AP State Syllabus AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 2nd Lesson Fractions, Decimals and Rational Numbers InText Questions

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Question 1.
Write five examples, each of proper, improper, mixed fractions. ? (Page No. 27)
Solution:
Proper fractions
$$\frac{1}{5}, \frac{2}{3}, \frac{4}{7}, \frac{3}{8}, \frac{4}{9}$$

Improper fractions
$$\frac{7}{2}, \frac{3}{2}, \frac{9}{4}, \frac{11}{5}, \frac{8}{3}$$

Mixed fractions
$$1 \frac{2}{3}, 2 \frac{3}{5}, 4 \frac{1}{7}, 8 \frac{6}{7}$$

Question 2.
Write five equivalent fractions for. i) $$\frac{3}{5}$$ ii) $$\frac{4}{7}$$ (Page No. 28)
Solution:

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Question 1. (Page No. 31)
i) 4 x $$\frac { 2 }{ 7 }$$
ii) 4 x $$\frac { 3 }{ 5 }$$
iii) 7 x $$\frac { 1 }{ 3 }$$
Solution:
i) 4 x $$\frac{2}{7}=\frac{4 \times 2}{7}=\frac{8}{7}$$
ii) 4 x $$\frac{3}{5}=\frac{4 \times 3}{5}=\frac{12}{5}$$
iii) 7 x $$\frac{1}{3}=\frac{7 \times 1}{3}=\frac{7}{3}$$

Question 2.
Find i) 5 x $$\frac { 3 }{ 2 }$$ =
ii) 4 x $$\frac { 7 }{ 5 }$$ =
iii) 7 x $$\frac { 8 }{ 3 }$$ = (Page No. 31)
Solution:
i) 5 x $$\frac{3}{2}=\frac{5 \times 3}{2}=\frac{15}{2}=7 \frac{1}{2}$$
ii) 4 x $$\frac{7}{5}=\frac{4 \times 7}{5}=\frac{28}{5}=5 \frac{3}{5}$$
iii) 7 x $$\frac{8}{3}=\frac{7 \times 8}{3}=\frac{56}{3}=18 \frac{2}{3}$$

Question 3.
Find the following: (Page No. 32)
i) 3 x 2 $$\frac{2}{7}$$
ii) 5 x 2$$\frac{1}{3}$$
iii) 8 x 4$$\frac{1}{7}$$
iv) 4 x 1$$\frac{2}{9}$$
v) 5 x 1$$\frac{1}{3}$$
Solution:

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Question 1.
Fill in these boxes. (Page No. 35)
i) $$\frac{1}{5} \times \frac{1}{7}=\frac{1 \times 1}{5 \times 7}$$ = ……………
ii) $$\frac{1}{2} \times \frac{1}{6}=\frac{1 \times 1}{2 \times 6}=$$ = …………………
Solution:
i) $$\frac{1}{5} \times \frac{1}{7}=\frac{1 \times 1}{5 \times 7}=\frac{1}{35}$$
ii) $$\frac{1}{2} \times \frac{1}{6}=\frac{1 \times 1}{2 \times 6}=\frac{1}{12}$$

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Question 1.
Find (Page No. 39)
i) 2 ÷ $$\frac{1}{4}$$
ii) 7 ÷ $$\frac{1}{2}$$
iii) 3 ÷ $$\frac{1}{5}$$ (Page No. 39)
Solution:
i) 2 ÷ $$\frac{1}{4}=2 \times \frac{4}{1}=\frac{8}{1}$$ = 8
ii) 7 ÷ $$\frac{1}{2}=7 \times \frac{2}{1}$$ = 14
iii) 3 ÷ $$\frac{1}{5}=3 \times \frac{5}{1}$$ = 15

Question 2.
Find (Page No. 41)
i) 9 ÷ $$\frac{2}{5}$$
ii) 3 ÷ $$\frac{4}{7}$$
iii) 2 ÷ $$\frac{8}{9}$$
Solution:
i) 9 ÷ $$\frac{2}{5}$$ = $$9 \times \frac{5}{2}=\frac{45}{2}$$
ii) 3 ÷ $$\frac{4}{7}$$ = $$3 \times \frac{7}{4}=\frac{21}{4}$$
iii) 2 ÷ $$\frac{8}{9}$$ = $$2 \times \frac{9}{8}=\frac{9}{4}$$

Question 3.
Find (Page No. 41)
i) 7 ÷ 5$$\frac{1}{3}$$
ii) 5 ÷ 2$$\frac{4}{7}$$
Solution:
i) 7 ÷ 5$$\frac{1}{3}$$ = $$7 \div \frac{16}{3}=7 \times \frac{3}{16}=\frac{21}{16}$$
ii) 5 ÷ 2$$\frac{4}{7}$$ = $$5 \div \frac{18}{7}=5 \times \frac{7}{18}=\frac{35}{18}$$

Question 4.
Find (Page No. 42)
i) $$\frac{3}{5} \div \frac{1}{2}$$
ii) $$\frac{1}{2} \div \frac{3}{5}$$
iii) $$2 \frac{1}{2} \div \frac{3}{5}$$
iv) $$5 \frac{1}{6} \div \frac{9}{2}$$
Solution:

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Question
Find (Page No. 45)
i) 0.25 + 5.30
ii) 29.75 – 25.97
Solution:
i) 0.25 + 5.30

ii) 29.75 – 25.97

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Question 1.
Find (Page No. 48)
i) 1.7 x 3
ii)2.0 x 1.5
iii) 2.3 x 4.35
Solution:
i)1.7 x 3 = 5.1
ii) 2.0 x 1.5 = 3.00
iii) 2.3 x 4.35 = 10.005

Question 2.
Arrange the products obtained in (I) In descending order.
Solution:
Arranging above answers in descending order 10.005 > 5.1 > 3.00

Question 3.
Find (Page No. 50)
i) 35.7 ÷ 3
ii) 25.5 ÷ 3
Solution:

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Question 1.
Find the greatest and the smallest numbers among the following groups. (Page No. 52)
i) 2, -2, -3, 4, 0, -5
ii) -3, -7, -8,0,-5,-2
Solution:
i) 2, -2, -3, 4, 0, -5 : greatest number = 4; smallest number = -5
ii) -3, -7, -8, 0, -5, -2: greatest number = 0; smallest number = -8

Question 2.
Write the following numbers In ascending order. (Page No. 52)
i) -5,-75,3,-2,4, $$\frac{3}{2}$$
ii) $$\frac{2}{3}, \frac{3}{2}$$, 0, -1, -2, 5
Solution:
i) -5, -75, 3, -2, 4, $$\frac{3}{2}$$
Ascending order = -75 <-5 <-2 < $$\frac{3}{2}$$ <3 < 4 or -75, -5, -2, $$\frac{3}{2}$$, 3, 4

ii) $$\frac{2}{3}$$,$$\frac{3}{2}$$, 0, -1, -2, 5
Ascending order = -2, -1, 0, $$\frac{2}{3}$$, $$\frac{3}{2}$$, 5

Question 3.
Write 5 equlvalent rational numbers to (i) $$\frac{5}{2}$$ (Page No. 56)
(ii) $$\frac{-7}{8}$$
(iii) $$\frac{-3}{7}$$
Solution:

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Question 1.
Which is bigger $$\frac{5}{8}$$ or $$\frac{3}{5}$$ ? (PageNo.28)
Solution:
$$\frac{5}{8} \times \frac{5}{5}=\frac{25}{40}$$ and $$\frac{3}{5} \times \frac{8}{8}=\frac{24}{40}$$
As $$\frac{24}{40}<\frac{25}{40}$$ $$\frac{5}{8}$$ is bigger than $$\frac{3}{5}$$

Question 2.
Determine if the following pairs are equal by writing each in their simplest form. (Page No. 28)
i) $$\frac{3}{8}$$ and $$\frac{375}{1000}$$
Solution:

ii) $$\frac{18}{54}$$ and $$\frac{23}{69}$$
Solution:

iii) $$\frac{6}{10}$$ and $$\frac{600}{1000}$$
Solution:

iv) $$\frac{17}{27}$$ and $$\frac{25}{45}$$
Solution”

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Question 1.
Identify the equivalent rational number is each question
i) $$\frac{-1}{2}, \frac{-3}{4}, \frac{-2}{4}, \frac{-4}{8}$$
Solution:
$$\frac{-1}{2}=\frac{-2}{4}=\frac{-4}{8}$$

ii) $$\frac{1}{4}, \frac{3}{4}, \frac{5}{3}, \frac{10}{6}, \frac{2}{4}, \frac{20}{12}$$
Solution:
$$\frac{5}{3}=\frac{20}{12}=\frac{10}{6}$$

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Question 1.
You have seen that the product of two natural numbers is one or more than one is bigger than each of the two natural numbers. For example 3 x 4 = 12; 12 > 4 and 12 > 3. What happens to the value of the product when we multiply two proper fractions? (Page No.37)
Fill the following table and conclude your observations.

Solution:

Question 2.
Will the reciprocal of a proper fraction be a proper fraction? (Page No. 40)
Solution:
No. Reciprocal of a proper fraction is always an improper fraction.

Question 3.
Will the reciprocal of an Improper fraction be an Improper fraction?
Solution:
No. The reciprocal of an improper fraction is always a proper fraction.

Question 4.
Look at the following table and fill up the blank spaces. (Page No. 44)

Solution:

Question 5.
WrIte the following numbers in their expanded form. (Page No.44)
i) 30.807
ii) 968.038
iii) 8370. 705
Solution:
i) 30.8O7 = 10 x 3 + 1 x 0 + $$\frac{1}{10}$$ x 8 +$$\frac{1}{100}$$ x 0 + $$\frac{1}{1000}$$ x 7 = 30 + $$\frac{8}{10}+\frac{7}{1000}$$

ii) 968.038 = 100 x 9 + 10 x 6 + 1 x 8 + $$\frac{1}{10}$$ x 0 + $$\frac{1}{100}$$ x 3 + $$\frac{1}{1000}$$ x 8 = 900 + 60 + 8 + $$\frac{3}{100}+\frac{8}{1000}$$

iii) 8370.705 = 1000 x 8 + 100 x 3 + 10 x 7 + $$\frac{1}{10}$$ x 7 + $$\frac{1}{1000}$$ x 5 = 8000 + 300 + 70 + $$\frac{7}{10}+\frac{5}{1000}$$

Question 6.
Take any5 Integers and make all possible rational numbrs with them. (Page No. 54)
Solution:
Consider 2, 3, 4, 5 and 7
Ratlonalnumberare $$\frac{2}{3}, \frac{2}{4}, \frac{2}{5}, \frac{2}{7}, \frac{3}{4}, \frac{3}{5}, \frac{3}{7}, \frac{3}{2}, \frac{4}{2}, \frac{4}{3}, \frac{4}{5}, \frac{4}{7}, \frac{5}{2}, \frac{5}{3}, \frac{5}{4}, \frac{5}{7}, \frac{7}{2}, \frac{7}{3}, \frac{7}{4}, \frac{7}{5}$$

Question 7.
Consider any 5 rational numbers. Find out which itegers constitute them? (Page No.54)
Solution:
Take $$\frac{3}{4}, \frac{5}{8}, \frac{6}{11}, \frac{2}{7}$$ and $$\frac{1}{5}$$.
The integers are 1, 2, 3, 4, 5, 6, 7, 8 and 11.

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Question 1.
Find (i) 50 paise = ₹………….. (ii) 22 g = ………….. kg (iii) 80 cm = ………………m (Page No. 44)
Solution:
(i) 50 paise =₹$$\frac{50}{100}$$ = ₹ 0.5
(ii) 22 g = $$\frac{22}{1000}$$ kg = 0.022 kg
(iii) 80 cm = $$\frac{80}{100}$$ m = 0.8 m

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Question 1.
Represent $$\frac{3}{4}$$ and $$\frac{1}{4}$$ in different ways using different figures. Justify your representation. Share, and check it with your friends. (Page No.27)
Solution:

Question 2.
Represents 2 1/4 pictorially. How many units are needed for this. (Page No. 27)
Solution:

We need 3 units to represent 2½

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Question 1.
Represent pictorially 2 x $$\frac{1}{5}=\frac{2}{5}$$ (Page No. 32)
Solution:

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Question 1.
Find $$\frac{1}{2} \times \frac{1}{5}$$ and $$\frac{1}{5} \times \frac{1}{2}$$ using diagram check whether $$\frac{1}{2} \times \frac{1}{5}=\frac{1}{5} \times \frac{1}{2}$$ (Page No. 35)
Solution:

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Question 1.
Write 5 more fractions between (i) 0 and 1 (ii) 1 and 2. (Page No. 52)
Solution:
i) Fractions between 0 and 1 are $$\frac{1}{7}, \frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7}$$
ii) Fractions between land 2 are $$\frac{8}{7}, \frac{9}{7}, \frac{10}{7}, \frac{11}{7}, \frac{12}{7}, \frac{13}{7}$$

Question 2.
Where does 4$$\frac{3}{5}$$ lie on the number line? (Page No. 52)
Solution:
4$$\frac{3}{5}$$ lies between 4 and 5 on the number line.

Question 3.
On the number line given below represent the following numbei. (Page No.53)
i) $$\frac{-7}{2}$$
ii) $$\frac{3}{2}$$
iii) $$\frac{7}{4}$$
iv) $$\frac{-7}{4}$$
v) $$\frac{-1}{2}$$
vi) $$\frac{1}{4}$$

Solution:

Question 4.
Consider the following numbers on a number line. (Page No. 53)
27, $$\frac{-7}{8}, \frac{11}{943}, \frac{54}{17}$$, -68, -3, $$\frac{-9}{6}, \frac{7}{2}$$
i) Which of these are to the left of a) 0
Solution:
Left to zero are negative numbers
∴ $$\frac{-7}{8}$$, -68, -3, $$\frac{-9}{6}$$

b) -2
Left to – 2 are less than – 2.
∴ -3, -68

c) 4
Left to 4 are less than 4.

d) 2
Left to 2 are less than 2.
∴ $$\frac{-7}{8}, \frac{11}{943}-68,-3, \frac{-9}{6}$$

ii) Which of these would be to the right of
a) 0
Right to zero are positive number.
∴ $$27, \frac{11}{943}, \frac{54}{17}, \frac{7}{2}$$

b) -5
Right to -5 are greater than -5.
$$27, \frac{-7}{8}, \frac{11}{943}, \frac{54}{17}-3, \frac{-9}{6}, \frac{7}{2}$$

c) 3$$\frac{1}{2}$$
Right to 3$$\frac{1}{2}$$ are more than 3$$\frac{1}{2}$$.
∴ 27

d) $$\frac{-5}{2}$$
Right to $$\frac{-5}{2}$$ are more than $$\frac{-5}{2}$$
∴ $$-27, \frac{-7}{8}, \frac{11}{943}, \frac{54}{17} \frac{-9}{6}, \frac{7}{2}$$

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Question 1.
Write three more equivalent fractions of $$\frac{3}{4}$$ and mark them on the number line. What do you observe? (Page No. 55)
Solution:
Equivalent fractions of $$\frac{3}{4}$$ lie on the same mark.

Question 2.
Do all equivalent fractions of $$\frac{6}{7}$$ represent the same point on the number line.
(Page No. 55)
Solution:
Yes.

Question 3.
Are $$\frac{-1}{2}$$ and $$\frac{-3}{6}$$ represent same point on the number line? (Page No. 55)
Solution:
Yes.

Question 4.
Are $$\frac{-2}{3}$$ and $$\frac{-4}{6}$$ equivalent? . (Page No. 55)
Solution:
Yes.

Question 5.
Mark the following rational numbers on the number line. (In Ex 7,3)
(i) $$\frac{1}{2}$$
(ii) $$\frac{3}{4}$$
(iii) $$\frac{3}{2}$$
(iv) $$\frac{10}{3}$$
Solution: