Question

2 5/8 2 5/6 2 3/4 2 4/7 greatest to least

Answer 1

`2 (5)/(6)<2 (3)/(4)<2 (5)/(8)<2 (4)/(7)`

Explanation:

Step 1: The given numbers are
`2 (5)/(6)<2 (3)/(4)<2 (5)/(8)<2 (4)/(7)`

Step 2: Let us first convert the mixed fraction into whole numbers.

`2 (5)/(8)=((2 * 8)+5)/(8)=(21)/(8)`,
`2 (5)/(6)=((2 * 6)+5)/(6)=(17)/(6)`

`2 (3)/(4)=((2 * 4)+3)/(4)=(11)/(4)`,
`2 (4)/(7)=((2 * 7)+4)/(7)=(18)/(7)`

Step 3: Now, take LCM of the denominators and make the fraction into same denominator.

LCM of 8, 6, 4, 7 is 168.

`(21)/(8)=(21 * 21)/(8 * 21)=(441)/(168)`,
`(17)/(6)=(17 * 28)/(6 * 28)=(476)/(168)`

`(11)/(4)=(11 * 42)/(4 * 42)=(462)/(168)`,
`(18)/(7)=(18 * 24)/(7 * 24)=(432)/(168)`

Step 4: Arrange the fractions from greatest to least.

`(476)/(168)<(462)/(168)<(441)/(168)<(432)/(168)`

Now, write the corresponding mixed fraction.

`\Rightarrow 2 (5)/(6)<2 (3)/(4)<2 (5)/(8)<2 (4)/(7)`