Question

1. how can you use estimation to find $9\frac{1}{2} + 9\frac{1}{2} + 9\frac{1}{2} + 9\frac{1}{2} + 9\frac{1}{2}$?

Explanation:

Step1: Round each mixed number

Round $9\frac{1}{2}$ to the nearest whole number. Since $\frac{1}{2}=0.5$, we round up to 10.

Step2: Multiply by the count of terms

There are 5 identical terms, so calculate the estimated sum.
$10 \times 5 = 50$

Step3: Adjust for overestimation

Each term was overestimated by $10 - 9\frac{1}{2} = \frac{1}{2}$. For 5 terms, total overestimation is $5 \times \frac{1}{2} = \frac{5}{2}=2.5$. Subtract this from the estimate:
$50 - 2.5 = 47.5$

Answer:

First, estimate by rounding each $9\frac{1}{2}$ to 10, calculate $10\times5=50$. Then adjust by subtracting the total overestimation ($5\times\frac{1}{2}=2.5$) to get the exact estimated/actual value of $47\frac{1}{2}$ (or 47.5). The final sum is $\boldsymbol{47\frac{1}{2}}$ (or $\boldsymbol{\frac{95}{2}}$).