RD Sharma Solutions Class 7 Operations On Rational Numbers Exercise 5.3

RD Sharma Class 7 Solutions Chapter 5 Ex 5.3 PDF Free Download

RD Sharma Solutions Class 7 Chapter 5 Exercise 5.3

Exercise 5.3

Q1. Multiply:

(i) \(\frac{7}{11}\;\;by\;\;\frac{5}{4}\)

\(\frac{7}{11}\times\frac{5}{4}\\ =\frac{35}{44}\)

 (ii) \(\frac{5}{7}\;\;by\;\;\frac{-3}{4}\)

\(\frac{5}{7}\times\frac{-3}{4}\\ =\frac{-15}{28}\)

(iii) \(\frac{-2}{9}\;\;by\;\;\frac{5}{11}\)

\(\frac{-2}{9}\times\frac{5}{11}\\ =\frac{-10}{99}\)

(iv) \(\frac{-3}{17}\;\;by\;\;\frac{-5}{-4}\)

\(\frac{-3}{17}\times\frac{-5}{-4}\\ =\frac{15}{-68}\\ =\frac{-15}{68}\)

Q2. Multiply:

(i) \(\frac{-5}{17}\;\;by\;\;\frac{51}{-60}\)

\(\frac{-5}{17}\times\frac{51}{-60}\\ =\frac{-255}{-1020}\\ =\frac{255}{1020}\\ =\frac{1}{4}\\\)

(ii) \(\frac{-6}{11}\;\;by\;\;\frac{-55}{36}\)

\(\frac{-5}{17}\times\frac{51}{-60}\\ =\frac{-255}{-1020}\\ =\frac{255}{1020}\\ =\frac{1}{4}\\\)

(iii) \(\frac{-8}{25}\;\;by\;\;\frac{-5}{16}\)

\(\frac{-8}{25}\times\frac{-5}{16}\\ =\frac{40}{400}\\ =\frac{1}{10}\\\)

(iv) \(\frac{6}{7}\;\;by\;\;\frac{-49}{36}\)

\(\frac{6}{7}\times\frac{-49}{36}\\ =\frac{-7}{6}\\\)

Q3. Simplify each of the following and express the result as a rational number in standard form:

(i) \(\frac{-16}{21}\times\frac{14}{5}\)

\(\frac{-16}{21}\times\frac{14}{5}\\ =\frac{-224}{105}\\ =\frac{-32}{15}\)

(ii) \(\frac{7}{6}\times\frac{-3}{28}\)

\(\frac{7}{6}\times\frac{-3}{28}\\ =\frac{-1}{8}\)

(iii) \(\frac{-19}{36}\times16\)

\(\frac{-19}{36}\times16\\ =\frac{-304}{36}\\ =\frac{-76}{9}\\\)

(iv) \(\frac{-13}{9}\times\frac{27}{-26}\)

\(\frac{-13}{9}\times\frac{27}{-26}\\ =\frac{3}{2}\\\)

Q4. Simplify:

(i) \(\left(-5\times\frac{2}{15} \right )-\left(-6\times\frac{2}{9} \right )\)

\((-5\times\frac{2}{15})-(-6\times\frac{2}{9})\\ =\frac{-10}{15}-(\frac{-12}{9})\\ =\frac{-10\times3}{15\times3}-(\frac{-12\times5}{9\times5})\\ =\frac{-30}{45}-(\frac{-60}{45})\\ =\frac{-30+60}{45})\\ =\frac{30}{45})\\ =\frac{2}{3})\\\)

(ii) \(\left(\frac{-9}{4}\times\frac{5}{3} \right )+\left(\frac{13}{2}\times\frac{5}{6} \right )\)

\(\left(\frac{-9}{4}\times\frac{5}{3} \right )+\left(\frac{13}{2}\times\frac{5}{6} \right )\\ =\left(\frac{-3}{4}\times5 \right )+\left(\frac{65}{12} \right )\\ =\left(\frac{-15}{4} \right )+\left(\frac{65}{12} \right )\\ =\frac{-15\times3}{4\times3}+\frac{65}{12}\\ =\frac{-45}{12}+\frac{65}{12}\\ =\frac{-45+65}{12}\\ =\frac{20}{12}\\ =\frac{10}{6}\\ =\frac{5}{3}\\\)

Q5. Simplify:

(i) \(\left(\frac{13}{9}\times\frac{-15}{2} \right )+\left(\frac{7}{3}\times\frac{8}{5} \right ) -\left(\frac{3}{5}\times\frac{1}{2} \right ) \)

\(\left(\frac{13}{9}\times\frac{-15}{2} \right )+\left(\frac{7}{3}\times\frac{8}{5} \right ) +\left(\frac{3}{5}\times\frac{1}{2} \right ) \\ =\left(\frac{13}{3}\times\frac{-5}{2} \right )+\left(\frac{56}{15} \right ) +\left(\frac{3}{10} \right ) \\ =\left(\frac{-65}{6} \right )+\left(\frac{56}{15} \right ) +\left(\frac{3}{10} \right ) \\ =\left(\frac{-65\times5}{6\times5} \right )+\left(\frac{56\times2}{15\times2} \right ) +\left(\frac{3\times3}{10\times3} \right ) \\ =\left(\frac{-325}{30} \right )+\left(\frac{112}{30} \right ) +\left(\frac{9}{30} \right ) \\ =\left(\frac{-325}{30} \right )+\left(\frac{112}{30} \right ) +\left(\frac{9}{30} \right ) \\ =\left(\frac{-204}{30} \right )\\ =\left(\frac{-34}{5} \right )\\\)

(ii) \(\left(\frac{3}{11}\times\frac{5}{6} \right )-\left(\frac{9}{12}\times\frac{4}{3} \right ) +\left(\frac{5}{13}\times\frac{6}{15} \right )\)

\(\left(\frac{3}{11}\times\frac{5}{6} \right )-\left(\frac{9}{12}\times\frac{4}{3} \right ) +\left(\frac{5}{13}\times\frac{6}{15} \right )\\ =\left(\frac{1}{11}\times\frac{5}{2} \right )-\left(\frac{3}{3}\times\frac{1}{1} \right ) +\left(\frac{1}{13}\times\frac{6}{3} \right )\\ =\left(\frac{1}{11}\times\frac{5}{2} \right )-\left(\frac{3}{3}\times\frac{1}{1} \right ) +\left(\frac{1}{13}\times\frac{2}{1} \right )\\ =\left(\frac{5}{22} \right )-\left(1 \right ) +\left(\frac{2}{13} \right )\\ =\left(\frac{5\times13}{22\times13} \right )-\left(\frac{1\times286}{1\times286}\right )+\left(\frac{2\times22}{13\times22} \right )\\ =\left(\frac{65}{286} \right )-\left(\frac{286}{286} \right ) +\left(\frac{44}{286} \right )\\ =\left(\frac{65-286+44}{286} \right )\\ =\left(\frac{-177}{286} \right )\\\)

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