Question: Which is the most accurate way to estimate 49% of 319? \[ \frac{1}{2} \times 320 \quad…

Which is the most accurate way to estimate 49% of 319?

\[ \frac{1}{2} \times 320 \quad \frac{1}{3} \times 330 \quad \frac{1}{4} \times 320 \quad \frac{3}{4} \times 320 \]

Solution

Step 1: Calculate 49% of 319. \[ 0.49 \times 319 = 156.31 \] Step 2: Evaluate each option. Option 1: \[ \frac{1}{2} \times 320 = 160 \] Option 2: \[ \frac{1}{3} \times 330 \approx 110 \] Option 3: \[ \frac{1}{4} \times 320 = 80 \] Option 4: \[ \frac{3}{4} \times 320 = 240 \] Step 3: Compare each estimate to the actual value. - Option 1: \(|160 - 156.31| = 3.69\) - Option 2: \(|110 - 156.31| = 46.31\) - Option 3: \(|80 - 156.31| = 76.31\) - Option 4: \(|240 - 156.31| = 83.69\) Step 4: Determine the most accurate estimate. Option 1 has the smallest difference from the actual value. The most accurate way to estimate 49% of 319 is: \[ \frac{1}{2} \times 320 \]