Lesson 1: Estimate sums and differences using benchmark numbers.

Property

To round a mixed number to the nearest half or whole for a more precise estimate, compare its fractional part to the benchmarks $\frac{1}{4}$ and $\frac{3}{4}$.

• If the fraction is less than $\frac{1}{4}$, round down to the whole number.
• If the fraction is between $\frac{1}{4}$ and $\frac{3}{4}$, round to the half (e.g., $x \frac{1}{2}$).
• If the fraction is greater than $\frac{3}{4}$, round up to the next whole number.

Examples

Property

To determine if an estimate is an overestimate (greater than the actual answer) or an underestimate (less than the actual answer), analyze how each number was rounded.

• Addition: If both numbers are rounded up, the sum is an overestimate. If both are rounded down, the sum is an underestimate.
• Subtraction ($A - B$): If $A$ is rounded up and $B$ is rounded down, the difference is an overestimate. If $A$ is rounded down and $B$ is rounded up, the difference is an underestimate.

Examples