Ratios part 2

As we move along with ratios/proportions, we start to look at equivalent ratios.  Finding equivalent ratios is exactly the same as equivalent fractions (fractions are ratios in the sense of part to whole).  We can find equivalent ratios in a number of different ways.

Lets start with halving and doubling.  Any ratio can be halved (if both numbers are even), or doubled.  Take a look at this ratio.  The easiest way to find the simplest fraction is to divide the denominator (bottom number) and the numerator (top number) by the GCF.

4 boys to 8 girls.  This means for every 4 boys in a class, there are 8 girls.  We can simplify this by halving both numbers.

2 boys to 4 girls is equivalent.   We can even half this again to get a unit rate (we will cover this more later)

1 boy to 2 girls = 2 boys to 4 girls = 4 boys to 8 girls.

Alternatively, we could find equivalent ratios by doubling each number in the ratio.

4 boys to 8 girls is equal to 8 boys to 16 girls.

These two ways are, in my opinion, the easiest way to find equivalent ratios.  You can also multiply each number in the ratio by the same number and find larger equivalent ratios.


What about finding equivalent ratios when given a fraction?  Let's take a look.  In class we have been using $300 to describe a fundraising goal.  Let's say over the course of a few days that 3/5 of the goal has been raised.  We can set this up like an equation

3      
--- =  --------
5         300

We have to determine what number 5 has to be multiplied by to get to 300.  We can do this by dividing 300 by 5, which gives us 60.  So we would know that 5 * 60 equals 300, so 3 * 60 would give use what 3/5 of 300 is.

3 * 60        180
---       =   --------
5 * 60        300

We can do this with any fraction and ratio.