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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Multiplying And Dividing Fractions

Fractions are used when we don't have a whole number of something. When you combine fractions together, you often need to multiply and divide fractions.

Multiplication

To multiply fractions, convert all mixed numbers to improper fractions, and write them on a common bar.

Example:

To reduce your labor, cancel factors that appear in both numerator and denominator. That is, if the same number appears in both the top and bottom then you can cross out the pair. This keeps the numbers smaller and makes them easier to use.

Example:

Identity Element of Multiplication

and are equivalent fractions.

To understand this, we need to consider the identity element of multiplication:

Whenever the same non-zero number appears in both the numerator and denominator, the fraction is equal to 1.

Thus, , and even .

The number 1 is the identity element of multiplication. That means whenever we multiply a number by 1, we get the same number.

Think: What is the identity element of division?

To prove that and are equivalent fractions, we will show how has been multiplied by 1 to get the new fraction:

The identity element can be written in many forms. Note that anything (except zero) divided by itself is 1, so any of these forms could be used for the identity element of multiplication:

Choose the form of the identity element that simplifies your calculations.

One is the identity element for multiplication of numbers, since a Ã—1 = 1 Ã— a = a for all values of a.