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Sagot :
[tex]5\frac{1}{4}-3\frac{8}{9}[/tex]
To make the estimate of the substraction of the mixed numbers we use the fraction that is accompaning the whole number. If the number is less than 1/2 we say that the number is closer to the whole number before the fraction, if it is 1/2 or more then we add one to the whole number.
For the first number
[tex]5\frac{1}{4}\approx5[/tex]This is approximate to 5 because 1/4 is less than 1/2
For the second number
[tex]3\frac{8}{9}\approx4[/tex]This is approximate to 4 because 8/9 is greater than 1/2.
ESTIMATE
[tex]\begin{gathered} 5\frac{1}{4}-3\frac{8}{9}=\text{?} \\ 5-4\approx1 \end{gathered}[/tex]To pass a mixed number into a fraction we use the following procedure
[tex]a\frac{b}{c}=\frac{(a\cdot c)+b}{c}[/tex]Pass both mixed numbers
[tex]\begin{gathered} 5\frac{1}{4}=\frac{(5\cdot4)+1}{4}=\frac{20+1}{4}=\frac{21}{4} \\ 3\frac{8}{9}=\frac{(3\cdot9)+8}{9}=\frac{27+8}{9}=\frac{35}{9} \end{gathered}[/tex]To find the exact value
[tex]\frac{21}{4}-\frac{35}{9}=\frac{21\cdot9-35\cdot4}{9\cdot4}=\frac{49}{36}[/tex]answer
The exact value of the substraction is
[tex]\frac{21}{4}-\frac{35}{9}=\frac{49}{36}=1\frac{13}{36}[/tex]
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