Question

4·(4 - 7)² - 6·7 + 20

Explanation:

Step1: Calculate the value inside the parentheses

First, we calculate the expression inside the parentheses: \(4 - 7=-3\)

Step2: Square the result of the parentheses

Then we square the result: \((-3)^2 = 9\)

Step3: Calculate the division

Next, we do the division: \(6\div7=\frac{6}{7}\)

Step4: Combine all parts

Now we combine all the parts of the expression: \(4\div9-\frac{6}{7} + 20\)
First, \(4\div9=\frac{4}{9}\)
Then, find a common denominator for \(\frac{4}{9}\) and \(\frac{6}{7}\), which is \(63\)
\(\frac{4}{9}=\frac{28}{63}\), \(\frac{6}{7}=\frac{54}{63}\)
So \(\frac{28}{63}-\frac{54}{63}=\frac{28 - 54}{63}=\frac{- 26}{63}\)
Finally, \(\frac{-26}{63}+20 = 20-\frac{26}{63}=\frac{1260 - 26}{63}=\frac{1234}{63}\approx19.59\) (If we want a decimal approximation)
Or we can keep it as a fraction: \(\frac{1234}{63}\) or as a mixed number: \(19\frac{37}{63}\)

Wait, maybe I misread the original expression. Let's re - examine the image. The expression seems to be \(4\div(4 - 7)^2-6\div7 + 20\) (assuming the original is \(4\div(4 - 7)^2-6\div7 + 20\))

Step1: Calculate the exponent part

First, calculate the value inside the parentheses: \(4-7=-3\)
Then square it: \((-3)^2 = 9\)

Step2: Calculate the divisions

Calculate \(4\div9=\frac{4}{9}\) and \(6\div7=\frac{6}{7}\)

Step3: Combine the terms

Now the expression is \(\frac{4}{9}-\frac{6}{7}+20\)
Find a common denominator for \(\frac{4}{9}\) and \(\frac{6}{7}\), which is \(63\)
\(\frac{4}{9}=\frac{4\times7}{9\times7}=\frac{28}{63}\)
\(\frac{6}{7}=\frac{6\times9}{7\times9}=\frac{54}{63}\)
So \(\frac{28}{63}-\frac{54}{63}=\frac{28 - 54}{63}=\frac{-26}{63}\)
Then add \(20\): \(\frac{-26}{63}+20=\frac{-26 + 20\times63}{63}=\frac{-26+1260}{63}=\frac{1234}{63}\approx19.59\)

Answer:

If we keep it as a fraction, the answer is \(\frac{1234}{63}\) or as a mixed number \(19\frac{37}{63}\), and as a decimal approximately \(19.59\)