How do you order the numbers from least to greatest: #2 2/5, 11/5, 2 3/10, 31/10#?

1 Answer
Dec 9, 2016

#"Least to greatest "->" "11/5", "2 3/10", "2 2/5", "31/10#

Explanation:

A fraction's structure is of form:#" "("count")/("size indicator") -> ("numerator")/("denominator")#

You can not directly #ul("compare the counts")# unless the size indicators are the same.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("The first one is done in detail. The rest not so.")#

Consider #" "2 2/5#

Write as #2+2/5#

#color(brown)("Multiply by 1 and you do not change the value. However, 1 comes in")##color(brown)("many forms. So you can change the way it looks without")##color(brown)("changing its actual value.")#

#color(green)([2color(red)(xx1)]+[2/5color(red)(xx1)])#

#color(green)([2color(red)(xx10/10)]+[2/5color(red)(xx2/2)])#

#[20/10] +[4/10] = 24/10#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider #11/5=22/10#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider #2 3/10 = 23/10#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

Given fraction#" "2 2/5" "11/5" "2 3/10" "31/10#

Equivalent fraction#" "24/10" "22/10" "23/10" "31/10 #

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Least to greatest count#" "22/10," "23/10", "24/10", "31/10#

#"Least to greatest "->" "11/5", "2 3/10", "2 2/5", "31/10#