Question

How do you solve `\frac { 29} { 62} = \frac { a } { 39}`?

Answer 1

`a=18.24`

Explanation:

Use the butterfly method. Just multiply the numbers and you'll get this:

`62a=1131`

Answer 2

`18 15/62` or `18.24` to the nearest 2 decimal places

Explanation:

`29/62=a/39`

`:.a/39=29/62`

multiply both sides by`39`

`:.a=29/62xx39/1`

`:.a=1131/62`

`:.a=18 15/62` or `18.24` to the nearest 2 decimal places.

Answer 3

`a=1131/62`

A lot of detail given (first principle method) so you can see where everything comes from. Short cut principles are just remembering the consequence of first principles.

Explanation:

`color(blue)("Preamble")`

We need `a` on its own on one side of the equals and everything else on the other side.

So we need to 'get rid' of the 39 on the right.

We do this by changing it to 1.

1 times anything does not change the value and this process end up with the 39 on the other side of the equals.
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`color(blue)("Answering the question")`

Given: `29/62=a/39`

Write as: `29/62=axx1/39`

Multiply both sides by `39`

`29/62xx39=axx1/39xx39`

`(29xx39)/62=axx39/39`

But `39/39` is just another way of writing 1

`(29xx39)/62=axx1`

Swap everything round the other way (convention)

`a=(29xx39)/62`

`a=1131/62`