Video Transcript
Find the value of one-third plus negative one-third minus 11 over 13 plus 11 over 13 using the properties of addition.
In this question, we are asked to evaluate an expression involving the sum and difference of rational numbers by applying the properties of the addition of rational numbers.
To do this, we first recall that the addition of rational numbers is associative. So we can evaluate the sum in any order that we want. We will evaluate the sum of the first two terms and the last two terms separately since these terms are of the same form.
In fact, we can note that in both cases we are adding a rational number to its negative. We can use the additive inverse property of the addition of rational numbers to recall that 𝑎 plus negative 𝑎 is equal to zero and negative 𝑏 plus 𝑏 is equal to zero for any rational numbers 𝑎 and 𝑏. This gives us zero plus zero. We know that zero is the additive identity, so adding zero will not affect the value. Hence, zero plus zero is just equal to zero.
