Page 35 - 新思维数学学生用书9 样章

2 Expressions and formulae

Think like a mathematician

5 Harsha and Sasha simplify the expression 6x ÷ 3x as shown.
5
2

Harsha’s method Sasha’s method
2 6x 5
6x ÷ 3x 2 = 2x 5−2 = 2x 3
5
1 3x 2
6 ÷ 3 = 2 and x ÷ x = x 5−2 = x 3
5
2
So the answer is 2x 3 So the answer is 2x 3

a Critique Harsha’s and Sasha’s methods. Whose method do you prefer?
Why?
Can you think of a better method to use?

b Do you prefer to write a division expression using a division sign (6x ÷ 3x )
2
5
or as a fraction ( 6x 2) ? Why?
5
3x
c Discuss your answers to parts a and b with other learners in your class.
Discuss how you could simplify expressions such as 4x ÷ 6x , 12y ÷ 8y
7
6
3
5
4
9
and 6z ÷ 36z .
For these expressions, would Harsha’s method or Sasha’s method be
easier to use?
6 Simplify each expression.
a 6q ÷ 2q 6 b 9r ÷ 3r 5 c 15t ÷ 5t
9
7
10
d 8u 7 e 2v 6 f 5w 7
4u 2 v 2 w 6
7 Which answer is correct, A, B, C or D?

a Simplify 6x 6 A 2x B 2x C 1 x D 1 x 3
3
2
2
12x 3 2 2
b Simplify 4y 8 A 2 y B 2 y C 2 y D 2 y 4
1
1
4
6
6
10y 2 5 5 2 2
c Simplify 25k 3 A 3 k B 3 k C 5 k D 5 k 15
15
.
.
15k 2 5 5 3 3
d Simplify 20m 6 A 3 m B 3 C 3 m D 3
1
1
6m 6 3 3 10 10

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