Ratio and proportion practice sums for grade 9no.........

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Lorraine Caplan | College Teacher | (Level 1) Educator Emeritus

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A ratio is a relationship between two numbers.  For example, if I see three people in a room and one of them is female and the other two are male, there is a two to one ratio of male to female.  This is expressed in numbers like this:  2:1. 

When I have a series of numbers and they each have the same relationship between them, that is a proportion.  For example, the relationship between two and one is the same as the relationship between four and two, each being a "doubling" of the numbers.  This is expressed in numbers like this:  2:1 ::4:2.  In words we say, "Two is to one as four is to two. 

The two end numbers in a proportion are called the extremes.  The two middle numbers are called the means.  In the example above, the means are two and two, both numbers being at the ends.  The means are one and four, both numbers being in the middle. 

In a proportion, the extremes multiplied times one another will always equal the means times one another.  In the example above,  this means that 2 times 2 equals 1 times 4, which is, of course, a true statement.  In an equation, that looks like this:   (2)(2) = (1)(4).

Now, suppose you don't know one of the numbers.  By using this formula, we can find a missing number in a proportion.  The missing number, which I will call X, could be at any spot in this equation.  Here is an example:  6:2 :: 3: X.  X is the number we don't know. 

If we use the formula, we can figure out what X is.  Here is how that will look:  (6) (X) = (2) (3)  Moving along to solve the formula, we get 6X = 6.  Now we can divide both sides of the equation by 6 and determine that X = 1. 

I hope this explanation helps you.  Good luck! 

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