If the ratio of boys to girls is 3:2 and there are 25 students in a class, how do you make equal ratios to show how many students in the class are boys and how many are girls?

Consider the starting point:
We have 3 boys and 2 girls. This gives a total count of 5

So we need to see how many lots of 5 will fit into 25.

5 lots of 5 gives 25

So we have 5 lots of the ratio 3:2
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`color(blue)("Method 1")`

5 lots of 3:2 `-> 5xx ( 3:2) =(5xx3) : (5xx2) = 15:10`
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`color(blue)("Method 2")`

Write the ratio in fractional form

`color(magenta)("We can do this as long as we do not view and treat it like a fraction")`

It does not matter in this case which we put on the top. I chose:

`("boys")/("girls") -> 3/2`

Multiply a value (or system) by 1 and you do not change the value. However, 1 comes in many forms.

`color(green)(3/2color(red)(xx1) " "->" "3/2color(red)(xx5/5))`

`" "=color(green)((3color(red)(xx5))/(2color(red)(xx5))`

`" "=15/10 =("boys")/("girls")`

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The ratio of 15 boys to 10 girls is equivalent to the ratio of 3:2

`15:10-=(15-:5):(10-:5)=3:2`

where `-=` means equivalent to