In Saxon Algebra 1 Lesson 90, Grade 9 students learn to add and subtract rational expressions with both like and unlike denominators. The lesson covers finding the least common multiple to create common denominators, combining numerators, and simplifying results by factoring and canceling common factors, including cases with opposite denominators. Students also apply these skills to real-world problems using the distance formula.
Section 1
📘 Adding and Subtracting Rational Expressions
Adding and subtracting rational expressions follow the same rules as adding and subtracting fractions.
Next, you’ll apply these rules, starting with common denominators and then tackling expressions that require finding the least common multiple to combine them.
Section 2
Adding With Common Denominators
If the denominators are the same, add or subtract the numerators and keep the common denominator. For example, .
Think of it like adding pizza slices! If the slices are the same size (common denominator), you just count up how many you have (the numerators). The slice size doesn't change, so the denominator stays the same. Simple!
Section 3
Example Card: Subtracting Expressions with Common Denominators
Subtracting fractions can sometimes lead to a surprisingly simple whole number—let's see how. This example shows our first key idea: combining rational expressions that already have a common denominator.
Example Problem
Subtract and simplify:
Section 4
Finding a Common Denominator
When denominators are different, find the least common multiple (LCM) and rename each expression to have the same denominator before adding or subtracting.
You can't add fifths and thirds directly! First, you have to find a common ground, like fifteenths. By multiplying the top and bottom by the "missing piece," you make the denominators match so you can finally combine them.
Section 5
Example Card: Subtracting Expressions with Unlike Denominators
What happens when denominators don't match? We just need to build a common ground. This example demonstrates our second key idea: combining expressions with different denominators.
Example Problem
Subtract and simplify:
Section 6
Caution
Not enclosing the numerator of the subtrahend in parentheses may result in sign errors. .
That minus sign is a ninja, trying to attack everything that follows. Parentheses act like a shield, reminding you to distribute the negative sign to every single term inside, flipping all their signs. Don't fall into the trap!
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Section 1
📘 Adding and Subtracting Rational Expressions
Adding and subtracting rational expressions follow the same rules as adding and subtracting fractions.
Next, you’ll apply these rules, starting with common denominators and then tackling expressions that require finding the least common multiple to combine them.
Section 2
Adding With Common Denominators
If the denominators are the same, add or subtract the numerators and keep the common denominator. For example, .
Think of it like adding pizza slices! If the slices are the same size (common denominator), you just count up how many you have (the numerators). The slice size doesn't change, so the denominator stays the same. Simple!
Section 3
Example Card: Subtracting Expressions with Common Denominators
Subtracting fractions can sometimes lead to a surprisingly simple whole number—let's see how. This example shows our first key idea: combining rational expressions that already have a common denominator.
Example Problem
Subtract and simplify:
Section 4
Finding a Common Denominator
When denominators are different, find the least common multiple (LCM) and rename each expression to have the same denominator before adding or subtracting.
You can't add fifths and thirds directly! First, you have to find a common ground, like fifteenths. By multiplying the top and bottom by the "missing piece," you make the denominators match so you can finally combine them.
Section 5
Example Card: Subtracting Expressions with Unlike Denominators
What happens when denominators don't match? We just need to build a common ground. This example demonstrates our second key idea: combining expressions with different denominators.
Example Problem
Subtract and simplify:
Section 6
Caution
Not enclosing the numerator of the subtrahend in parentheses may result in sign errors. .
That minus sign is a ninja, trying to attack everything that follows. Parentheses act like a shield, reminding you to distribute the negative sign to every single term inside, flipping all their signs. Don't fall into the trap!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter