7.4a - Rational Addition/Subtraction and LCMs

Section 7.4
Adding and Subtracting Rational Expressions

Adding/Subtracting Fractions

Adding/Subtracting Fractions

Math Response

Evaluate below. Make sure your answer is

fully simplified, and written as an improper fraction

$$\frac{8}{9}+\frac{4}{9}$$

Type answer here

Correct Answer: \frac{4}{3}

Deg^°

Rad

Math Response

Evaluate below. Make sure your answer is

fully simplified, and written as an improper fraction

$$\frac{8}{9}-\frac{4}{9}$$

Type answer here

Correct Answer: \frac{4}{9}

Deg^°

Rad

Math Response

Evaluate below. Make sure your answer is

fully simplified, and written as an improper fraction

$$\frac{5}{6}+\frac{3}{2}$$

Type answer here

Correct Answer: \frac{7}{3}

Deg^°

Rad

If we have "x" in the denominator, we still follow the same steps

Math Response

Evaluate below. Make sure your

answer is fully simplified.

(both sides must be fully factored to simplify)

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

Type answer here

Correct Answer: \frac{5}{2x}

Deg^°

Rad

Math Response

Evaluate below. Make sure your

answer is fully simplified.

(both sides must be fully factored to simplify)

$$\frac{2x}{x+6}-\frac{5}{x+6}$$

Remember: you can't cross out values with +/- between. Only full factors (see your 7.3 simplifying notes for more detail)

Type answer here

Correct Answer: \frac{2x-5}{x+6}

Deg^°

Rad

Multiple Choice

Evaluate below. Make sure your

answer is fully simplified.

(both sides must be fully factored to simplify)

$$\frac{2x}{x-6}-\frac{12}{x-6}$$

Remember: you can't cross out values with +/- between. Only full factors (see your 7.3 simplifying notes for more detail)

YOU MUST STATE EXCLUSIONS!!

• 2, $$x\ne0$$

• 2

• $$\frac{2x-12}{x-6}$$

• 2, $$x\ne6$$

Multiple Definition

A multiple is a value you get, when multiplying two numbers together.
Ex: 20 is a multiple of 10 and 2, but so is 40

The least common multiple (LCM) is the smallest multiple two numbers have in common
Ex: 24 is a common multiple of 4 and 6, but 12 is the LCM because it is the smaller number

Multiple Select

Which of the numbers below are multiples of 16?

• 16

• 8

• 32

• 96

LCM with Polynomials

Multiple Choice

What is $$4x^2-16$$ fully factored?

• It is fully factored

• $$4\left(x-2\right)\left(x+2\right)$$

• $$4\left(x^2-4\right)$$

• $$\left(2x-4\right)\left(2x+4\right)$$

Multiple Choice

What is $$6x^2-24x+24$$ fully factored?

• It is fully factored

• $$6\left(x^2-24x+24\right)$$

• $$6\left(x-2\right)^2$$

• $$\left(x-24\right)\left(x+1\right)$$

Math Response

Check in:

What is the LCM of $$4x^2-16$$ and $$6x^2-24x+24$$ ?

Type answer here

Correct Answer: 12\left(x-2\right)^2\left(x+2\right)

Deg^°

Rad

Try these.
You can also ask your classmates for help.

Multiple Choice

What is the LCM of $$9x^2$$ and $$3x^2+3x$$ ?

Hint: Make sure you factor first.

• $$9x^2\left(3x^2+3x\right)$$

• $$9x^2$$

• $$3x\left(x+1\right)$$

• $$9x^2\left(x+1\right)$$

Math Response

What is the LCM of $$4x^3\left(x-2\right)\left(x+7\right)^2$$ and $$6x\left(x-2\right)^3\left(x+7\right)\left(x-3\right)$$ ?

Hint: It's already factored

Type answer here

Correct Answer: 12x^3\left(x-2\right)^3\left(x+7\right)^2\left(x-3\right)

Deg^°

Rad

Math Response

What is the LCM of $$x^2-25$$ and $$2x^2-20x+50$$ ?

Type answer here

Correct Answer: 2\left(x-5\right)^2\left(x+5\right)

Deg^°

Rad

Try it on your own!

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