Question

The property under addition used in each of the following are
(i) $\left(\frac{-3}{7}\right)+\frac{1}{9}=\frac{1}{9}+\left(\frac{-3}{7}\right)$
(ii) $\frac{4}{9}+(\frac{7}{8}+\frac{1}{2})=(\frac{4}{9}+\frac{7}{8})+\frac{1}{2}$
(iii) $8+\frac{7}{10}=\frac{7}{10}+8$
(iv) $\left(\frac{-7}{15}\right)+0=\frac{-7}{15}=0+\left(\frac{-7}{15}\right)$
(v) $\frac{2}{5}+\left(\frac{-2}{5}\right)=0$

(i) Commutative
(ii) Associative
(iii) Commutative
(iv) Additive identity
(v) Additive inverse.

• A. True
• B. False

Answer 1

The correct option is A True

1) A binary operation is commutative if changing the order of the operands does not change the result.
$\left(\frac{-3}{7}\right)+\frac{1}{9}=\frac{1}{9}+\left(\frac{-3}{7}\right)$

2) The associative property states that you can add or multiply regardless of how the numbers are grouped.
$\frac{4}{9}+(\frac{7}{8}+\frac{1}{2})=(\frac{4}{9}+\frac{7}{8})+\frac{1}{2}$

3) A binary operation is commutative if changing the order of the operands does not change the result.
$8+\frac{7}{10}=\frac{7}{10}+8$

4) The additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the set, yields x.
$\left(\frac{-7}{15}\right)+0=\frac{-7}{15}=0+\left(\frac{-7}{15}\right)$

5) the additive inverse of a number a is the number that, when added to a, yields zero
$\frac{2}{5}+\left(\frac{-2}{5}\right)=0$