Question

Which inequality is true?
2/5<7/12
2/3<1/8
1/4>7/10
3/10>5/8

Answer 1

`\sf (2)/(5) < (7)/(12) \: is \: true`

We will cross multiply the fraction and check them!

To compare the fraction we need common denominators.

Let's solve~

#1

`\sf (2)/(5) < (7)/(12) \\ \sf 2 * 12 < 5 * 7 \\ \sf 24 < 35 \\ \tt true`

`\rule{300pt}{3pt}`

#2

`\sf (2)/(3) < (1)/(8) \\ \sf 8 * 2 < 3 * 1 \\ \sf \: 16 < 3 \\ \tt \: false`

`\rule{300pt}{3pt}`

#3

`\sf (1)/(4) > (7)/(10) \\ \sf 10 * 1 > 7 * 4 \\ \sf 10 > 8 \\ \tt \: false`

`\rule{300pt}{3pt}`

#4

`\sf (3)/(10) > (5)/(8) \\ \sf 8 * 3 > 10 * 5 \\ \sf 24 > 50 \\ \tt \: false`