Subtracting Rational Numbers by adding the Inverse

Subtracting Rational Numbers by Adding the Inverse

In this text, we're tackling a handy mathematical technique Subtracting Rational Numbers by Adding the Inverse. This method can simplify your calculations and save you time. Don't let the terminology intimidate you — we're going to explore this topic step by step, ensuring you grasp the concept and learn how to apply it effectively.

Subtracting by Adding the Inverse – Explanation

When we talk about subtracting rational numbers by adding the inverse, we're essentially discussing a more efficient way to perform subtraction.

The inverse of a number refers to its additive inverse, which is the number that, when added to the original number, results in zero. For example, the additive inverse of $7$ is $-7$ because $7 + (-7) = 0$.

Subtracting a negative rational number is particularly interesting because you effectively add the opposite of a negative, which is a positive. For instance, subtracting $-3$ is the same as adding $3$. This makes calculations easier because adding is often more straightforward than subtracting, especially when dealing with negatives. You may have been taught that two subtraction or negative signs next to each other in a calculation become a plus sign. This is essentially the same thing just shortened down. Now you know the true maths behind it and how to use additive inverses.

Subtracting Rational Numbers by Adding the Inverse – Example

Let's go through an example to see this process in action.

Subtract $\frac{2}{3}$ from $3$ using the inverse.

• Identify the number to subtract: We want to subtract $\frac{2}{3}$ from $3$.
• Find the inverse: The inverse of $\frac{2}{3}$ is $-\frac{2}{3}$.
• Add the inverse: Perform the addition $3 + (-\frac{2}{3})$.

• Result: $3 + (-\frac{2}{3}) = 2\frac{1}{3}$.

Let’s now take a look at subtracting a negative rational number.

Subtract $-\frac{4}{5}$ from $2$ using the inverse.

• Identify the number to subtract: We want to subtract $-\frac{4}{5}$ from $2$.
• Find the inverse: The inverse of $-\frac{4}{5}$ is $\frac{4}{5}$ because the additive inverse of a negative number is its positive counterpart.
• Add the inverse: Perform the addition $2 + \frac{4}{5}$.

Illustration request: A number line with $2$ on it and then showing a move of $\frac{4}{5}$ to the right, landing at $2\frac{4}{5}$.

• Result: $2 + \frac{4}{5} = 2\frac{4}{5}$.

Subtracting Rational Numbers by Adding the Inverse – Guided Practice

Now, let's do a guided practice together.

If you’re still needing to build more confidence on this topic, it often helps to associate a topic with something we experience in everyday life to help us understand it more. If you think about temperatures and adding and subtracting hot or cold air to a room it might assist you further with understanding this topic. Let’s go through another example to see how thinking about temperature can help us further.

Let’s look at another example to demonstrate this further.

Now apply this to your independent practice!

Subtracting Rational Numbers by Adding the Inverse – Summary

Keep practising this technique, and you'll soon master subtracting rational numbers with ease. Don't forget to check out other interactive practice problems and learning materials on our platform!

Subtracting Rational Numbers by Adding the Inverse – Frequently Asked Questions