Download presentation

Presentation is loading. Please wait.

Published byGiles Henry Modified over 8 years ago

1
Year 8: Algebraic Fractions Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 11 th June 2013

2
Are these algebraic steps correct? 40 - x 3 FailWin! (Click your answer) = x + 4 40 3 = 2x + 4 2(4 – 2x) = 3x - 2 2(4) = 5x - 2 FailWin! FailWin! Starter

3
Are these algebraic steps correct? FailWin! (Click your answer) Starter

4
Are these algebraic steps correct? (x+3) 2 FailWin! (Click your answer) x 2 + 3 2 (3x) 2 FailWin! 32x232x2 9x 2 Starter

5
To cancel or not to cancel, that is the question? y 2 + x 2 + x s(4 + z) s (2x+1)(x – 2) x – 2 pq(r+2) + 1 pq FailWin! FailWin! FailWin! FailWin! FailWin! 1 + r 2 FailWin! - 1 (Click your answer) Starter

6
What did we learn? Bro Tip #1: You can’t add or subtract a term which is ‘trapped’ inside a bracket, fraction or root.

7
Adding/Subtracting Fractions What’s our usual approach for adding fractions? Sometimes we don’t need to multiply the denominators. We can find the Lowest Common Multiple of the denominators. ? ? ?

8
Adding/Subtracting Algebraic Fractions The same principle can be applied to algebraic fractions. ? ? Bro Tip: Notice that with this one, we didn’t need to times x and x 2 together: x 2 is a multiple of both denominators.

9
Further Examples ? ? ? Bro Tip: Be careful with your negatives!

10
“To learn the secret ways of the ninja, add fractions you must.” ? ? ? ? Test Your Understanding ?

11
1 2 3 4 5 7 8 9 10 11 6 12 13 14 15 16 17 18 19 20 21 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Exercise 1

12
Remember that we can multiply the denominators to find something that is a multiple of both. But the ‘simplest’ thing we can use is the Lowest Common Multiple. Lowest Common Multiple of 3 and 4? 12 Lowest Common Multiple of x and y? xy Lowest Common Multiple of 2x and 3x 2 ? 6x 2 Lowest Common Multiple of x and x+1? x(x+1) ? ? ? ? More Difficult Algebraic Fractions

13
? ? Step 1: Identify the Lowest Common Multiple. Step 2: Whatever we multiplied the denominator by, we have to do the same to the numerator. ?? Example

14
? ? Step 1: Identify the Lowest Common Multiple. Step 2: Whatever we multiplied the denominator by, we have to do the same to the numerator. ?? Example

15
Harder Questions ? ? ? We can do a cross-multiplication type thing just as before.

16
? ?? ? Test Your Understanding ? ? ??

17
1 2 3 4 5 7 8 9 10 11 ? ? ? ? ? ? ? ? ? ? ? 6 Exercise 2 22 ?

18
y22y22 x3x3 ×= xy 2 6 z24z24 x3x3 = 3z 2 4x x+1 3 x+2 4 = 4(x+1) 3(x+2) ?? ? Multiplying and Dividing The same rules apply as with normal fractions. ?

19
Test Your Understanding ( ) = x22x22 4 3x ×= 2x 3 x2y3z5x2y3z5 3 x 6 y 9 z 15 2x+1 3 y+4 5 = 5(2x+1) 3(y+4) ? ? ?

20
1 2 3 4 5 7 8 9 10 11 6 y32y32 xyxy × = xy 2 2 x 2y xyxy × = x 2 2y 2 x+1 x 2 xyxy × = x+1 xy 2x y zqzq = 2qx yz x+1 y z+1 q = q(x+1) y(z+1) q 2 y+1 xqxq = q 3 x(y+1) ( ) xy2xy2 = x2y4x2y4 2 2q 5 z 3 = 4q 10 z 6 2 ( ) 3x y = 9x 2 y 2 2 ( ) 3x 2 y 3 2z 4 = 27x 6 y 9 8z 12 3 ( ) x+1 3y = (x+1) 2 9y 2 2 12 ( ) x+1 3y = (x+1) 2 9y 2 2 ? ? ? ? ? ? ? ? ? ? ? ? 13 14 15 16 18 ? ? ? ? ? 17 ? Exercise 3

21
Head Table 2 3 45 6 7 89 10 11 1213 14 15 Rear Table Head To Head

22
Question 1

23
Question 2

24
Question 3

25
Question 4

26
Question 5

27
Question 6

28
Question 7

29
Question 8

30
Question 9

31
Question 10

32
Question 11

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google