Page 44 - 新思维数学学生用书9 样章

2.5 Simplifying algebraic fractions

4 Here are some algebraic fraction cards.

The red cards are question cards. The blue cards are answer cards.
A 9x − 13x B x + x C 2x + 3x D 11x − 13x
10 20 6 3 7 14 18 36

E 7x − 5x F x + x G x + 3 x
9 18 12 6 30 10

i x ii x
4 2

a Which question cards match answer card i? Show your working.
b Which question cards match answer card ii? Show your working.

c Which question card does not match either of the answer cards?
Work out the answer to this card.

Think like a mathematician

5 Work with a partner to answer this question.
This is part of Su-Lin’s homework. Question
y
x
a Substitute x = 1 and y = 2 into + and Simplify x + y
2
6
work out the answer. 2 6
b Substitute x = 1 and y = 2 into x + y and Answer 3x y
x
y
2
work out the answer. 2 + 6 = 6 + 6
c Use your answers to parts a and b to 3x + y
show that Su-Lin’s answer is incorrect. = 6
d Look back at Su-Lin’s solution and = 1 3 x + y = x + y
explain the mistake she has made. 2 6 2
Write the correct answer.
e Discuss your answers to parts a to d with other learners in your class.

f Use what you have learned to decide if these simplified fractions are
correct or incorrect.
If they are incorrect, work out the correct answer.
i 2x + y = 6x + y = 6x + y
3 9 9 9 9
ii 2x − y = 4x − y = 2 4x − y = 2x − y
5 10 10 10 5 10 5
4
2
iii 11x −= 11x − 14 = 11x − 4
7
14
14
14
2
iv 9x −= 9x − 8 = 9x − 2 8 = 9x − 2
20 5 20 20 5 20 5
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