Lesson 1: Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations.

Property

To compare a fraction $\frac{a}{b}$ to the benchmarks $0$, $\frac{1}{2}$, and $1$:

• If the numerator $a$ is very small compared to the denominator $b$, the fraction is close to $0$.
• If the numerator $a$ is about half of the denominator $b$ (i.e., $a \approx \frac{b}{2}$), the fraction is close to $\frac{1}{2}$.
• If the numerator $a$ is very close to the denominator $b$, the fraction is close to $1$.

Examples

Property

To assess the reasonableness of a sum or difference, estimate the result by rounding each fraction to the nearest benchmark ($0, \frac{1}{2}, 1$) or each mixed number to the nearest half.
Compare this estimated result to the given answer.
If the estimate and the answer are close, the answer is reasonable.

Examples