Maths-
General
Easy

Question

The difference of blank 1 3 over 16 blank and its reciprocal is

  1. 1 fraction numerator 1 over denominator 8 end fraction    
  2. 1 fraction numerator 1 over denominator 3 end fraction    
  3. fraction numerator 15 over denominator 16 end fraction    
  4. none of these    

hintHint:

The reciprocal of any number in mathematics is equal to that number divided by one. The reciprocal of any number "a" is 1/a. The value 1 is obtained by multiplying the given integer by its reciprocal. Example: 1/7 is the reciprocal of the number 7. Here we have given the number blank 1 3 over 16 blankand we have to find the difference in between this number and its reciprocal.

The correct answer is: none of these


    Now as we know that the definition of reciprocal in mathematics is the inverse of a value or a number. If n is a real number, then 1/n will be n's reciprocal. Therefore, we must change the number to its upside-down form. There are other additional definitions as well:
    • Additionally, it is known as the multiplicative inverse.
    • It is comparable to flipping the number on its side.
    • The numerator and denominator can also be switched around to find it.
    • Except for 0, all numbers have a reciprocal.
    Here we have given the term: blank 1 3 over 16 blank
    blank L e t s space s i m p l i f y space t h i s space t e r m comma space w e space g e t colon
1 3 over 16 equals fraction numerator left parenthesis 16 cross times 1 right parenthesis plus 3 over denominator 16 end fraction
equals fraction numerator 16 plus 3 over denominator 16 end fraction equals 19 over 16
N o w space t h e space r e c i p r o c a l space o f space t h i s space n u m b e r space w i l l space b e colon
equals 16 over 19
N o w space w e space h a v e space a s k e d space t h e space d i f f e r e n c e comma space s o space w e space g e t colon
equals 19 over 16 minus 16 over 19
C r o s s space m u l t i p y i n g comma space w e space g e t colon
equals fraction numerator left parenthesis 19 cross times 19 right parenthesis minus left parenthesis 16 cross times 16 right parenthesis over denominator 16 cross times 19 end fraction
equals fraction numerator left parenthesis 361 right parenthesis minus left parenthesis 256 right parenthesis over denominator 304 end fraction
equals 105 over 304

    So here the concept of reciprocals and reciprocating the numbers is used. It is basically comparable to flipping the number on its side. Here we were given the numberblank 1 3 over 16 blankand the difference between this number and its reciprocal is 105/304.

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