Parity (Even/Odd) Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy

Without fully computing, determine the parity (odd or even) of

2{,}345 + 6{,}782

and of

7 \times 14

Solution

1
Parity rules: odd + even = odd. $2{,}345$ is odd (ends in $5$ ); $6{,}782$ is even (ends in $2$ ). Sum: odd.
2
Parity rule for multiplication: odd $\times$ even = even. $7$ is odd; $14$ is even. Product: even.
3
Verify mentally: $2345 + 6782 = 9127$ (odd ✓); $7 \times 14 = 98$ (even ✓).

Answer

2{,}345 + 6{,}782 = 9{,}127

is odd;

7 \times 14 = 98

is even.

Parity (odd/even) is determined by the last digit and follows simple rules: odd + even = odd; even + even = even; odd + odd = even; any number times an even is even; odd