do 18 - 9 4/9 + 7/9 - 8 and show your work in an easy to understand fashion

Answer 1

To solve the expression \(18 - 9 \frac{4}{9} + \frac{7}{9} - 8\), we will break it down step by step.

Step 1: Convert the mixed number to an improper fraction

First, we need to convert \(9 \frac{4}{9}\) into an improper fraction.

\[ 9 \frac{4}{9} = 9 + \frac{4}{9} = \frac{9 \times 9 + 4}{9} = \frac{81 + 4}{9} = \frac{85}{9} \]

So the expression now looks like this:

\[ 18 - \frac{85}{9} + \frac{7}{9} - 8 \]

Step 2: Simplify the expression

Combine the constants \(18\) and \(-8\):

\[ 18 - 8 = 10 \]

Now we can rewrite the expression:

\[ 10 - \frac{85}{9} + \frac{7}{9} \]

Step 3: Combine the fractions

Next, combine the fractions \(-\frac{85}{9}\) and \(\frac{7}{9}\):

\[ -\frac{85}{9} + \frac{7}{9} = \frac{-85 + 7}{9} = \frac{-78}{9} \]

Step 4: Rewrite the expression

Now our expression is:

\[ 10 - \frac{78}{9} \]

Step 5: Convert the whole number to a fraction

To subtract the fraction from the whole number, convert \(10\) into a fraction with the same denominator, which is \(9\):

\[ 10 = \frac{90}{9} \]

Step 6: Perform the subtraction

Now we need to subtract \(\frac{78}{9}\) from \(\frac{90}{9}\):

\[ \frac{90}{9} - \frac{78}{9} = \frac{90 - 78}{9} = \frac{12}{9} \]

Step 7: Simplify the fraction

Now simplify \(\frac{12}{9}\):

\[ \frac{12}{9} = \frac{4}{3} \]

Final Result

So the result of the expression \(18 - 9 \frac{4}{9} + \frac{7}{9} - 8\) is:

\[ \frac{4}{3} \]

Or, if you prefer, \(1 \frac{1}{3}\) as a mixed number.

Answer 2

write it the shortest way possible with an easy way to understand

Answer 3

Sure! Here’s a concise and clear breakdown of the calculation:

Expression to Solve

\[ 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \]

Step 1: Convert Mixed Number

Convert \(9 \frac{4}{9}\) to an improper fraction: \[ 9 \frac{4}{9} = \frac{85}{9} \]

Step 2: Rewrite the Expression

Now the expression is: \[ 18 - \frac{85}{9} + \frac{7}{9} - 8 \]

Step 3: Combine Whole Numbers

Combine \(18\) and \(-8\): \[ 18 - 8 = 10 \]

Step 4: Combine Fractions

Now the expression becomes: \[ 10 - \frac{85}{9} + \frac{7}{9} = 10 - \frac{78}{9} \]

Step 5: Convert to Same Denominator

Convert \(10\) to a fraction with a denominator of \(9\): \[ 10 = \frac{90}{9} \]

Step 6: Subtract Fractions

Now subtract: \[ \frac{90}{9} - \frac{78}{9} = \frac{12}{9} \]

Step 7: Simplify

Simplify \(\frac{12}{9}\): \[ \frac{12}{9} = \frac{4}{3} \] \[ \frac{4}{3} = 1 \frac{1}{3} \] (as a mixed number)

Final Result

\[ \boxed{\frac{4}{3}} \quad \text{or} \quad 1 \frac{1}{3} \]