Arrange the fractions \(\dfrac{6}{7},\ \dfrac{7}{8},\ \dfrac{4}{5},\ \dfrac{3}{4}\) in descending order.
\(\dfrac{7}{8} > \dfrac{6}{7} > \dfrac{4}{5} > \dfrac{3}{4}\)
Find a common denominator.
The denominators are (7, 8, 5, 4). A common multiple is (280).
Change each fraction to a denominator of (280).
(displaystyle rac{6}{7}= rac{6 imes 40}{7 imes 40}= rac{240}{280})
(displaystyle rac{7}{8}= rac{7 imes 35}{8 imes 35}= rac{245}{280})
(displaystyle rac{4}{5}= rac{4 imes 56}{5 imes 56}= rac{224}{280})
(displaystyle rac{3}{4}= rac{3 imes 70}{4 imes 70}= rac{210}{280})
Compare the numerators (bigger numerator means bigger fraction).
(245 > 240 > 224 > 210)
Write the fractions in descending order.
(displaystyle rac{7}{8} > rac{6}{7} > rac{4}{5} > rac{3}{4})
(Quick check with decimals)
( rac{7}{8}=0.875, rac{6}{7}approx0.857, rac{4}{5}=0.8, rac{3}{4}=0.75) — same order.