72 Basic Engineering Mathematics
Problem 22. Simplify
5a + 3a × 2a + a ÷ 2a − 7a
5a + 3a × 2a + a ÷ 2a − 7a
= 5a + 3a × 2a +
a
2a
− 7a
(D)
= 5a + 3a × 2a +
1
2
− 7a
by cancelling
= 5a + 6a
2
+
1
2
− 7a
(M)
= −2a + 6a 2 +
1
2
(S)
= 6a 2 − 2a +
1
2
Problem 23. Simplify
(4y + 3y)2y + y ÷ 4y − 6y
(4y + 3y)2y + y ÷ 4y − 6y
= 7y × 2y + y ÷ 4y − 6y
(B)
= 7y × 2y +
y
4y
− 6y
(D)
= 7y × 2y +
1
4
− 6y
by cancelling
= 14y
2
+
1
4
− 6y
(M)
Problem 24. Simplify
5b + 2b × 3b + b ÷ (4b − 7b)
5b + 2b × 3b + b ÷ (4b − 7b)
= 5b + 2b × 3b + b ÷ −3b
(B)
= 5b + 2b × 3b +
b
−3b
(D)
= 5b + 2b × 3b +
1
−3
by cancelling
= 5b + 2b × 3b −
1
3
= 5b + 6b
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
= −30p
Now try the following Practice Exercise
Practice Exercise 41 Laws of precedence
(answers on page 344)
Simplify the following.
1. 3x + 2x × 4x − x
2. (2y + y) × 4y − 3y
3. 4b + 3b × (b − 6b)
4. 8a ÷ 2a + 6a − 3a
5. 6x ÷ (3x + x) − 4x
6. 4t ÷ (5t − 3t + 2t )
7. 3y + 2y × 5y + 2y ÷ 8y − 6y
8. (x + 2x)3x + 2x ÷ 6x − 4x
9. 5a + 2a × 3a + a ÷ (2a − 9a)
10. (3t + 2t )(5t + t ) ÷ (t − 3t )
11. x ÷ 5x − x + (2x − 3x)x
12. 3a + 2a × 5a + 4a ÷ 2a − 6a