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Complete the addition-subtraction box...

Complete the addition-subtraction box

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Discuss the commutativity of the binary operation * on R defined by a * b=a-b+a b for all a , b in R , where on RHS we have usual addition, subtraction and multiplication of real numbers.

Show that addition, subtraction and multiplication are binary operations on R, but division is not a binary operation on R. Further, show that division is a binary operation on the set R of nonzero real numbers.

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We have learnt about fractions and decimals alongwith the operations of addition and subtraction on them, in the earlier class

Make up as many expressions with numbers (no variables) as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.