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?

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Feb 11, 2017

Answer:

The explanation is much longer than doing the mathematics.

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

Explanation:

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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Method 1")#

5 lots of 3:2 #-> 5xx ( 3:2) =(5xx3) : (5xx2) = 15:10#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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") #

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

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