Topic: 7.52 Adding Rational with different denominators.

Review: Can you find the common denominator of these fractions?

1. 1 + 1 Common Denominator? 3 4

2. 1 - 1 2x 3x

3. 1 + 1 (x + 1) 5

12

6x

5(x + 1)

The rule: Take one of everything you see. If you have more of one item, take the largest.

Lets do some more…

Topic: 7.52 Adding Rational with different denominators.

Please find the common denominator…

1. 2x, 3x, x

2. 5, 8, 2

3. (x + 1), 7, 14

4. (x – 2), (x + 1)

5. 2x2, 4x

6x40

14(x + 1)(x – 2)(x + 1)

4x2 (take the largest “x”)

Topic: 7.52 Adding Rational with different denominators.

Awesome! I can find the common denominator. Now what?

Steps…

1. Draw a line

2. Place a box

3. Fill in the box

4. Distribute and CLT

Topic: 7.52 Adding Rational with different denominators.

Now we’re ready to try some problems…

Write the problem first

3 + 2 (x + 1) (x – 2)

Steps:1. Draw a line2. Place a Box3. Fill a Box4. Distribute and CLT

= (x + 1)(x – 2)

What does “Fill a Box” mean?• Find the LCD• Find what’s missing

(x + 1) =(x + 1)(x – 2)

What’s missing?

(x – 2)

(x – 2) ?(x + 1)3(x – 2) + 2(x + 1)

Topic: 7.52 Adding Rational with different denominators.

Now we’re ready to try some problems…

Write the problem first

Steps:1. Draw a line2. Place a Box3. Fill a Box4. Distribute and CLT

(x + 1)(x – 2)

3(x – 2) + 2(x + 1) =

3x – 6 + 2x + 2

(x + 1)(x – 2)

5x – 4(x + 1)(x – 2)