Question

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

Answer 1

`x=5281`

Explanation:

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`

Answer 2

`x=5281`

Explanation:

`19/x=19/5281`

Cross multiply:

`19 xx 5281 = x xx 19`

`cancel19 xx 5281 = x xx cancel19`

`x = 5281`

Answer 3

`x=5281`

Explanation:

`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.
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`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`