Question

Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 77/... 333

Answer 1

3333 and 4333

Explanation:

To know this, and to convert the fraction 77/...333 into a reducible fraction, we need first to analyze the numerator.

77 has two multiples. These are 7 and 11. This means that this number can only be divided by 7 or 11. You can prove this, bye multiplying 7*11 = 77.

So, the denominator should be a multiple of 7 and 11.

In order to know this,we should divide by 7 and 11 and see if the result is multiple of 7 or 11.

1. 1333/7 = 190.4; 1333/11 = 121.2 They are Not multiples

2. 2333/7 = 333.3; 2333/11 = 212.1 They are Not multiples

3. 3333/7 = 476.1; 3333/11 = 303 Multiple of 11

4. 4333/7 = 619; 4333/11 = 393.9 Multiple of 7

5. 5333/7 = 761.9; 5333/11 = 484.8 They are Not multiples

6. 6333/7 = 904.7; 6333/11 = 575.7 They are Not multiples

7. 7333/7 = 1047.6; 7333/11 = 666.6 They are Not multiples

8. 8333/7 = 1190.4; 8333/11 = 757.5 They are Not multiples

9. 9333/7 = 1333.3; 9333/11 = 848.5 They are Not multiples

Therefore we can conclude that only 3333 and 4333 are the possible cases to turn 77/...333 into a fraction reducible.

Answer 2

Answer: The only two numbers that allow us to make the fraction reducible are 4333 and 3333. (So the digit can be 4 or 3)

Explanation:

77 can be written using prime numbers as:

7*11 = 77

So the only way in which we can make the fraction reducible is if the number ...333 is a multiple of 7 or 11. (so we can write it as 7*something or 11*something)

333 is not a multiple of 7 nor 11.

1333 is not a multiple of 7 nor 11

2333 is not a multiple of 7 nor 11

3333 is a multiple of 11, (11*303 = 3333) then this number can make the fraction reducible.

then 77/3333 = 7/303

4333 is a multiple of 7, (7*619 = 4333) then this number can make the fraction reducible

then 77/4333 = 11/619

5333 is not a multiple of 7 nor 11

6333 is not a multiple of 7 nor 11

7333 = is not a multiple of 7 nor 11

8333 = is not a multiple of 7 nor 11

9333 = is not a multiple of 7 nor 11

The only two numbers that allow us to make the fraction reducible are 4333 and 3333.