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Standard VII

Mathematics

Reciprocal of a Rational Number

Pair the give...

Question

Pair the given rational numbers with their respective multiplicative inverses.

\frac{2}{5}

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- \frac{2}{5}

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\frac{3}{11}

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\frac{1}{11}

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- \frac{5}{2}

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11

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\frac{5}{2}

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\frac{11}{3}

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$Write the reciprocal (multiplicative inverse) of each rational number, given below : (i) 5 (i i) - 3 (i i i) \frac{5}{11} (i v) \frac{- 7}{- 8} (v) \frac{- 7}{- 8} (v i) \frac{15}{- 17}$

Q. Write the following rational numbers according to convention.

(1)

\frac{5}{- 1}

(2)

\frac{- 5}{- 1}

(3)

\frac{2}{- 9}

(4)

\frac{- 2}{- 9}

(5)

\frac{0}{- 4}

(6)

\frac{11}{- 8}

In each of the following determine rational numbers a and b :

(i) $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a - b \sqrt{3}$

(ii) $\frac{4 + \sqrt{2}}{2 + \sqrt{2}} = a - \sqrt{b}$

(iii) $\frac{3 + \sqrt{2}}{3 - \sqrt{2}} = a + b \sqrt{2}$

(iv) $\frac{5 + 3 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

(v) $\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77}$

(vi) $\frac{4 + 3 \sqrt{5}}{4 - 3 \sqrt{5}} = a + b \sqrt{5}$

Write the multiplicative inverse of the following:

(1) $\frac{13}{4}$
(2) $\frac{4}{13}$
(3) $\frac{- 3}{8}$
(4) $\frac{- 8}{3}$
(5) $\frac{- 16}{7}$
(6) $\frac{7}{6}$
(7) 5
(8) −2
(9) 1
(10) 11

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

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