How do you solve #\frac { 19} { x } = \frac { 19} { 5281}#?

Question

Nathan Axel · Accepted Answer

#x=5281# There is actually no need for multiplication, transferring and stuff.. you can clearly see that The numerators on both hand sides are equal.... so the denominators must be equal... Only #19/5281=19/5281#

Avery Alexander · Answer

#x=5281# #19/x=19/5281# Cross multiply: #19 xx 5281 = x xx 19# #cancel19 xx 5281 = x xx cancel19# #x = 5281 #

Genesis Allen · Answer

#x=5281#

#color(brown)("You can do this! It is a very quick sort of cheat.")#

Turn everything upside down. There is a mathematical method for achieving the same thing. So we have:

#x/19=5281/19#

As the bottom numbers (denominators) are the same we can forget about them and just write:

#x=5281#

Again there is a mathematical method for achieving the same thing as 'forgetting' about the denominators. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(brown)("What a teacher would expect to see.")#

#color(brown)("Or the shortcut equivalents. This is first principles")#

Shown almost every step

Given: #19/x=19/5281#

Multiply both sides by 5281 giving:

#19/x xx5281 = 19xx5281/5281#

#19/x xx 528=19 xx 1#

Multiply both sides by #x#

#19xx528=19xx x#

Divide both sides by 19

#528=x#

Write in conventional form

#x=528#