SChand Composite Mathematics Class 7 Chapter 4 Rational Numbers Exercise 4C

 Exercise 4C

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Q1 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 1

(i) $\frac{4}{9} \text{ by } \frac{5}{7}$

Sol :

$=\frac{4}{9} \times \frac{5}{7}=\frac{20}{63}$

(ii) $\frac{-7}{10} \text{ by } \frac{5}{8}$

Sol :

$=\frac{-7}{10} \times \frac{5}{8}=\frac{-7}{16}$

(iii) $\frac{11}{12} \text{ by } \frac{-8}{15}$

Sol :

$=\frac{11}{12} \times \frac{-8}{15}=\frac{-22}{45}$

(iv) $\frac{-9}{13} \text{ by } \frac{65}{-3}$

Sol :

$=\frac{-9}{13} \times \frac{65}{-3}=15$

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Q2 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 2

Multiplying :

(i) $\frac{-9}{16} \text{ by } 60$

Sol :

$=\frac{-9}{16} \times 60=\frac{-135}{4}$

(ii) $\frac{-9}{7} \text{ by } -14$

Sol :

$=\frac{-9}{7}  \times -14 =18$

(iii) $\frac{28}{-9} \text{ by } -27$

Sol :
$=\frac{28}{-9} \times -27=84$

(iv) $-48 \text{ by } \frac{17}{-16}$

Sol :

$=-48 \times \frac{17}{-16}=51$

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Q3 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 3

Simplify and express in standard form :

(i) $\frac{-9}{7} \times \frac{-35}{6}$

Sol :

$=\frac{-3}{1} \times \frac{-5}{2}=\frac{15}{2}$

(ii) $\frac{-115}{28} \times \frac{-49}{69}$

Sol :

$=\frac{-5}{4} \times \frac{-7}{3}=\frac{35}{12}$

(iii) $\frac{-15}{14} \times \frac{112}{-105}$

Sol :

$=\frac{8}{7}$

(iv) $\frac{-39}{3} \times \frac{19}{5} \times \frac{-45}{38}$

Sol :

$=\frac{117}{2}$

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Q4 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 4

(i) $\frac{11}{18} \times (-9) +\frac{-3}{4} \times \frac{5}{6}$

Sol :

$=\frac{-11}{2}-\frac{5}{8}=\frac{-44-5}{8}=\frac{-49}{8}$

(ii) $\left(\frac{26}{9} \times \frac{3}{7}\right)-\left(\frac{13}{14} \times \frac{-2}{3}\right)$

Sol :

$=\frac{26}{21}+\frac{13}{21}=\frac{26+13}{21}=\frac{39}{21}$

(iii) $\left(\frac{-3}{2} \times \frac{4}{5}\right)+\left(\frac{9}{5}\times \frac{10}{3}\right)-\left(\frac{1}{2} \times \frac{3}{4}\right)$

Sol :

$=\frac{-6}{5}+\frac{6}{1}-\frac{3}{8}$

$=\frac{-48+240-15}{40}=\frac{177}{40}=4\frac{17}{40}$

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Q5 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 5

Write the reciprocal of :

(i) $\frac{6}{23}$

Sol :

$=\frac{23}{6}$

(ii) -8

Sol :

$=\frac{1}{-8}$

(iii) $\frac{-10}{21}$

Sol :

$=\frac{-21}{10}$

(iv) $\mid \frac{-4}{5} \mid$

Sol :

$=\frac{4}{5}$

$\frac{5}{4}$

(v) $\frac{2}{3}-\frac{4}{5}$

Sol :

$=\frac{10-12}{15}=\frac{-2}{15}=\frac{15}{-2}$

(v) $\frac{-7}{-8}$

Sol :

$=\frac{7}{8}=\frac{8}{7}$

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Q6 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 6

(i) $1 \text{ by } \frac{1}{8}$

Sol :

$=1 \div \frac{1}{8}=1 \times \frac{8}{1}$

=8

(ii) $8 \text{ by } \frac{-4}{9}$

Sol :

$=8 \div \frac{-4}{9}=8 \times \frac{-9}{4}$

=-18

(iii) $\frac{1}{-4} \text{ by } \frac{1}{12}$

Sol :

$=\frac{1}{-4} \div \frac{1}{12}$

$=\frac{1}{-4} \times  \frac{12}{1}$

=-3

(iv) $\frac{1}{2} \text{ by } \frac{1}{-4}$

Sol :

$=\frac{1}{2} \div \frac{1}{-4}$

$=\frac{1}{2} \times \frac{-4}{1}$

=-2

(v) $\frac{-5}{6} \text{ by } \frac{1}{-2}$

Sol :

$=\frac{-5}{6} \div \frac{1}{-2}$

$=\frac{-5}{6} \times \frac{-2}{1}$

$=\frac{5}{3}$

(vi) $\frac{65}{12} \text{ by } \frac{13}{15}$

Sol :

$=\frac{65}{12} \div \frac{13}{15}$

$=\frac{65}{12} \times \frac{15}{13}$

$=\frac{5}{4} \times \frac{5}{1}=\frac{25}{4}$

(vii) $\frac{50}{77} \text{ by } (-25)$

Sol :

$=\frac{50}{77} \times \frac{1}{-25}=\frac{-2}{77}$

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Q7 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 7

Verify that $(x \div y)^{-1}=x^{-1} \div y^{-1}$ by taking $x=\frac{7}{11}$  , $y=\frac{-22}{21}$ 

Sol :

$\left(\frac{7}{11} \div \frac{-22}{21}\right)^{-1}=\left(\frac{7}{11}\right)^{-1} \div \left(\frac{-22}{21}\right)^{-1}$

$\left(\frac{7}{11} \times \frac{-21}{22}\right)^{-1}=\frac{11}{7} \div \left(\frac{-21}{22}\right)$

$\left(\frac{-147}{242} \right)^{-1}=\frac{11}{7} \times \left(\frac{-22}{21}\right)$

$\frac{-242}{147}=\frac{-242}{147}$

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Q8 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 8

Divide the reciprocal of $\frac{2}{5} \times \frac{-10}{3} \text{ by } \left(\frac{1}{2}-\frac{1}{3}\right)$

Sol :

$=\frac{2}{5} \times \frac{-10}{3}=\frac{-4}{3}$

Reciprocal$=\frac{-3}{4}$

A.T.Q

$=\frac{2}{5} \times \frac{-10}{3} \text{ by } \left(\frac{1}{2}-\frac{1}{3}\right)$

$=\frac{-3}{4} \div \left(\frac{1}{2}-\frac{1}{3}\right)$

$=\frac{-3}{4} \div \left(\frac{1 \times 3-1 \times 2}{6}\right)$

$=\frac{-3}{4} \div \left(\frac{3-2}{6}\right)$

$=\frac{-3}{4} \times \left(\frac{6}{1}\right)$

$=\frac{-3}{4} \times \left(\frac{6}{1}\right)$

$=\frac{-3 \times 3}{2}=\frac{-9}{2}$

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Q9 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 9

The product of two rational numbers is $\frac{-35}{18}$. If one of the numbers is $\frac{5}{12}$ , find the other.

Sol :

Let the other number is x

A.T.Q

$x \times \frac{5}{12}=\frac{-35}{18}$

$x=\frac{-35}{18} \times \frac{12}{5}$

$x=\frac{-7}{9} \times \frac{6}{1}$

$x=\frac{-7}{3} \times \frac{2}{1}=\frac{-7 \times 2}{3}=\frac{-14}{3}$

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Q10 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 10

By what number should $\frac{-55}{18}$ be divided to get $\frac{-22}{9}$ ?

Sol :

Let that number be x

$\frac{-55}{18} \div x=\frac{-22}{9}$

$\frac{-55}{18} \times \frac{1}{x}=\frac{-22}{9}$

$\frac{1}{x}=\frac{-22}{9}\times \frac{-18}{55}$

$\frac{1}{x}=\frac{-2}{1}\times \frac{-2}{5}$

$\frac{1}{x}=\frac{-2 \times -2}{1 \times 5}=\frac{4}{5}$

$x=\frac{5}{4}$

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Q11 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 11

How many pieces of tape $3\frac{4}{7}$ cm long can be cut from a long tape , which is 1 meter 75 cm?

Sol :

[1 meter = 100 cm]

1 meter 75 cm = 100 cm + 75 cm =175 cm

Number of pieces=Total length ÷ small portion

$=175 \div 3\frac{4}{7}$

$=175 \div \frac{3 \times 7+4}{7}$

$=175 \div \frac{25}{7}=175 \times \frac{7}{25}$

=7×7=49 pieces

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Q12 | Ex-4C |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

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Question 12

The cast of $5\frac{1}{3}$ m of cloth is $85\frac{1}{3}$. Find the cost of cloth per meter.

Sol :

$5\frac{1}{3}$ m of cloth is ₹$85\frac{1}{3}$

$\frac{5 \times 3+1}{3}$ m=₹$\frac{85 \times 3+1}{3}$

$\frac{16}{3}m=₹ \frac{256}{3}$

16 m = ₹ 256

$1 m =\frac{256}{16}$

1m=₹ 16