Estimate 10/12 - 3/8 using benchmark values. your equation must show the estimate for each fraction and for the solution.

The estimated values of given fraction are 1/2, 1/4 and 1/2 for benchmark values  1/2,  1/4 and  1/8 respectively.

Step-by-step explanation:

The given expression is

Case 1: Let the benchmark value be 1/2.

10/12 > 3/4 so we round it to 1.

1/4 ≤ 3/8 ≤ 3/4 so we round it to 1/2.

Estimating the solution:

1 - 1/2 = 1/2

Case 2: Let the benchmark value be 1/4.

5/8 ≤ 10/12 < 7/8 so we round it to 3/4.

3/8 ≤ 3/8 < 5/8 so we round it to 2/4.

Estimating the solution:

3/4 - 2/4 = 1/4

Case 3: Let the benchmark value be 1/8.

13/16 ≤ 10/12 < 15/16 so we round it to 7/8.

5/16 ≤ 3/8 < 7/16 so we round it to 3/8.

Estimating the solution:

7/8 - 3/8 = 1/2

Therefore the estimated values of given fraction are 1/2, 1/4 and 1/2 for benchmark values  1/2,  1/4 and  1/8 respectively.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

there would be 162.15 calories in this cereal.

step-by-step explanation: