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3 years ago

Which fraction is equivalent to 5/12 + 2/3

Mathematics

1 answer:

lesya692 [45]3 years ago

6 0

Answer:

5/12 + 8/12 = 13/12 = 1 1/12

Step-by-step explanation:

This is the answer because:

1) You have to add the fractions, in order to add the fractions you have to find the common denominato.

2) The common denominato is 12 because 2 x 4 = 8 and 3 x 4 = 12. Therefore, 2/3 = 8/12.

3) Finally, once you add 5/12 and 8/12, you should get 13/12 which is also equal to 1 1/12.

Hope this helps! :D

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2 years ago

Find the common fraction equivalent to 0.12

jonny [76]

The answer is: " $\frac{4}{33}$ "  .
______________________________
Given: 0.1212121212..... repeating ; write that value as a fraction;
______________________________________________________
In other words; we are given: "0.1212121212..... repeating infinitely" ;

→ that is to say; "0.12 ... ; {the "12" decimal portion repeats infinitely} ;
_______________________________________________________
→ We write this value, as a fraction, as: "12/99" ;
__________________________________________
→Explanation:
__________________________________________

Note: "0.99999999...... repeating infinitely; = "1" .
_________________________________________
→Since:

Let us say that we have:

"x = 0.999999 ; repeating infinitely;

In order words, let us say we have: "x = 0.9.... ; the "9" decimal repeats infinitely;
_____________________________________________________
Then "10x" ; (that is: "10" multlipled by "x"; or "10*x" or "10x" ); is equal to:

"10" * (0.999999.....) = 9.99999999...... (the "9" decimal repeats infinitely);

in other words: 10x = 9.99999999....

Divide each side by "10" ;

to get "x = 0.9999999....." ; the decimal "9" repeats indefinitely...." ;

But if you have: "10x = 10" ; divide each side of the equation by "10" ;
you get: "x = 1" .
____________________
Also, if "x = 0.9999...(repeating infinitely);

then: 10x = 9.99999.
_______________________________________________
10x = 9.999999999999999......
−   x = 0.999999999999999.......
_____________________________________
9x = 9.00000000000000000000.....

→ 9x = 9 ;

Divide each side of the equation; to get;

9x /9 = 9/ 9 ; to get: x = 1 ; and we have: x = 0.9999.... ; so
x= 0.99999.... = 1 ;
__________________________________________________
So, if the numbers "12" is repeating, we divie "12" by "99" ;
that is; we divide "12" by "two 9's" ; since "12" is a "TWO-digit number"; a "two-digit number" is being repeated infinitely.
________________________________________
So; 0.12121212.....(the "12" is the decimal that repeats infinitely);

= 12/99 ; which can be simplified;

Divide each side (both the numerator AND the denominator); by "3" ;
_________________________________________
" 12/99 " = "(12÷3) / (99÷3) = 4/33 " .
_________________________________________
The answer is: $\frac{4}{33}$   .
_________________________________________

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