Page 171 - ArithBook5thEd ~ BCC

Solution. The first expression is evaluated as follows:

a − b − c =(2) − (−11) − (10)
=13 − 10 (left subtraction before right subtraction)

=3.

For the second expression,

" #
a − (b − c)= (2) − (−11) − (10)
=2 − (−21) (subtraction within grouping symbols first)

=23.

3 1 5
Example 212. Evaluate 3 − (p − r ÷ t)if p = , r = − and t = .
4 8 12
Solution. Within grouping symbols, division comes first.

3 1 5
* " # " #+
3 − (p − r ÷ t)= 3 − − − ÷ (changing parentheses to brackets for clarity)
4 8 12
3 1 ✚ 12
* " # " ✚❃ 3 #+
=3 − − − · (division as multiplication by the reciprocal)
4 ✚❃ 2 5
✚ 8
* " #+
3 3
=3 − − −
4 10
* +
3 3
=3 − + (subtraction within grouping symbols first)
4 10
15 6
* +
=3 − + (using the LCD = 20)
20 20
21 60 21 39 19
* +
=3 − = − = = 1 .
20 20 20 20 20
2
3
3x − 5x +13x − 4
Example 213. Evaluate if x =0.
2
x +2
3
2
3(0) − 5(0) +13(0) − 4 −4
Solution. = = −2.
2
0 +2 2
√
2
2
Example 214. Evaluate the expressions a + b and a + b if a = −0.6, and b =0.8.
Solution. For the first expression,
.
!
2
2
2
a + b = (−0.6) +(0.8) 2
√ √
= .36 + .64 = 1= 1.
Page 171