What fraction lies between 2/3 and 6/7 on the number line?
a. 3/5
b. 4/8
c. 3/7
d. 5/6

  D.  5/6

Step-by-step explanation:

The given fractions have decimal values of ...

  2/3 ≈ 0.67

  6/7 ≈ 0.86

The answer choices are approximately 0.60, 0.50, 0.43, and 0.83.

The last choice (5/6) is between 2/3 and 6/7.

Using a common denominator of 42, these three fractions are ...

  2/3 = 28/42

  5/6 = 35/42

  6/7 = 36/42

The fraction 5/6 lies between 2/3 and 6/7.

It is useful to memorize the decimal equivalents of fractions with denominators of 10 or less. There are some patterns involved that make it easier.

60: 45 =12: 9 =4: 3 so the answer is 4: 3