Gena and her friends each estimated the quotient of –137.56 divided by –6.12 using compatible numbers. Which shows the best estimate using compatible numbers? Negative 140 divided by negative 7 = 20 Negative 140 divided by 6 = 23.3 with bar Negative 135 divided by negative 7 = 22.5 Negative 135 divided by negative 5 = 27

Negative 135 divided by negative 7 = 22.5

Step-by-step explanation:

Estimating the quotient of :

–137.56 divided by –6.12

The compatible number which gives the best estimate ;

Negative 140 divided by negative 7 = 20

-140 ÷ - 7 = 20

Negative 140 divided by 6 = 23.3 with bar

-140 ÷ 6 = - 23.3

Negative 135 divided by negative 7 = 22.5

-135 ÷ - 7 = 22.5

Negative 135 divided by negative 5 = 27

-135 ÷ - 5 = 27

Comparing the result with the actual quotient obtained using the actual value;

–137.56 ÷ ( –6.12) = 22.477

Hence,

Negative 135 divided by negative 7 = 22.5

-135 ÷ - 7 = 22.5 gives the closest estimate.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18