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Tuesday, April 12, 2016

Maths Yr 4: More and more fractions

The denominator of any fraction cannot have the value zero. If the denominator of a fraction is zero, the expression is not a legal fraction because it's overall value is undefined

This means tex2html_wrap_inline48 , tex2html_wrap_inline50 , tex2html_wrap_inline52 are not legal fractions. Their values are all undefined, and hence they have no meaning. Once you encounter such a fraction in a problem, stop. You cannot proceed with the problem.

A numerator is allowed to take on the value of zero in a fraction. Any legal fraction (denominator not equal to zero) with a numerator equal to zero has an overall value of zero.



This means tex2html_wrap_inline44 , tex2html_wrap_inline46 , tex2html_wrap_inline48 all have a fraction value of zero because the numerators are equal to zero.

 Different Faces of the Number 1




The number 1 can take on many forms. 4 - 3 = 1 and 10 - 9 = 1 can be used as a substitution for the number 1 because they have a value of 1. When the numerator of a fraction is equivalent to the denominator of a fraction, the value of the fraction is 1. This only works when you have a legal fraction; i.e., the denominator does not equal zero. You can substitute one of these fractions for the numer 1.

Any Integer Can Be Written as a Fraction




You can express an integer as a fraction by simply dividing by 1, or you can express any integer as a fraction by simply choosing a numerator and denominator so that the overall value is equal to the integer.

To reduce a simple fraction, follow the following three steps:
1.
Factor the numerator.
2.
Factor the denominator.
3.
Find the fraction mix that equals 1.



For example, reduce tex2html_wrap_inline89 .
First: Rewrite the fraction with the numerator and the denominator factored.
displaymath91
Note all factors in the numerator and denominator are separated by multiplication signs.
Second: Find the fraction that equals 1. tex2html_wrap_inline93 can be written tex2html_wrap_inline95 which in turn can be written tex2html_wrap_inline97 which in turn can be written tex2html_wrap_inline99 .
Third: We have just illustrated that tex2html_wrap_inline101 . Although the left side of the equal sign does not look identical to the right side of the equal sign, both fractions are equivalent because they have the same value. Check it with your calculator.tex2html_wrap_inline103 and tex2html_wrap_inline105 . This proves that the fraction tex2html_wrap_inline89 can be reduced to the equivalent fraction tex2html_wrap_inline99 .

A compound fraction is sometimes called a mixed number. Recall that tex2html_wrap_inline161 , tex2html_wrap_inline163 , and tex2html_wrap_inline165 are examples of compound fractions.


  • To manipulate compound fractions, just convert them to simple fractions and follow rules 1 through 23 for simple fractions.Example 1: Convert tex2html_wrap_inline161 to a simple fraction.
    Answer. tex2html_wrap_inline161 can be written tex2html_wrap_inline171 . Write 3 as the fraction tex2html_wrap_inline173 . Now tex2html_wrap_inline171 can be written tex2html_wrap_inline177 and
    displaymath179
  • To convert a simple fraction to a compound fraction, the numerator must be larger than the denominator. Separate the whole number first.Example 2: Convert tex2html_wrap_inline181 to a compound fraction.
    Answer. Rewrite tex2html_wrap_inline181 as tex2html_wrap_inline185 . We have
    displaymath187
  • To add or subtract two compound fractions, convert the fractions to simple fractions and follow the steps you use to add or subtract two simple fractions.Example 3: Calculate tex2html_wrap_inline189 .
    Solution We have
    displaymath191
  • To multiply or divide two compound fractions, convert the fractions to simple fractions and follow the steps you use to multiply or divide two simple fractions.Example 4: Calculate tex2html_wrap_inline193 .
    Solution. We have
    displaymath195
For this review, we will focus on terminating fractions. Divide the fraction by 1, and then multiply the result by 1 in a form that will remove the decimal.


Example: Convert 2.3 to a fraction.
Answer. 2.3 can be written tex2html_wrap_inline29 which can be multiplied by 1 and divided by 1 without changing its value. We have
displaymath31
Recall that tex2html_wrap_inline8 . To convert a percentage to a fraction, simply convert 1% to tex2html_wrap_inline37. To convert a percentage to a decimal, simply convert 1% to .01.


Example 1: Convert tex2html_wrap_inline44 to a fraction.
Answer. tex2html_wrap_inline44 can be written tex2html_wrap_inline48 which in turn can be written tex2html_wrap_inline50 . Multiply the two fractions using the multiplication rule to get
displaymath52

Example 2: Convert tex2html_wrap_inline54 to a decimal.
Answer. tex2html_wrap_inline54 can be written
displaymath58

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