Basic Engineering Mathematics, Fifth Edition

72 Basic Engineering Mathematics

Problem 22. Simplify

5 a+ 3 a× 2 a+a÷ 2 a− 7 a

5 a+ 3 a× 2 a+a÷ 2 a− 7 a

= 5 a+ 3 a× 2 a+

a

2 a

− 7 a (D)

= 5 a+ 3 a× 2 a+

1

2

− 7 a by cancelling

= 5 a+ 6 a^2 +

1

2

− 7 a (M)

=− 2 a+ 6 a^2 +

1

2

(S)

= 6 a^2 − 2 a+

1

2

Problem 23. Simplify

( 4 y+ 3 y) 2 y+y÷ 4 y− 6 y

( 4 y+ 3 y) 2 y+y÷ 4 y− 6 y

= 7 y× 2 y+y÷ 4 y− 6 y (B)

= 7 y× 2 y+

y

4 y

− 6 y (D)

= 7 y× 2 y+

1

4

− 6 y by cancelling

= 14 y^2 +

1

4

− 6 y (M)

Problem 24. Simplify

5 b+ 2 b× 3 b+b÷( 4 b− 7 b)

5 b+ 2 b× 3 b+b÷( 4 b− 7 b)

= 5 b+ 2 b× 3 b+b÷− 3 b (B)

= 5 b+ 2 b× 3 b+

b

− 3 b

(D)

= 5 b+ 2 b× 3 b+

1

− 3

by cancelling

= 5 b+ 2 b× 3 b−

1

3

= 5 b+ 6 b^2 −

1

3

(M)

Problem 25. Simplify

( 5 p+p)( 2 p+ 3 p)÷( 4 p− 5 p)

( 5 p+p)( 2 p+ 3 p)÷( 4 p− 5 p)

=( 6 p)( 5 p)÷(−p)(B)

= 6 p× 5 p÷−p

= 6 p×

5 p

−p

(D)

= 6 p×

5

− 1

by cancelling

= 6 p×− 5

=− 30 p

Now try the following Practice Exercise

PracticeExercise 41 Lawsof precedence

(answers on page 344)

Simplify the following.

1. 3x+ 2 x× 4 x−x


2. ( 2 y+y)× 4 y− 3 y


3. 4b+ 3 b×(b− 6 b)


4. 8a÷ 2 a+ 6 a− 3 a


5. 6x÷( 3 x+x)− 4 x


6. 4t÷( 5 t− 3 t+ 2 t)


7. 3y+ 2 y× 5 y+ 2 y÷ 8 y− 6 y


8. (x+ 2 x) 3 x+ 2 x÷ 6 x− 4 x


9. 5a+ 2 a× 3 a+a÷( 2 a− 9 a)


10. ( 3 t+ 2 t)( 5 t+t)÷(t− 3 t)


11. x÷ 5 x−x+( 2 x− 3 x)x


12. 3a+ 2 a× 5 a+ 4 a÷ 2 a− 6 a