Write the Additive Inverse of 3/13

In mathematics, the additive inverse of a number is the value that, when added to the original number, results in zero. For fractions, finding the additive inverse involves changing the sign of the fraction. Let’s explore this concept further with some examples and explanations.

Additive Inverse of 3/13

Solution:

Original fraction: 3/13

Additive inverse: -3/13

To find the additive inverse, we change the sign of the fraction from positive to negative. So, 3/13 becomes -3/13. When we add 3/13 to its additive inverse (-3/13), we get 0, because 3/13 + (-3/13) equals 0.

In summary, the additive inverse of 3/13 is -3/13.

Real-World Example

Imagine you owe a friend 3/4 of a pizza. The additive inverse of this debt would be -3/4 of a pizza, representing the amount your friend would need to give you to cancel out the debt, resulting in a total of 0 pizzas owed.

In summary, the additive inverse of a fraction is obtained by changing the sign of the fraction. It’s a fundamental concept in mathematics that helps in understanding the relationships between positive and negative numbers.

Example on Additive Inverse

Example 1: Finding the Additive Inverse of 3/5.

Solution:

To find the additive inverse of 3/5, we simply change the sign of the fraction:

Original fraction: 3/5

Additive inverse: -3/5

Explanation: 3/5 + (-3/5) = 0

To find the additive inverse, we change the sign of the fraction from positive to negative. So, 3/5 becomes -3/5. When we add 3/5 to its additive inverse (-3/5), we get 0, because 3/5 + (-3/5) equals 0.

Example 2: Finding the Additive Inverse of -1/3.

Solution:

Original fraction: -1/3

Additive inverse: 1/3

Explanation: -1/3 + 1/3 = 0

Here, the original fraction is already negative (-1/3). To find its additive inverse, we change the sign from negative to positive, so -1/3 becomes 1/3. When we add -1/3 to its additive inverse (1/3), we get 0, because -1/3 + 1/3 equals 0

Example 3: Finding the Additive Inverse of 2/7.

Solution:

Original fraction: 2/7

Additive inverse: -2/7

Explanation: 2/7 + (-2/7) = 0

Similar to example 1, we change the sign of the original fraction from positive to negative. So, 2/7 becomes -2/7. Adding 2/7 to its additive inverse (-2/7) gives us 0, because 2/7 + (-2/7) equals 0.

Example 4: Finding the Additive Inverse of -5/6.

Solution:

Original fraction: -5/6

Additive inverse: 5/6

Explanation: -5/6 + 5/6 = 0

Original fraction is negative (-5/6). To find its additive inverse, we change the sign from negative to positive, making -5/6 become 5/6. Adding -5/6 to its additive inverse (5/6) results in 0, because -5/6 + 5/6 equals 0.