Answer:
[tex]\dfrac{47}{42} \ \ \ \ \ OR \ \ \ \ 1.1[/tex]
Step-by-step explanation:
The objective of this question is to find the sum of the greatest and least numbers below:
[tex]\[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\][/tex]
To do this ; we will need to find the decimal component of each of them and equate them on a number line before summing the greatest and least numbers.
[tex]8 \frac{1}{5} = \dfrac{8*5+1}{5} \\ \\ = \dfrac{41}{5} \\ \\ = 8.2[/tex]
[tex]-8 \frac{2}{5} =- \dfrac{8*5+2}{5} \\ \\ =- \dfrac{42}{5} \\ \\ = -8.4[/tex]
[tex]-\dfrac{26}{3}= - 8.7[/tex]
[tex]-\dfrac{54}{7} = - 7.7[/tex]
[tex]\dfrac{53}{6}= 8.8[/tex]
Thus; the above decimal component of the fractions given are :
8.2, -8.4, -8.7 , -7.7 and 8.8
We are to find the sum of the greatest and the smallest number ; on a number line; we will realize that the positive side is greater than the negative side , As such the greatest number from the positive side will be 8.8 and the smallest number will be -7.7
The sum of 8.8 + ( -7.7 ) = 8.8 - 7.7
= 1.1
i.e
[tex]\dfrac{53}{6} + (- \dfrac{54}{7} )[/tex]
[tex]\dfrac{53}{6} - \dfrac{54}{7}[/tex]
[tex]\dfrac{53}{6} - \dfrac{54}{7} = \dfrac{53*7 - 6*54}{42} \\ \\ = \dfrac{47}{42} \\ \\ = 1.1[/tex]
