How do you find a midpoint of two numbers ?

Question

Ethan Adkins · Accepted Answer

undefined To find the midpoint of two numbers, you add the two numbers together and then divide the sum by 2.

Eva Abramson · Answer

Find their average: take their sum, and divide it by 2.

The midpoint #m# of two numbers #a# and #b# is, by definition, a number that is the same distance from #a# as it is from #b#. Using this, we can get a formula for the midpoint #m# in terms of #a# and #b#. Picture #a# and #b# as two points on a number line, with #a# to the left of #b#. Now, #m# must be between them, so #m# is greater than #a# but less than #b#. So if the distance from #a# to #m# is the same as the distance from #m# to #b#, we can set these two distances to be equal, like this: #m-a=b-m# This equation says: "The difference between #m# and #a# is the same as the difference between #b# and #m#." Now, all we do is rearrange this to equation to solve for #m#: #m-a color(green)(" "+ m)=b" "# (add #m# to both sides) #" "2m" "=bcolor(green)(" "+a)" "# (add #a# to both sides) #" "m" "=(b+a)/color(red)2" "# (divide both sides by 2) And there it is—the formula for the midpoint! This is often called the average of the two numbers #a# and #b#, and written as #m=(a+b)/2# What is the midpoint of 3 and 5? Well, the answer is intuitively 4, but with the formula, we get: #m=(3+5)/2=8/2=4# which matches our intuition.

Avery Alexander · Answer

The method Geoff K gave also works with a combination of negative and positive numbers

Suppose we have #-3 and +3# then the mid point is #(-3+3)/2=0#

#" "#or if you prefer you can write this as #(+3-3)/2=0#

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Suppose we have #-3 and +5# then the mid point is

#(-3+5)/2=2/2=1#