Page 22 - 新思维数学学生用书9 样章

2.1 Substituting into expressions

Worked example 2.1

a Work out the value of the expression 5a − 6b when a = 4

and b = −3.
b Work out the value of the expression 3x − 2y when x = −5
2
3
and y = 2.
q

c Work out the value of the expression p 5 − 4 p   when p = 2


and q = −3.
Answer

a 5a − 6b =×− ×− 3 Substitute a = 4 and b = −3 into Tip
546
the expression. In part a, there
= 20 − − 18 Work out the multiplications first:
5 × 4 = 20 and 6 × −3 = −18. are no brackets
+
= 20 18 Subtracting −18 is the same as and no indices,
= 38 adding 18. so first deal with
2
b 3x − 2y = ×− ( 5) −× 3 Substitute x = −5 and y = 2 into any divisions and
3
2
2 2
3
multiplications
the expression.
=× −× Work out the indices first: and then with any
3252 8
(−5) = −5 × −5 = 25 and additions and
2
3
= 75 16 2 = 2 × 2 × 2 = 8. subtractions.
−
Then work out the multiplications.
3 × 25 = 75 and 2 × 8 = 16.
= 59
Finally work out the subtraction.
q

=
c p 5 − 4 p   ( 4 ×− 3 ) Substitute p = 2 and q = −3 into
2 5 −


2
= ( 6) the expression.
25 − −
Work out the term in brackets
first. Start with the fraction.
4 × −3 = −12; −12 ÷ 2 = −6.
= 2 × ( 5 + 6) Subtracting −6 is the same as
×
= 211 adding 6.
Finally, multiply the value of the
= 22 term in brackets by 2; 2 × 11 = 22.

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