1. Adding and Subtracting Polynomial Fractions
Slideshow 5, Mathematics
Room 307, Mr. Sasaki

2. Objectives Recall how to multiply a polynomial by a number
Learn how to divide a polynomial by a number
A review on adding and subtracting regular fractions
How to add and subtract polynomial fractions with a numerical denominator

3. Multiplying Polynomials by a number
Calculate…
−4(7𝑥−3𝑦) =
−28𝑥 + 12𝑦
As you know, we multiply the number outside the brackets by each term inside. The minus also affects the terms within the brackets.

4. Dividing Polynomials by a number
Calculate…
(6𝑥−4𝑦)÷2 =
3𝑥−2𝑦
How can we do this?
If we multiply by two, each term is doubled.
So if we divide by two, we should half each term.

5. Dividing Polynomials by a number
Example
Here, let’s divide each term by 6.
Calculate…
(12𝑥+24𝑦)÷ 6 =
2𝑥+4𝑦
Example 2
We can just divide each term by 7.
Calculate…
14𝑦 – 7𝑧 + 21
2𝑦 – 𝑧 + 3 = 7
Try the short worksheet!

6. Adding and Subtracting Polynomial Fractions
Answers
2𝑎 + 2𝑏
𝑎 + 2
2𝑥 – 3𝑦
𝑎/2 + 𝑏/2 +𝑐/2
6𝑎 − 2
𝑎 – 2𝑏 − 4
𝑎 + 2𝑏 – 𝑐/5
6𝑥 + 2𝑦 − 4
2𝑦 − 3
6𝑎 + 2𝑏
6𝑥+5𝑦 –3𝑧 +2

7. Adding and Subtracting Fractions
Adding and Subtracting Polynomial Fractions
Adding and Subtracting Fractions
Let’s take a step back from algebra…
Calculate the following…
𝟐 𝟑 + 𝟒 𝟓
𝟏𝟎 𝟏𝟓
𝟏𝟐 𝟏𝟓
𝟐𝟐 𝟏𝟓
𝟕 𝟏𝟓 a. = =
or 1 +
𝟖 𝟗 − 𝟓 𝟏𝟏
𝟖𝟖 𝟗𝟗
𝟒𝟓 𝟗𝟗
𝟒𝟑 𝟗𝟗 = = b. −
Try the worksheet!

8. Adding and Subtracting Polynomial Fractions
Answers
3 7
3 5
5 6
1 2
1 3
7 10
1 3
5 12

9. Adding and Subtracting Polynomial Fractions
Adding and subtracting polynomials is very similar. The same basic rules apply.
Example
2𝑥 𝑥 −4 3
Calculate
First we need to make the denominators the same.
3(2𝑥+5) (9𝑥 −4) 6
6𝑥 𝑥 −8 6 =
And then simplify and combine!
6𝑥+15+18𝑥 −8 6
24𝑥+7 6 = =

10. Adding and Subtracting Polynomial Fractions
One more example!
Try the final worksheet!
Example
7𝑥+6 4 − 9𝑥 −3𝑦 7
Calculate
7(7𝑥+6) 28 − 4(9𝑥 −3𝑦) 28 =
Remember to keep your minus!
49𝑥 − 36𝑥 −12𝑦 28 =
49𝑥+42 −36𝑥+12𝑦 28
13𝑥+42+12𝑦 28 = =

11. Adding and Subtracting Polynomial Fractions
Answers
5𝑦+3 3
17𝑦−10 12
11𝑥 −8 6
54𝑥 −45 −14𝑦+14𝑧 63
𝑥 −11 6
−16𝑥+12𝑦 −16𝑧