Adding and Subtracting Rational Numbers

Presentation

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Mathematics

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9th - 11th Grade

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Hard

James Gonzalez

FREE Resource

7 Slides • 23 Questions

Adding/Subtracting Rational Expressions

Adding and Subtracting Rational Expressions

When we add or subtract rational expressions we need to find a common denominator (if there is not already one given)

Once we have a common denominator...

When adding, combine like terms in the numerator and keep the denominator as is
When subtracting, distribute the negative sign into the numerator of the second fraction and keep the denominator as is

Open Ended

What is the common denominator between these two fractions: $\frac{x}{3}$ and $\frac{x}{x-5}$

Type response here

Multiple Choice

What is the common denominator between these three fractions: $\frac{x}{2},\ \frac{3}{x},\ and\ \frac{6}{x^4}$

$2x^5$

$2x^4$

$2x$

$x^5$

Open Ended

Add: $\frac{3+x}{4}+\frac{7x-9}{4}$

Type response here

Multiple Choice

Subtract: $\frac{6x^2+4x-1}{x-4}-\frac{2x^3+3x^2-2x+5}{x-4}$

$\frac{4x^2-3x^2+6x-6}{\left(x-4\right)^2}$

$\frac{-2x^3+9x^2+2x+4}{x-4}$

$\frac{-2x^3+3x^2+6x-6}{x-4}$

$\frac{x^2+6x-6}{\left(x-4\right)^2}$

Finding equivalent fractions:

When you don't have a common denominator, you have to find one like we did in the first two examples
Then we need to write equivalent fractions for each fraction given
Then we can add or subtract
**Remember** we still need to find the values that make the denominator 0. These values are still where our expression is undefined.

Example: Add

$\frac{3}{x}+\frac{7-x}{4}$

Common denominator: 4x
Multiply the first fraction by $\frac{4}{4}$ and the second fraction by $\frac{x}{x}$
Write the equivalent expression: $\frac{12}{4x}+\frac{x\left(7-x\right)}{4x}$
We can now write this as one fraction: $\frac{12+x\left(7-x\right)}{4x}$
Distribute and combine like terms: $\frac{-x^2+7x+12}{4x}$ $x\ne0$

Example: Subtract

$\frac{3x}{2xy}-\frac{2y}{3y^3}$

Common denominator: $6xy^3$
Multiply the first fraction by $\frac{3y^2}{3y^2}$ and the second fraction by $\frac{2x}{2x}$

Write the equivalent fractions:

\frac{9xy^2}{6xy^3}-\frac{4xy}{6xy^3}

Write as one fraction:

\frac{9xy^2-4xy}{6xy^3}

There are no like terms here, so you cannot combine anything. HOWEVER, you can simplify!

\frac{9y-4}{6y^2},\ y\ne0

(divide ALL terms by xy)

Examples on Jamboard

We are going to do a few examples together on a Jamboard and then we'll come back and answer some questions on here.

Multiple Choice