Question

Complete solution. Calculate.

Answer 1

given a)
$- 1\frac{4}{5} - ( -3\frac{7}{10} ) - ( +2 \frac{8}{15})$
solution:
(1stly simplify all mixed fractions into improper fractions.)

= -9/5 - ( -37/10) - (+38/15)

(2ndly, simplify the integers. e.g. two negatives give one positive, etc)

= -9/5 + 37/10 - 38/15

(rearrange such that it's from + to - )

= 37/10 - 38/15 - 9/5

(now, add the absolute forms of all negative integral numbers within a bracket and put a - sign before the opening bracket.)
(ps. absolute value of a number is the number itself without a + or - . eg. |8| = 8. |-8| = 8. notice how both -8 and +8 have 8 as their absolute value.)


= 37/10 - (38/15 + 9/5)

(add within the bracket; BODMAS)

= 37/10 - {(38+9)/(LMC of 15 and 5)}
= 37/10 - 47/15

(subtract)

= (37-47)/(LCM of 10 and 15)
= -10/30

(reduce to the lowest form)

= -3/10 (answer)


now given b)
$( - 1 \frac{4}{21} ) - ( - 2\frac{2}{7} ) - ( + 3\frac{3}{14} )$
(basically apply the BODMAS rule.)
= ( -25/21) - ( -16/7) - (45/14)

(open all brackets)
= -25/21 + 16/7 - 45/14

(rearrange; + to - .)
= 16/7 - 45/14 - 25/21

(add the absolute forms of all negative integral numbers within a bracket and put a - sign before the opening bracket)

= 16/7 - (45/14 + 25/21)

(solve the problem within bracket)
= 16/7 - {(45+25)/(LCM of 14 and 21)}
= 16/7- {70/42}
= 16/7 - 70/42
= (16-70)/ (LCM of 7 and 42)
= -54/42

(reduce to the lowest form)
= -27/21
= -9/7
=
$- 1\frac{2}{7}$

now given c)
$( - \frac{16}{45} ) - ( + \frac{8}{27} ) - ( + \frac{25}{26} ) - ( - \frac{41}{54} )$
= -16/45 - 8/27 - 25/26 + 41/54
= 41/54 - 16/45 - 8/27 - 25/26
= 41/54 - (16/45 + 8/27 + 25/26)
= 41/54 - {(16+8+25)/(LCM of 45,27 and 26)}
= 41/54 - 49/34398
= (41+49)/(LCM of 54 and 34398)
= 90/10314