ADDING AND SUBTRACTING POLYNOMIAL FRACTIONSSlideshow 5, Mathematics

Room 307, Mr. Sasaki

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

Multiplying Polynomials by a number

Calculate…

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

Dividing Polynomials by a number

Calculate…

(6 𝑥−4 𝑦 )÷2=3 𝑥−2 𝑦How can we do this?

If we multiply by two, each term is doubled.

So if we divide by two, we should half each term.

Dividing Polynomials by a number

Example

Calculate…

(12 𝑥+24 𝑦 )÷ 6=Here, let’s divide each term by 6.

2 𝑥+4 𝑦Example 2Calculate…

14 𝑦 – 7 𝑧+217

We can just divide each term by 7.

=2 𝑦 – 𝑧+3Try the short worksheet!

Answers

2𝑎+2𝑏2 𝑥 –3 𝑦6 𝑎−2𝑎+2𝑏 –𝑐 /56 𝑥+2 𝑦−46 𝑎+2𝑏

𝑎+2

𝑎 – 2𝑏−4

2 𝑦−3

6 𝑥+5 𝑦 – 3𝑧+2

Adding and Subtracting Fractions

Let’s take a step back from algebra…

Calculate the following…𝟐𝟑

+𝟒𝟓 =

𝟏𝟎𝟏𝟓+¿𝟏𝟐𝟏𝟓=

𝟐𝟐𝟏𝟓or 1

𝟕𝟏𝟓

a.

b.𝟖𝟗−

𝟓𝟏𝟏=

𝟖𝟖𝟗𝟗−

𝟒𝟓𝟗𝟗=

𝟒𝟑𝟗𝟗

Try the worksheet!

Answers

35

56

710

13

37

12

13

512

Polynomial FractionsAdding and subtracting polynomials is very similar. The same basic rules apply.Example

Calculate .2𝑥+52

+9𝑥−43

First we need to make the denominators the same.3(2 𝑥+5)

6+2(9𝑥−4 )

6 =6 𝑥+156

+18 𝑥−86

=6 𝑥+15+18 𝑥−8

6

And then simplify and combine! =

24 𝑥+76

Polynomial FractionsOne more example!

Example

Calculate .7𝑥+64

−9 𝑥−3 𝑦7

7(7 𝑥+6)28

−4 (9 𝑥−3 𝑦 )

28

=49 𝑥+4228

−36 𝑥−12 𝑦

28

=49 𝑥+42−36 𝑥+12 𝑦

28 =13𝑥+42+12 𝑦

28

=Remember to keep your minus!

Try the final worksheet!

Answers5 𝑦+33

11𝑥−86

𝑥−116

17 𝑦−1012

54 𝑥−45−14 𝑦+14 𝑧63

−16 𝑥+12 𝑦−16 𝑧+11915