What are the properties of $R$ used in the following? $8 \times 7 = 7 \times 8$

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Solution

We know that the commutative property of multiplication states that two numbers $a$ and $b$ can be multiplied in either order that is $a \times b = b \times a$

Now, since it is given that $8 \times 7 = 7 \times 8$

Hence, the commutative property of multiplication is used in $8 \times 7 = 7 \times 8$ .

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\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{9}{7} + \frac{- 5}{16}

\frac{5}{7} \times \frac{2}{11} \times \frac{- 8}{7} \times \frac{6}{11}

(\frac{- 3}{7}) + \frac{1}{9} = \frac{1}{9} + (\frac{- 3}{7})

\frac{4}{9} + (\frac{7}{8} + \frac{1}{2}) = (\frac{4}{9} + \frac{7}{8}) + \frac{1}{2}

8 + \frac{7}{10} = \frac{7}{10} + 8

(\frac{- 7}{15}) + 0 = \frac{- 7}{15} = 0 + (\frac{- 7}{15})

\frac{2}{5} + (\frac{- 2}{5}) = 0

(3 + 7) + 8 = 3 + (7 + 8)

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