Round the numbers to estimate the answer. Then find the...

Round the numbers to estimate the answer. Then find the exact difference. In Exercise 67 , the estimate is done for you.
Estimate $\quad$ Exact \begin{tabular}{rr}
25 & $25 \frac{1}{4}$ \\
$-\frac{14}{11}$ & $-13 \frac{3}{4}$ \\
\hline
\end{tabular}

Key Concepts

Fraction and Mixed Number Arithmetic

Working with fractions and mixed numbers involves specific techniques such as finding common denominators, converting between improper fractions and mixed numbers, and performing addition or subtraction precisely. Mastery of these methods is crucial for obtaining exact results when dealing with non-integer values.

Exact Difference

The exact difference is obtained by performing precise arithmetic on the original numbers without rounding, ensuring that every digit and fractional part is accounted for. This concept highlights the importance of accuracy and is often used to compare with an estimated result to understand the potential error introduced by rounding.

Estimation

Estimation involves using approximations to quickly assess the value or result of a mathematical expression. When numbers are rounded before performing operations such as addition or subtraction, the estimated result gives a general idea of the exact answer. This is useful for verifying the reasonableness of calculations without needing to perform detailed arithmetic.

Rounding

Rounding is the process of adjusting a number to reduce its digits while keeping it close to its original value. It is especially useful for simplifying calculations and estimating results when exact precision is not necessary. This concept involves deciding which digits to keep based on a specified degree of accuracy or place value.

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