Question

Maria claims that any fraction located between 1/5 and 1/7 on a number line must have a denominator of 6.

Enter a fraction to show Maria's claim is incorrect.

Answer 1

13/70

Explanation:

In order to show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line, but does not have a denominator of 6.

Let's find the common multiple (CM) of 5 and 7, which is 70, or 35. But this case try 70 and then find a fraction with a denominator of 70 that falls between 1/5 and 1/7.

equivalent fractions of 1/5 and 1/7 with a denominator of 70
1/7 < x < 1/5 , will be equivalent to 1/7 ( 10/10 ) < x < 1/5 ( (14/14)
10/70 < x < 14/70..
x is the fraction between 10/70 and 14 /70. Unknown fraction is:

13/70

This fraction is located between 10/70 and 14/70 on the number line, but its denominator is 70 , not 6. Therefore, Maria's claim is incorrect.

Answer 2

To show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line but does not have a denominator of 6.

One way to do this is to find the least common multiple (LCM) of 5 and 7, which is 35, and then find a fraction with a denominator of 35 that falls between 1/5 and 1/7.

To do this, we can find the equivalent fractions of 1/5 and 1/7 with a denominator of 35:

1/5 = 7/35

1/7 = 5/35

Now we need to find a fraction between 7/35 and 5/35. One such fraction is:

6/35

This fraction is located between 7/35 and 5/35 on the number line, but its denominator is 35, not 6. Therefore, Maria's claim is incorrect.

Another way to show that Maria's claim is incorrect is to find a counterexample by simply listing all the fractions between 1/5 and 1/7 and showing that not all of them have a denominator of 6. For example:

1/6, 1/7, 1/8, 1/9, 1/10, ..., 1/34, 1/35

As we can see, not all of these fractions have a denominator of 6, so Maria's claim is incorrect.