Question

solve for the base in the following.
$6.25 is $1\frac{1}{4}\\%$ of ______ .

$6.25 is $1\frac{1}{4}\\%$ of $\square$. (simplify your answer.)

Explanation:

Step1: Convert mixed fraction to decimal

First, convert \(1\frac{1}{4}\%\) to a decimal. \(1\frac{1}{4}=\frac{5}{4} = 1.25\), so \(1\frac{1}{4}\% = 0.0125\) (since to convert a percentage to a decimal, we divide by 100, so \(1.25\%=\frac{1.25}{100}=0.0125\)).

Step2: Use the percentage formula

The formula for finding the base (let the base be \(b\)) when we know the part (\(p\)) and the rate (\(r\)) is \(p = r\times b\). We know \(p = 6.25\) and \(r=0.0125\), so we can solve for \(b\) by rearranging the formula to \(b=\frac{p}{r}\).
Substitute the values: \(b=\frac{6.25}{0.0125}\)

Step3: Perform the division

Calculate \(\frac{6.25}{0.0125}\). We can multiply numerator and denominator by 10000 to eliminate decimals: \(\frac{6.25\times10000}{0.0125\times10000}=\frac{62500}{125}\)
Divide 62500 by 125: \(62500\div125 = 500\)

Answer:

\(500\)