{25}{75}$$ is $$\frac{1}{3}$$.

Question 6.
Write two equivalent fractions to $$\frac{64}{36}$$.
Equivalent fractions to $$\frac{64}{36}$$
= $$\frac{64 \div 2}{36 \div 2}=\frac{32}{18}$$
= $$\frac{64 \div 4}{36 \div 4}=\frac{16}{9}$$.

Question 7.
Classify the following as like and unlike frations.
$$\frac{3}{5}, \frac{2}{7}, \frac{8}{5}, \frac{9}{5}, \frac{8}{4}, \frac{1}{5}$$
Like fractions: $$\frac{1}{5}, \frac{3}{5}, \frac{8}{5}, \frac{9}{5}$$
Unlike fractions = $$\frac{2}{7}, \frac{8}{4}$$.

Question 8.
Fill in the blanks.
a) $$\frac{15}{20}=\frac{3}{\square}$$
b) $$\frac{2}{5}=\frac{\square}{50}$$
c) $$\frac{3}{5}=\frac{\square}{30}$$
a) $$\frac{15}{20}=\frac{3}{4}$$
b) $$\frac{2}{5}=\frac{20}{50}$$
c) $$\frac{3}{5}=\frac{18}{30}$$

Question 9.
Fill in the blanks with = or ≠ (≠ denotes not equal to)
a) $$\frac{1}{2}$$ ____ $$\frac{8}{16}$$
b) $$\frac{9}{15}$$ ____ $$\frac{27}{30}$$
c) $$\frac{6}{13}$$ ____ $$\frac{12}{39}$$
a) $$\frac{1}{2}$$ = $$\frac{8}{16}$$
b) $$\frac{9}{15}$$ ≠ $$\frac{27}{30}$$
c) $$\frac{6}{13}$$ ≠ $$\frac{12}{39}$$

Question 10.
Fill in the blanks with equivalent fractions.
a) $$\frac{1}{2}$$ —- $$\frac{8}{16}$$ ____, ____, ____
a) $$\frac{1}{2}$$ —- $$\frac{8}{16} \frac{2}{4}, \frac{3}{6}, \frac{5}{10}$$.

Question 11.
a) $$\frac{6}{5}+\frac{1}{5}$$ = ———-
b) $$\frac{5}{7}+\frac{2}{14}$$ = ———-
c) $$\frac{15}{32}+\frac{3}{8}$$ = ———-
d) $$\frac{11}{16}+1 \frac{1}{8}$$ = ———-

Question 12.
Kavitha studied $$\frac{1}{2}$$ part of a book on 1st day, $$\frac{1}{3}$$ part on 2nd day. then how much part she studied in both the days ?
On I st day completed book part = $$\frac{1}{2}$$
On 2nd day completed book part = $$\frac{1}{3}$$
On both days completed book part = $$\frac{1}{2}$$ + $$\frac{1}{3}$$
LCM of 2 and 3 is 6.
= $$\frac{1}{2} \times \frac{3}{3}+\frac{1}{3} \times \frac{2}{2}$$
= $$\frac{3}{6}+\frac{2}{6}$$
= $$\frac{3+2}{6}=\frac{5}{6}$$.

Question 13.
Koushik went to school km by walk. He went on bicycle with his friend for the remaining distance $$\frac{3}{4}$$ km. Then find the distance to school from his house.
Distance covered by walk = $$\frac{1}{4}$$ km
Distance covered by bicycle = $$\frac{3}{4}$$ km
Total distance to school from his house = $$\frac{1}{4}$$ + $$\frac{3}{4}$$
= $$\frac{1+3}{4}=\frac{4}{4}$$ km

Question 14.
a) $$\frac{8}{10}-\frac{2}{10}$$ = ………………
b) $$\frac{1}{3}-\frac{1}{9}$$ = ………………
c) $$\frac{15}{32}-\frac{3}{8}$$ = ………………
d) $$6 \frac{1}{16}-1 \frac{1}{8}$$ = ………………

Question 15.
$$\frac{2}{3}$$rd nd part of students in a school is boys. Find the part of girls.
Part of boys in a school = $$\frac{2}{3}$$rd
Part of girls inaschool= 1 – $$\frac{2}{3}$$.
= $$\frac{3-2}{3}=\frac{1}{3}$$rd.

Question 16.
Subtract $$\frac{21}{4}$$ from the total of $$\frac{7}{2}$$ and $$\frac{8}{3}$$.
Total of $$\frac{7}{2}$$ and $$\frac{8}{3}$$ = $$\frac{7}{2} \times \frac{3}{3}+\frac{8}{3} \times \frac{2}{2}$$
= $$\frac{21}{6}+\frac{16}{6}=\frac{21+16}{6}=\frac{37}{6}$$
Subtract of $$\frac{37}{6}-\frac{21}{4}$$ =
LCM of 6 and 4 is 12 = $$\frac{37}{6} \times \frac{2}{2}-\frac{21}{4} \times \frac{3}{3}=\frac{74-63}{12}=\frac{11}{12}$$

Question 17.
Govind studied $$\frac{2}{5}$$ th part of a book on 1st day, $$\frac{1}{7}$$ th part on 2nd day. Then how much part is yet to be completed?
Completed part of book on 1st day = $$\frac{2}{5}$$th
Completed part of book on 2nd day = $$\frac{1}{7}$$th
Completed part of book on two days = $$\frac{2}{5}$$ + $$\frac{1}{7}$$
LCM of 5 and 7 is 35.
= $$\frac{2}{5} \times \frac{7}{7}+\frac{1}{7} \times \frac{5}{5}$$
= $$\frac{14}{35}+\frac{5}{35}=\frac{14+5}{35}=\frac{19}{35}$$
remaining part of book yet to be completed = 1 – $$\frac{19}{35}$$
= $$\frac{1 \times 35}{35}-\frac{19}{35} \times \frac{1}{1}$$
= $$\frac{35}{35}-\frac{19}{35}=\frac{35-19}{35}=\frac{14}{35}$$

Question 18.
Write in words 189.257
6 is in $$\frac{1}{100}$$th place.