How do you find the ratio 140 minutes to 9 hours in simplest form?

2 Answers
Jun 13, 2018

#7:27#

Explanation:

#"we require the quantities to have the same units of time"#

#"there are 60 minutes in 1 hour"#

#9"hours "=9xx60=540" minutes"#

#"we now have both times expressed in minutes"#

#"the ratio required is"#

#140:540larrcolor(blue)"divide both by 10"#

#=14:54larrcolor(blue)"divide both by 2"#

#=7:27larrcolor(red)"in simplest form"#

#"the ratio is in simplest form when no other factor but 1"#
#"divides into both values"#

Jun 15, 2018

#7:27#

Explanation:

Given: #140 \ "minutes" \ : \ 9 \ "hours"#.

First convert #9# hours to minutes. Note that #1# hour is equal to #60# minutes.

So, we get:

#9color(red)cancelcolor(black)"hours"*(60 \ "minutes")/(color(red)cancelcolor(black)"hour")=540 \ "minutes"#

The ratio becomes:

#=140 \ "minutes" \ : \ 540 \ "minutes"#

Divide.

#=(140color(red)cancelcolor(black)"minutes")/(540color(red)cancelcolor(black)"minutes")#

#=7/27#

Write back in ratio.

#=7 \ : \ 27#