Question

which is the most accurate way to estimate 35% of 770?
\\(\frac{1}{3} \times 780\\) \\(\frac{1}{3} \times 750\\)
\\(\frac{4}{5} \times 750\\) \\(\frac{4}{5} \times 780\\)

Explanation:

Step1: Analyze the percentage and number

We know that \(35\%=\frac{35}{100}=\frac{7}{20}\approx\frac{1}{3}\) (since \(\frac{1}{3}\approx0.333\) and \(35\% = 0.35\)), and \(770\approx780\) (because \(770\) is closer to \(780\) than to \(750\)).

Step2: Calculate the estimates

• For \(\frac{1}{3}\times780\), using the formula \(a\times\frac{b}{c}=\frac{ab}{c}\), we have \(\frac{1\times780}{3}=260\).
• For \(\frac{1}{3}\times750=\frac{750}{3} = 250\).
• For \(\frac{4}{5}\times750=\frac{4\times750}{5}=4\times150 = 600\).
• For \(\frac{4}{5}\times780=\frac{4\times780}{5}=\frac{3120}{5}=624\).

The actual value of \(35\%\text{ of }770=0.35\times770 = 269.5\).

Answer:

\(\frac{1}{3}\times780\)