Year 8 – Algebraic Fractions
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ζ Year 8 – Algebraic Fractions Dr Frost Objectives: Be able to add and subtract algebraic fractions.
description
ζ. Dr Frost. Year 8 – Algebraic Fractions. Objectives: Be able to add and subtract algebraic fractions. Starter. (Click your answer). Are these algebraic steps correct?. 40 - x 3. 40 3. = x + 4. = 2x + 4. . Fail. . Win!. 2(4) = 5x - 2. 2(4 – 2x) = 3x - 2. . Fail. . - PowerPoint PPT Presentation
Transcript of Year 8 – Algebraic Fractions
ζYear 8 – Algebraic FractionsDr Frost
Objectives: Be able to add and subtract algebraic fractions.
Starter
Are these algebraic steps correct?
40 - x3
Fail Win!
(Click your answer)
= x + 4 40 3
= 2x + 4
2(4 – 2x) = 3x - 2 2(4) = 5x - 2
Fail Win!√(2 - x) = 2x + 3 √2 = 3x + 2
Fail Win!
Starter
Are these algebraic steps correct?
(x+3)2
Fail Win!
(Click your answer)
x2 + 32
(3x)2
Fail Win!
32x2 9x2
Starter
To cancel or not to cancel, that is the question?
y2 + x2 + x
s(4 + z)s √(x2 + 2) = y + 2
(2x+1)(x – 2)x – 2
pq(r+2) + 1pq
Fail Win! Fail Win!
Fail Win!
Fail Win!
Fail Win!
1 + r2
Fail Win!
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(Click your answer)
Adding algebraic fractions
23+12=46+36=76
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What’s our usual approach for adding fractions?
The same principle can be applied to algebraic fractions.
1𝑥
+2
𝑥2=𝑥𝑥2
+2
𝑥2=𝑥+2𝑥2
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The Wall of Algebraic Fraction Destiny
“To learn the secret ways of the ninja, simplify fraction you must.”
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Exercises
1
2
3
4
5
7
8
9
10
11
6
12
13
14
15
16
17
18
19
20
21
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More Difficult Algebraic Fractions
For most of the examples so far, we’ve considered numerators that don’t contain variables. But when we have variables, the principle is the same!
Lowest Common
Multiple of 3 and 4?
12
Lowest Common
Multiple of x and y?
xy
Lowest Common
Multiple of 2x and 3x2?
6x2
Lowest Common
Multiple of x and x+1?
x(x+1)
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Example
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Step 1: Identify the Lowest Common Multiple.
Step 2: Whatever we multiplied the denominator by, we have to do the same to the numerator.
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Example
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Step 1: Identify the Lowest Common Multiple.
Step 2: Whatever we multiplied the denominator by, we have to do the same to the numerator.
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Examples
2𝑥
+ 3𝑥+1
=2 (𝑥+1 )+3 𝑥 𝑥(𝑥+1)
= 5 𝑥+2𝑥(𝑥+1)
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𝑥+1𝑥−
𝑥𝑥+1
=(𝑥+1 )2−𝑥2
𝑥 (𝑥+1 )= 2 𝑥+1𝑥 (𝑥+1 )
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𝑥−34
+ 𝑥−53
=3 (𝑥−3 )+4 (𝑥−5 )
12=7𝑥−29
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Exercises
1
2
3
4
5
7
8
9
10
11
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( ) =
Multiplying and Dividing Brackets
y2
2x3
× = xy2
6z2
4x3
= 3z2
4x
x3
22 x6
4x+1
3x+2
4 = 4(x+1)
3(x+2)
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Exercises
1
2
3
4
5
7
8
9
10
11
6
y3
2xy× = xy2
2
x2y
xy× = x2
2y2
x+1x2
xy× = x+1
xy
2xy
zq
= 2qxyz
x+1y
z+1q
= q(x+1)y(z+1)
q2
y+1xq
= q3
x(y+1)
( )xy2
= x2
y4
2
( )2q5
z3= 4q10
z6
2
( )3xy
= 9x2
y2
2
( )3x2y3
2z4= 27x6y9
8z12
3
( )x+13y
= (x+1)2
9y2
2
12
( )x+13y
= (x+1)2
9y2
2
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13
14
15
16
18
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Head to Head
vs
Head Table
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3
4 5
6
7
8 9
10
11
12 13
14
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Rear Table
Question 1
1
𝑥2+2
𝑥2
Answer:
Question 2
𝑥2
+𝑥4
Answer:
Question 3
23+𝑥+19
Answer:
Question 4
𝑥𝑦
+𝑥+1𝑦 2
Answer:
Question 5
1𝑥
+𝑥𝑦
Answer:
Question 6
1𝑧
+1
𝑧+2
Answer:
Question 7
1𝑥
+1𝑦
+1𝑧
Answer:
Question 8
1𝑥÷3
Answer:
Question 9
2÷1
𝑥2
Answer:
Question 10
1𝑥÷1
𝑥2 𝑦
Answer:
Question 11
( 𝑥𝑦 3 )2
Answer:
