Question

What is the sum of the greatest and least numbers below: \[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\]

Answer 1

47/42

Explanation:

Answer 2

`(47)/(42) \ \ \ \ \ OR \ \ \ \ 1.1`

Explanation:

The objective of this question is to find the sum of the greatest and least numbers below:

`\[8\frac15, \qquad -8\frac25, \qquad -(26)/(3), \qquad -\frac{54}7, \qquad (53)/(6).\]`

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.

`8 (1)/(5) = (8*5+1)/(5) \\ \\ = (41)/(5) \\ \\ = 8.2`

`-8 (2)/(5) =- (8*5+2)/(5) \\ \\ =- (42)/(5) \\ \\ = -8.4`

`-(26)/(3)= - 8.7`

`-(54)/(7) = - 7.7`

`(53)/(6)= 8.8`

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

`(53)/(6) + (- (54)/(7) )`

`(53)/(6) - (54)/(7)`

`(53)/(6) - (54)/(7) = (53*7 - 6*54)/(42) \\ \\ = (47)/(42) \\ \\ = 1.1`