Question

Select the proper order from least to greatest for 2⁄3 , 7⁄6 , 1⁄8 , 9⁄10 . A. 2⁄3 , 9⁄10 , 7⁄6 , 1⁄8 . B. 1⁄8 , 2⁄3 , 9⁄10 , 7⁄6 . C. 7⁄6 , 9⁄10 , 2⁄3 , 1⁄8 . D. 1⁄8 , 9⁄10 , 7⁄6 , 2⁄3 .

Answer 1

$\frac{2}{3}$, $\frac{7}{6}$, $\frac{1}{8}$, $\frac{9}{10}$

Convert the fractions to decimals by using a calculator. This will allow for easier comparing.

$\frac{2}{3}$ ⇒ 0.66
$\frac{7}{6}$ ⇒ 1.166
$\frac{1}{8}$ ⇒ 0.125
$\frac{9}{10}$ ⇒ 0.9

From least to greatest (decimals):
0.125, 0.66, 0.9, 1,116

So now find the fraction they correspond to:
$\frac{1}{8}$, $\frac{2}{3}$, $\frac{9}{10}$, $\frac{7}{6}$

B) 1⁄8, 2⁄3, 9⁄10, 7⁄6 is the correct answer.

Answer 2

To easily compare the fractions, you must make all of the fractions have a common denominator. You can do this by finding the LCM, least common multiple, of the denominators and multiplying each fraction, top and bottom, to equal the common multiple. In this case, the LCM of 8, 3, 10, and 6 is 120.
(1/8)*(15/15) = 15/120
(2/3)*(40/40) = 80/120
(9/10)*(12/12) = 108/120
(7/6)*(20/20) = 140/120
Now that all of the fractions have a common denominator, you can compare the numerators and order the fractions from least to greatest. With this information, the correct answer is B. 1/8, 2/3, 9/10, 7/6.

Hope this helps! :)