Question

24.b
find the value of each fraction. show your work.
\\(\frac{79^2 - 65^2}{420}\\)
answer

Explanation:

Step1: Apply difference of squares formula

The numerator \(79^2 - 65^2\) can be factored using the difference of squares formula \(a^2 - b^2=(a + b)(a - b)\), where \(a = 79\) and \(b = 65\). So we have:
\(79^2 - 65^2=(79 + 65)(79 - 65)\)

Step2: Calculate the values in the parentheses

First, calculate \(79+65 = 144\) and \(79 - 65 = 14\). Then multiply these two results:
\((79 + 65)(79 - 65)=144\times14\)
Calculate \(144\times14 = 2016\)

Step3: Divide by the denominator

Now we have the fraction \(\frac{2016}{420}\). Divide 2016 by 420:
\(\frac{2016}{420}=\frac{2016\div84}{420\div84}=\frac{24}{5} = 4.8\) (or we can do the division directly: \(2016\div420 = 4.8\))

Answer:

\(4.8\) (or \(\frac{24}{5}\))