Understanding Engineering Mathematics

1.1.3 Highest common factor and lowest common multiple

➤ 828 ➤➤

A.Express in terms of prime factors

(i) 15 (= 3 ×5) (ii) 21 (iii) 60

(iv) 121 (v) 405 (vi) 1024

(vii) 221

B. Find the highest common factor (HCF) of each of the following sets of numbers

(i) 24, 30 (6) (ii) 27, 99 (iii) 28, 98

(iv) 12, 54, 78 (v) 3, 6, 15, 27

C.Find the lowest common multiple (LCM) of each of the following sets of numbers

(i) 3, 7 (21) (ii) 3, 9 (iii) 12, 18

(iv) 3, 5, 9 (v) 2, 4, 6

1.1.4 Manipulation of numbers ➤^1028 ➤➤

Evaluate

(i) 2+ 3 − 7 (=− 2 ) (ii) 4× 3 ÷ 2 (iii) 3+ 2 × 5

(iv) ( 3 + 2 )×5(v)3+( 2 × 5 ) (vi) 18÷ 2 × 3

(vii) 18÷( 2 × 3 ) (viii) − 2 −( 4 − 5 ) (ix) ( 4 ÷(− 2 ))× 3 − 4

(x) ( 3 + 7 )÷ 5 +( 7 − 3 )×( 2 − 4 )

1.1.5 Handling fractions ➤^1228 ➤➤

A.Simplify

(i)

4

6

(

=

2

3

)

(ii)

18

9

(iii)

7

3

×

4

7

(iv)

7

5

×

3

14

(v)

3

4

÷

4

5

(vi)

1

2

+

1

3

(vii)

1

2

−

1

3

(viii)

4

15

−

7

3

(ix) 1+

1

2

+

1

3

(x)

2

3

−

3

4

+

1

8

B.If the numbersaandbare in the ratioa:b=3:2anda=6, what isb?