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

AP Board 7th Class Maths Solutions Chapter 2 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
\(1 \frac{2}{3}, 2 \frac{3}{5}, 4 \frac{1}{7}, 8 \frac{6}{7}\)

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

Question 2.
Write five equivalent fractions for. i) \(\frac{3}{5}\) ii) \(\frac{4}{7}\) (Page No. 28)
Solution:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 1

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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 \(\frac{8}{3}=\frac{7 \times 8}{3}=\frac{56}{3}=18 \frac{2}{3}\)

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

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:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 2

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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 ÷ \(\frac{8}{9}\) = \(2 \times \frac{9}{8}=\frac{9}{4}\)

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

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:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 3

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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
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 4

ii) 29.75 – 25.97
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 5

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

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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:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 6

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

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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

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

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:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 8

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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:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 9

ii) \(\frac{18}{54}\) and \(\frac{23}{69}\)
Solution:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 10

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

iii) \(\frac{6}{10}\) and \(\frac{600}{1000}\)
Solution:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 11

iv) \(\frac{17}{27}\) and \(\frac{25}{45}\)
Solution”
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 12

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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:
\(\frac{5}{3}=\frac{20}{12}=\frac{10}{6}\)

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

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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.
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 13
Solution:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 14

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.

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

Question 4.
Look at the following table and fill up the blank spaces. (Page No. 44)
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 15
Solution:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 16

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 + \(\frac{7}{10}+\frac{5}{1000}\)

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

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

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

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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:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 17

Question 2.
Represents 2 1/4 pictorially. How many units are needed for this. (Page No. 27)
Solution:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 18
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:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 19

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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:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 20

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

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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) \(\frac{1}{4}\)
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 21
Solution:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 22

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, \(\frac{-9}{6}\)

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

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

c) 4
Left to 4 are less than 4.
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 23

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 \(\frac{-5}{2}\)
∴ \(-27, \frac{-7}{8}, \frac{11}{943}, \frac{54}{17} \frac{-9}{6}, \frac{7}{2}\)

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

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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.
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 24

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.

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

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:
AP Board 7th Class Maths Solutions Chapter 2 Fractions, Decimals and Rational Numbers InText Questions 25