How To Find Ratio: Tutorial, Examples, And More

In this class, we going to focus on providing information about how to find ratios.

The term ratio can be described as a mathematical expressions that compare two or more quantities and numbers.

Ratio can compare absolute amounts and quantities, and can also be used to compare portions of a larger whole. Ratios can be written and calculated in fractions and in percentages.

However, the basic principles governing the use of ratios are universally the same.

Uses Of Ratios
Ratios can be used in both real world and in school settings to compare the differences between two or more quantities.

The simplest form of ratio compare only two numbers or quantities.

However, ratios can also be used to compare more than 3 quantities and numbers.

For example:

In a basket containing different types of vegetables and fruits such as spinach, apricot, cabbage, carrot, avocado, apple, and oranges. All these can be expressed in form of a ratio.

Ratio is only used when two or more numbers and quantities ar…

Distributive Property With Variables And Fractions: Tutorial And Examples

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What is the distributive property? In math, a distributive property is simply separating addends or subtrahends in a parenthesis into parts, and then multiplying or dividing every addend or subtrahend separately with the given factor outside of the parenthesis.

In mathematics, variables are symbols which represent an arbitrary value in arithmetic expression or equation. Variables can change from one value to another. Examples of variables are x, y, a, b, and so on.

Distributive Property With Variables

Example 1

Evaluate x(2+3y+3)


x(2+3y+3) = 2x+3xy+3x

Collect like terms

x(2+3y+3) = 2x+3x+3xy
                   = 5x+3xy

Example 2

Evaluate y(2+4+5y)


y(2+4+5y) = 2y+4y+5y^2

Collect like terms
y(2+4+5y) = 2y+4y+5y^2
                   = 6y + 5y^2

Distributive Property With Variables And Fractions

Example 1 



4/8(y+16) = 4/8y+16/8
                  = 4/8y + 2

Example 2

Evaluate 1/x(1/2+2/3)


The above example can be operated by distributing 1/x to each of the addends in the parenthesis, then adding and simplifying the resulting products together.

In practice:

1/x(1/2+2/3) = 1/x(1/2) + 1/x(2/3)
                      = 1/2x + 2/3x

Now, simplify by multiplying each addend with the LCM of both denominators.

The LCM of 2x and 3x is 6x

Multiply both sides of the equation by 6x


   1/x(1/2 + 2/3)(6x) = 6x(1/2x) + 6x(2/3x)

    1/x(1/2 + 2/3)(6x) = 6x/2x + 12x/3x
                                   = 3 + 4
                                   = 7

Now, divide both sides of the equation by 6x


1/x(1/2 + 2/3) =  7/6x


As you can see operation involving distributive property with variables and fractions is a little bit tricky, but with time and practice, you can become familiar.

Hope this guide gives you excellent help in understanding the distributive property with variables and fractions.

We would like listening to your view about distributive property with variables and fractions. So do write to us in the comment section below.


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