Question

When you answer the question, please don’t use decimalsWhen you answer the question for example: Part A then put the answer same for part B and C

Answer 1

Part A

We need to estimate the subtraction between the two fractions below:

`(10)/(12)-(3)/(8)`

To do that we need to estimate a more appropriate value for each expression, using benchmarks. We will use the benchmark values 1 and 1/2. We can then approximate each function:

`(10)/(12)\cong1`

Since the numerator 10 is very close to the denominator 12, we can estimate that its value is very close to 1.

`(3)/(8)\cong(1)/(2)`

We can estimate that the fraction 3/8 is very close to 1/2, because the numerator is one unit off being half of the denominator. With these estimations we can quickly calculate the estimate for the whole subtraction:

`1-(1)/(2)=(1)/(2)`

We estimate that the subtraction is approximately equal to 1/2.

Part B.

Now we need to actually solve the problem, the first step we will take is to simplify both fractions as much as we can:

`(10)/(12)=(5)/(6)`

Now we can actually subtract them:

`\begin{gathered} (5)/(6)-(3)/(8)=(4\cdot5-3\cdot3)/(24) \\ (5)/(6)-(3)/(8)=(11)/(24) \end{gathered}`

The actual value for the subtraction is 11/24.

Part C

Now we need to calculate the difference between our estimate and the actual value, for that we will subtract the actual value from the estimate:

`(1)/(2)-(11)/(24)=(1)/(24)`

The difference between the two is 1/24 of a unit, which means that our estimate was very close to the actual value, therefore it was reasonable.