A farmer plants corn on #2/5# of his field and beans on .25 of his field. He plants potatoes on the rest of the field. How much of the field is potatoes?

2 Answers
smendyka
Feb 21, 2018

See a solution process below:

Explanation:

First, we should understand the farmer has 1 field.

So the amount of his 1 field containing potatoes would be:

#1 - 2/5 - 0.25#

We can solve this two ways

**The first by converting the #2/5# to a decimal:

#2/5 = 2/2 xx 2/5 = (2 xx 2)/(2 xx 5) = 4/10 = 0.4#

Then

#1 - 2/5 - 0.25 =>#

#1 - 0.4 - 0.25 =>#

#1 - 0.65 =>#

#0.35#

So, 0.35 of his field would be planted with potatoes.

**The first by converting the #1#, #2/5# and #0.25# to fractions with common denominators:

#1 = 20/20 xx 1 = 20/20#

#2/5 = 4/4 xx 2/5 = (4 xx 2)/(4 xx 5) = 8/20#

#0.25 = 25/100 = (5 xx 5)/(5 xx 20) = (color(red)(cancel(color(black)(5))) xx 5)/(color(red)(cancel(color(black)(5))) xx 20) = 5/20#

Then

#1 - 2/5 - 0.25 =>#

#20/20 - 8/20 - 5/20 =>#

#(20 - 8 - 5)/20 =>#

#(20 - 13)/20 =>#

#7/20#

So, #7/20# of his field would be planted with potatoes.

Jim G.
Feb 21, 2018

#7/20#

Explanation:

#"express "0.25" as a proper fraction"#

#"that is "0.25=1/4#

#"add "2/5+1/4#

#"the "color(blue)"lowest common multiple of 5 and 4 is 20"#

#rArr(2/5xx4/4)+(1/4xx5/5)#

#=8+20+5/20=(8+5)/20=13/20#

#"corn and beans account for "13/20" of the field"#

#"consider the "color(red)"whole"" field to be "=20/20#

#"fraction of field for potatoes "=20/20-13/20=7/20#

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