Page 172 - ArithBook5thEd ~ BCC

For the second expression,

a + b = −0.6 + 0.8
=0.2.

This example shows that, in general,
!
2
2
a + b ̸= a + b.

6.1.1 Exercises
Evaluate the expressions for the given values of the variables. Reduce fractions to lowest terms and
express improper fractions as mixed numbers.

1. 2a − b if a =11 and b = −5

2. 2rt if r =5 and t = −6
2
3. −6x 2 if x = −
3
2
4. p − q 2 if p = −2and q =3
5. a − ab − b if a = −0.6 and b =0.8

2
2
6. −x +3y − 8y +5 if x = −2and y =0
2
2
7. (d − e)(d + ed + e ) if d = −1and e = −4
2x + y
8. if x =4 and y = −6
x − 2y
9. 2pq − q 2 if p =1.2 and q =2.3
3a − 2b 1 1
10. if a =1 and b =
5a + b 2 4
2 1
!
2
11. x + y 2 if x = and y = −
3 2
√
2
12. −b + b − 4ac if a = −2, b =7 and c = −3
6.2 Using Formulae

A formula expresses one quantity in terms of others. For example, the formula for the area A of a
rectangle of length l and width w is
A = lw.
If we know the length and width of a rectangle, we can calculate its area, using the formula. For
example, the area of a rectangle of width 17 feet and length 50 feet is

A = lw = (17)(50) = 850 square feet.

Page 172