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Sagot :
Mixed numbers
A mixed number is a way to write a fractional number that is greater than 1. Mixed numbers have two parts: an integer and a fraction smaller than 1. If the integer is a and the fraction is b/c then the mixed number can be written as a fraction following this procedure:
[tex]a\text{ }\frac{b}{c}=a+\frac{b}{c}=\frac{ac+b}{c}[/tex]Simplifying
We must simplify this expression:
[tex]6\text{ }\frac{3}{5}-2\text{ }\frac{1}{4}[/tex]We can write both numbers as fractions using the formula above:
[tex]\begin{gathered} 6\text{ }\frac{3}{5}-2\text{ }\frac{1}{4}=(6+\frac{3}{5})-(2+\frac{1}{4})=\frac{6\cdot5+3}{5}-\frac{2\cdot4+1}{4} \\ 6\text{ }\frac{3}{5}-2\text{ }\frac{1}{4}=\frac{6\cdot5+3}{5}-\frac{2\cdot4+1}{4}=\frac{33}{5}-\frac{9}{4} \end{gathered}[/tex]In order to perform the last substraction we can multiply and divide each fraction by the denominator of the other:
[tex]\frac{33}{5}\cdot\frac{4}{4}-\frac{9}{4}\cdot\frac{5}{5}=\frac{132}{20}-\frac{45}{20}=\frac{132-45}{20}=\frac{87}{20}[/tex]Now we have to write 87/20 as a mixed number. We can rewrite the numerator like this:
[tex]\frac{87}{20}=\frac{7+80}{20}=\frac{7+4\cdot20}{20}[/tex]Then we distribute the division:
[tex]\frac{7+4\cdot20}{20}=\frac{7}{20}+\frac{4\cdot20}{20}=\frac{7}{20}+4=4\text{ }\frac{7}{20}[/tex]Then the answer is 4 7/20.
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