Question

Can somebody help me please, thank you

Answer 1

Second Option

Step-by-step explanation:

`\sf\\\textsf{A simple way to compare any two fractions is by making the denominators of both}\\\textsf{fractions same. And an efficient way of doing this is taking the L.C.M. of }\\\textsf{denominators.}`

Checking first option:

`\sf\\\\\textsf{The L.C.M. of the denominators 16 and 10 is 80. }\\\textsf{The denominator of the first fraction is 16, so we multiply both numerator and }\\\textsf{denominator by 5 to get 80 on denominator.}\\\\(6)/(16)=(6*5)/(16*5)=(30)/(80)\\\\\textsf{Likewise, the denominator of the second fraction is 10. So we multiply both }\\\textsf{numerator and denominator by 8 to get 80 on the denominator.}\\\\(4)/(10)=(4* 8)/(10* 8)=(32)/(80)\\`

`\sf\\\textsf{Now that the two given fractions have same denominator, we can directly compare}\\\textsf{the numerators and determine which fraction is greater.}\\30 < 32\\\\or,\ (30)/(80) < (32)/(80)\\\\\therefore\ (6)/(16) < (4)/(10)\\\\\textsf{This makes our first option incorrect.}`

Checking second option:

`\sf\\\textsf{The L.C.M. of the denominators 16 and 24 of the given fraction is 48.}\\\textsf{So, in case of first fraction, we multiply 3 on both numerator and denominator}\\\textsf{to get 48 in the denominator.}\\\\(6)/(16)=(6*3)/(16*3)=(18)/(48)\\\\\textsf{In case of second fraction, we multiply 2 on both numerator and denominator to}\\\textsf{get 48 in the denominator.}\\\\(7)/(24)=(7*2)/(24*2)=(14)/(48)\\`

`\sf\\\textsf{Now we compare the numerators of these fractions as in previous option:}\\18 > 14\\\\or,\ (18)/(48) > (14)/(48)\\\\or,\ (6)/(16) > (7)/(24)`

`\textsf{This makes the second option correct.}`

Checking third option:

`\sf\\\textsf{Multiplying 2 on both numerator and denominator in first fraction,}\\\\(4)/(8)=(4*2)/(8* 2)=(8)/(16)\\\\\textsf{We know,}\\8 > 5\\\\or,\ (8)/(16) > (5)/(16)\\\\\textsf{So this makes the third option incorrect.}`

Checking fourth option:

`\sf\\\\\\(3)/(5)=(3*16)/(5* 16)=(48)/(80)\\\\(5)/(16)=(5*5)/(16* 5)=(25)/(80)\\\\\textsf{We know,}\\48 > 25\\\\or,\ (48)/(80) > (25)/(80)\\\\or,\ (3)/(5) > (5)/(16)`