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Estimating with Fractions

Determine if an equation is reasonable based on an estimation of fractions

Determine if $3 \frac{1}{4} + 7 \frac{7}{8} = 10 \frac{1}{4}$

Round fractions to nearest whole

$3 \frac{1}{4}$ -> 3 $+ 7 \frac{7}{8}$ -> 8

3+8=11

looking at rounding we rounded down by $\frac{1}{4}$ and we rounded up by $\frac{1}{8}$ . Actual answer is larger, our estimate shows $10 \frac{1}/{4}$ is not a reasonable answer

Determine if $4 \frac{3}{4} \cdot 5 \frac{7}{8} = 27.9$ is reasonable

Round

$4 \frac{3}{4}$ -> 5 $\frac{7}{8}$ ->6

$5 \cdot 6$ = 30

The estimate is close, check which way the actual answer will be by looking at the direction of rounding. Because both numbers are rounded up the actual answer is smaller then the estimated 30, therefore 27.0 is reasonable.