Basic Engineering Mathematics, Fifth Edition

(Amelia) #1

Fractions 11


(iv) Hence,

3
4


7
16

=

12
16


7
16

=

5
16

− =

Problem 6. Simplify 4

2
3

− 1

1
6

4


2
3

− 1

1
6

is the same as

(
4

2
3

)

(
1

1
6

)
which is the

same as


(
4 +

2
3

)

(
1 +

1
6

)
which is the same as

4 +


2
3

− 1 −

1
6

which is the same as 3+

2
3


1
6

which

is the same as 3+


4
6


1
6

= 3 +

3
6

= 3 +

1
2

Thus, 4


2
3

− 1

1
6

= 3

1
2

Problem 7. Evaluate 7

1
8

− 5

3
7

7

1
8

− 5

3
7

=

(
7 +

1
8

)

(
5 +

3
7

)
= 7 +

1
8

− 5 −

3
7

= 2 +

1
8


3
7

= 2 +

7 × 1 − 8 × 3
56

= 2 +

7 − 24
56

= 2 +

− 17
56

= 2 −

17
56

=

112
56


17
56

=

112 − 17
56

=

95
56

= 1

39
56
Problem 8. Determine the value of

4

5
8

− 3

1
4

+ 1

2
5

4

5
8

− 3

1
4

+ 1

2
5

=( 4 − 3 + 1 )+

(
5
8


1
4

+

2
5

)

= 2 +

5 × 5 − 10 × 1 + 8 × 2
40

= 2 +

25 − 10 + 16
40

= 2 +

31
40

= 2

31
40

Now try the following Practice Exercise

PracticeExercise 5 Introduction to
fractions (answers on page 340)


  1. Change the improper fraction


15
7

into a
mixed number.


  1. Change the improper fraction


37
5

into a
mixed number.


  1. Change the mixed number 2


4
9

into an
improper fraction.


  1. Change the mixed number 8


7
8

into an
improper fraction.


  1. A box contains 165 paper clips. 60 clips
    are removed from the box. Express this as
    a fraction in its simplest form.

  2. Order the followingfractions from the small-
    est to the largest.


4
9

,

5
8

,

3
7

,

1
2

,

3
5


  1. A training college has 375 students of which
    120 are girls. Express this as a fraction in its
    simplest form.
    Evaluate, in fraction form, the expressions given in
    Problems 8 to 20.


8.
1
3

+

2
5

9.

5
6


4
15

10.

1
2

+

2
5

11.

7
16


1
4

12.
2
7

+

3
11

13.

2
9


1
7

+

2
3


  1. 3
    2
    5


− 2

1
3

15.

7
27


2
3

+

5
9


  1. 5
    3
    13


+ 3

3
4


  1. 4


5
8

− 3

2
5


  1. 10


3
7

− 8

2
3


  1. 3


1
4

− 4

4
5

+ 1

5
6


  1. 5


3
4

− 1

2
5

− 3

1
2
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