Question

1. Find :-

$\rm\frac{1}{3} \: + \: \bigg( \frac{ - 4}{5} \bigg) \: + \: \bigg( \frac{- 3}{2} \bigg) \: + \: \frac{6}{7}$


2. Find :-

$\rm\frac{5}{14} \: \times \: \frac{ - 2}{11} \: \times \: \frac{ - 7}{10} \: \times \: \frac{33}{16}$


3. Find :-

$\rm\frac{2}{5} \: \times \: \frac{4}{7} \: - \: \frac{1}{3} \: + \: \frac{4}{7} \: \times \: \frac{8}{5}$


4. Find using distributivity :-

$\rm\bigg( \frac{9}{16} \: \times \: \frac{4}{12} \bigg) \: + \: \bigg( \frac{9}{16} \: \times \: \frac{ - 3}{9} \bigg)$

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Answer 1

Step-by-step explanation:

1)Given that :-

(1/3)+(-4/5)+(-3/2)+(6/7)

LCM of the denominators 3,5,2,7 is 210

=>[(1×70)+(-4×42)+(-3×105)+(6×30)]/210

=>[70+(-168)+(-315)+180]/210

=>(70-168-315+180)/210

=>(250-483)/210

=> - 233/210

(1/3)+(-4/5)+(-3/2)+(6/7) = - 233/210

2)Given that :-

(5/14)×(-2/11)×(-7/10)×(33/16)

=>(5×-2×-7×33)/(14×11×10×16)

=>(10×7×33)/(14×11×10×16)

=>3/(2×16)

=>3/32

(5/14)×(-2/11)×(-7/10)×(33/16) = 3/32

3)Given that :-

(2/5)×(4/7) - (1/3)+(4/7)×(8/5)

=>(4/7)[(2/5)+(8/5)] -(1/3)

(Distributive law)

=>(4/7)(10/5)-(1/3)

=>(4/7)(2)-(1/3)

=>(8/7)-(1/3)

LCM of 7 and 3 = 21

=>[(8×3)-(1×7)]/21

=>(24-7)/21

=>17/21

(2/5)×(4/7) - (1/3)+(4/7)×(8/5) = 17/21

4)

Given that :-

[(9/16)×(4/12]+ [(9/16)×(-3/9)]

=>[(9/16)×(1/3)]+[(9/16)×(-1/3)]

Distributive law

=>(9/16)[(1/3)+(-1/3)]

=>(9/16)[(1-1)/3]

=>(9/16)×(0/3)

=>(9/16)×0

=>(9×0)/16

=>0/16

=>0

[(9/16)×(4/12]+ [(9/16)×(-3/9)] = 0

Used formulae:-

Distributive law:-

If a,b,c are three numbers then a×(b+c)=(a×b)+(a×c) and

(b+c)×a = (b×a)+(c×a) are called Distributive laws