Adding and Subtracting Rational Numbers

Let's check in from Multiplying and Dividing Rational Expressions

Open Ended

Based on yesterday's lesson...what should happen next?

Adding Rational Expressions

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Refresher: Adding and Subtracting Fractions

• Must have common denominators.

• Common denominators are found by determining the LEAST COMMON MULTIPLE between the denominators

• In adding them, only add the numerators.

• In subtracting them, subtract the numerators

• Simplify!

Multiple Select

Check off ALL that are vital to add or subtract fractions?

• Add/Subtract denominators

• Add/Subtract numerators

• Find a common denominator using the Least Common Multiple

• Find a common denominator using the Greatest Common Multiple

Adding Rational Expressions an Example

• Watch the video and take note of how the problem is solved.

Poll

When we add or subtract and rational expression we need...

• common denominators

• LCM between denominators

• to combine only the numerators

• simplify

Multiple Choice

Based on the video, what's the easiest way to find common denominators?

• multiply the two denominators

• multiply the two numerators

Multiple Choice

Based on the video, whatever you multiply the denominator of each rational expression by you multiplied...

• the opposite by

• the numerator by

Multiple Select

Based on the video, Sal should have had...in the numerator.

Correct answer is 8x^3

• 8x^2

• 8x^3

• 8x^4

Open Ended

What do you need to have or do in order to add or subtract rational expressions?

What process do we need to take to add or subtract rational expressions? Let's see!

• We need a common denominator (the LCM between the two)

• We need to make sure that WHATEVER we multiplied the denominator by we MUST multiply the numerator by.

• We ONLY add or subtract the numerators once we have common denominators

Multiple Choice

The denomiator should be the... between the two denominatrs.

• Least Common Numerator

• Least Common Answer

• Least Common Multiple

• Least Common Path

Let's look at a worked example.

Multiple Choice

What is happening in this step?

• Combining like terms/Simplifying if we can.

• Writing both expressions from the numerators in the same numerator.

• Multiplying each numerator by the corresponding denominator.

• Finding the Common Denominator by determine the least common multiple.

Multiple Choice

What's happening in this step?

• Finding the Common Denominator by determine the least common multiple.

• Each numerator has been multiplied by the corresponding denominator.

• Combining like terms/Simplifying if we can.

• Distributing the negative, so we can combine like terms.

Multiple Choice

What should have happened JUST before in this step?

• Writing both expressions from the numerators in the same numerator.

• Finding the Common Denominator by determine the least common multiple.

• Distributing the negative, so we can combine like terms.

• Distributing the negative, so we can combine like terms.

Now you try one!

Practice Problem

Add the given rational expressions/

Write the problem in your notes and try to work it out.

Practice Problem

Here's the solution! How did you do?

Poll

Based on what I've seen I now know about....a little bit better.

• Common Denominators

• Distributing the Negative

• Only Combining the Numerators

• I already knew this! I'm a champ!