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Addition and Subtraction of Rational Numbers

Write the mul...

Question

Write the multiplicative inverse of each of the following rational numbers:
$7$ ; $- 11$ ; $\frac{2}{5}$ ; $\frac{- 7}{15}$

\frac{- 1}{7}; \frac{1}{- 11}; \frac{5}{2}; \frac{15}{- 7}

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\frac{1}{7}; \frac{1}{- 11}; \frac{5}{2}; \frac{15}{- 7}

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\frac{1}{7}; \frac{1}{11}; \frac{5}{2}; \frac{15}{- 7}

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\frac{1}{7}; \frac{1}{- 11}; \frac{- 5}{2}; \frac{15}{- 7}

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Solution

The correct option is B $\frac{1}{7}; \frac{1}{- 11}; \frac{5}{2}; \frac{15}{- 7}$
Multiplicative inverse of $7$ is $\frac{1}{7}$ i.e. $7^{- 1} = \frac{1}{7}$
Multiplicative inverse of $- 11$ is $\frac{1}{- 11}$ i.e. $(- 11)^{- 1} = \frac{1}{- 11}$
Multiplicative inverse of $\frac{2}{5}$ is $\frac{5}{2}$ i.e. ${(\begin{matrix} \frac{2}{5} \end{matrix})}^{- 1} = \frac{5}{2}$
Multiplicative inverse of $\frac{- 7}{15}$ is $\frac{15}{- 7}$ i.e ${(\begin{matrix} \frac{- 7}{15} \end{matrix})}^{- 1} = \frac{15}{- 7}$

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Similar questions

Multiplicative inverse of

1) -7/9

2) 13/15

3) 1/3×4/7

4) -13/11×1/5

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

\frac{2 a}{3} - 1 = \frac{a}{2}; \frac{15 - 4 b}{7} = \frac{2 b - 1}{3}

\frac{4}{9}

\frac{- 13}{7}

\frac{5}{- 11}

\frac{- 11}{- 14}

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

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