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:

Do These

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:

Do These

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:

Do These

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:

Do These

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: