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Add the following rational numbers:

(i) \(\frac{-2}{5}\) and \(\frac{4}{5}\)

(ii) \(\frac{-6}{11}\) and \(\frac{-4}{11}\)

(iii) \(\frac{-11}{8}\) and \(\frac{5}{8}\)

(iv) \(\frac{-7}{3}\) and \(\frac{1}{3}\)

(v) \(\frac{5}{6}\) and \(\frac{-1}{6}\)

(vi) \(\frac{-17}{15}\) and \(\frac{-1}{15}\)

1 Answer

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Best answer

(i) \(\frac{-2}{5}+\frac{4}{5}\)

\(\frac{-2+4}{5}\)

\(\frac{2}{5}\)

(ii) \(\frac{-6}{11}+\frac{-4}{11}\)

\(\frac{-6+(-4)}{11}\)

\(\frac{-10}{11}\)

(iii) \(\frac{-11}{8}+\frac{5}{8}\)

\(\frac{-11+5}{8}\)

\(\frac{-6}{8}\)

To convert it into lowest terms, divide both numerator and denominator by common divisor of both 6 and 8 that is, 2

\(\frac{-6÷2}{8÷2}\)

\(\frac{-3}{4}\)

(iv) \(\frac{-7}{3}+\frac{1}{3}\)

\(\frac{-7+1}{3}\)

\(\frac{-6}{3}\)

To convert it into lowest terms, divide both numerator and denominator by common divisor of both 6 and 3 that is, 3.

\(\frac{-6÷3}{3÷3}\)

\(\frac{-2}{1}\)

= 2

(v) \(\frac{5}{6}+ \frac{-1}{6}\)

\(\frac{5+(-1)}{6}\)

\(\frac{5-1}{6}\)

\(\frac{4}{6}\)

To convert it into lowest terms, divide both numerator and denominator by common divisor of both 4 and 6 that is, 2.

\(\frac{4÷2}{6÷2}\)

\(\frac{2}{3}\)

(vi) \(\frac{-17}{15}+\frac{-1}{15}\)

\(\frac{-17+(-1)}{15}\)

\(\frac{-18}{15}\)

To convert it into lowest terms, divide both numerator and denominator by common divisor of both 18 and 15 that is, 3.

\(\frac{-18÷3}{15÷3}\)

\(\frac{-6}{5}\)

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