Question

estimate the sum. round each number to the nearest whole number, then add.
$11\frac{1}{2} + 3\frac{17}{18}$
the sum is approximately \boxed{}.

Explanation:

Step1: Round \(11\frac{1}{2}\) to nearest whole number

The fraction \(\frac{1}{2}\) is equal to \(0.5\), so \(11\frac{1}{2}=11.5\). Rounding \(11.5\) to the nearest whole number, we look at the decimal part \(0.5\), and since \(0.5\) is exactly halfway, we round up (by convention) to \(12\). So \(11\frac{1}{2}\approx12\).

Step2: Round \(3\frac{17}{18}\) to nearest whole number

First, convert \(\frac{17}{18}\) to a decimal. \(\frac{17}{18}\approx0.944\) (since \(17\div18\approx0.944\)). Then \(3\frac{17}{18}=3 + 0.944 = 3.944\). The decimal part \(0.944\) is closer to \(1\) than to \(0\), so we round up \(3.944\) to \(4\). So \(3\frac{17}{18}\approx4\).

Step3: Add the rounded numbers

Now we add the two rounded numbers: \(12 + 4 = 16\).

Answer:

\(16\)