Arrange the following ratios in descending order.
$(5 : 6), (7 : 8), (9 : 10)$

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Solution

$\frac{5}{6}, \frac{7}{8}, \frac{9}{10} l e a s t c o m m o n m u l t i p l e o f 6, 8 a n d 10 i s 120 M u l t i p l y t h e a n y n u m b e r w i t h d e n o m i n a t o r t o g e t a 120 (l c m) t h e n m u l t i p l y t h e s a m e n u m b e r w i t h n u m e r a t o r a l s o \frac{5}{6} = \frac{5 \times 20}{6 \times 20} = \frac{100}{120} \frac{7}{8} = \frac{7 \times 15}{8 \times 15} = \frac{105}{120} \frac{9}{10} = \frac{9 \times 10}{10 \times 12} = \frac{90}{120} \frac{105}{120} > \frac{100}{120} > \frac{90}{120} \frac{7}{8} > \frac{5}{6} > \frac{9}{10}$

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